diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/Makefile b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..3703b27cea227aa053fb6d1d73f861e4384dbcee
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/bias.ves1.iter-10.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/bias.ves1.iter-10.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..55fc4b90e0bb8e0a74059ba4d1ad0bc14e44ef67
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/bias.ves1.iter-10.data.reference
@@ -0,0 +1,105 @@
+#! FIELDS phi ves1.bias der_phi
+#! SET min_phi -pi
+#! SET max_phi pi
+#! SET nbins_phi  100
+#! SET periodic_phi true
+   -3.141592654   -1.962887340  -12.338802116
+   -3.078760801   -1.169414064  -12.715200498
+   -3.015928947   -0.391297555  -11.842670932
+   -2.953097094    0.293014687   -9.744489584
+   -2.890265241    0.810780738   -6.578621340
+   -2.827433388    1.103213002   -2.628636251
+   -2.764601535    1.132736781    1.718540218
+   -2.701769682    0.888479952    6.006285748
+   -2.638937829    0.389363553    9.750412598
+   -2.576105976   -0.315622008   12.485919949
+   -2.513274123   -1.150108758   13.813956198
+   -2.450442270   -2.015880754   13.444439030
+   -2.387610417   -2.800832289   11.230078693
+   -2.324778564   -3.388698586    7.188264732
+   -2.261946711   -3.669712459    1.508346390
+   -2.199114858   -3.551225879   -5.456835497
+   -2.136283004   -2.967309202  -13.214845369
+   -2.073451151   -1.886407100  -21.171200499
+   -2.010619298   -0.316284409  -28.677475468
+   -1.947787445    1.694275951  -35.085823711
+   -1.884955592    4.057277381  -39.805102330
+   -1.822123739    6.650758491  -42.353552663
+   -1.759291886    9.327116398  -42.403222481
+   -1.696460033   11.923851076  -39.811998967
+   -1.633628180   14.275849793  -34.640194909
+   -1.570796327   16.228180200  -27.149996573
+   -1.507964474   17.648302059  -17.787615275
+   -1.445132621   18.436646858   -7.149543685
+   -1.382300768   18.534648860    4.064242212
+   -1.319468915   17.929528507   15.106108250
+   -1.256637061   16.655410154   25.240764953
+   -1.193805208   14.790675170   33.804217774
+   -1.130973355   12.451779631   40.256530152
+   -1.068141502    9.784073053   44.223828351
+   -1.005309649    6.950413066   45.525955652
+   -0.942477796    4.118557135   44.187485578
+   -0.879645943    1.448409775   40.431307959
+   -0.816814090   -0.919796122   34.655567695
+   -0.753982237   -2.875401651   27.396218871
+   -0.691150384   -4.344509048   19.278719545
+   -0.628318531   -5.293907399   10.963319829
+   -0.565486678   -5.731488729    3.088904596
+   -0.502654825   -5.703221985   -3.779600964
+   -0.439822972   -5.287056426   -9.195669122
+   -0.376991118   -4.584390419  -12.863688798
+   -0.314159265   -3.709942861  -14.656970625
+   -0.251327412   -2.780984749  -14.620029905
+   -0.188495559   -1.906918090  -12.955414618
+   -0.125663706   -1.180127187   -9.996768596
+   -0.062831853   -0.668881003   -6.171056989
+    0.000000000   -0.412850137   -1.953818247
+    0.062831853   -0.421539575    2.178140178
+    0.125663706   -0.675654705    5.792062628
+    0.188495559   -1.131140428    8.538354992
+    0.251327412   -1.725387947   10.179965544
+    0.314159265   -2.384913757   10.609550868
+    0.376991118   -3.033697597    9.853189732
+    0.439822972   -3.601330342    8.060748792
+    0.502654825   -4.030170819    5.484305244
+    0.565486678   -4.280835606    2.447166697
+    0.628318531   -4.335534258   -0.693110509
+    0.691150384   -4.198993981   -3.583796504
+    0.753982237   -3.896968936   -5.914139727
+    0.816814090   -3.472574521   -7.446871847
+    0.879645943   -2.980902025   -8.041001900
+    0.942477796   -2.482532833   -7.663790383
+    1.005309649   -2.036668522   -6.390943538
+    1.068141502   -1.694615038   -4.395294320
+    1.130973355   -1.494304801   -1.925415089
+    1.193805208   -1.456416832    0.723380390
+    1.256637061   -1.582475512    3.242441860
+    1.319468915   -1.855092601    5.343983442
+    1.382300768   -2.240287277    6.792439000
+    1.445132621   -2.691599109    7.429676026
+    1.507964474   -3.155521657    7.191454953
+    1.570796327   -3.577648783    6.113468227
+    1.633628180   -3.908855525    4.326406440
+    1.696460033   -4.110837235    2.040661900
+    1.759291886   -4.160404057   -0.477626840
+    1.822123739   -4.052064683   -2.936575167
+    1.884955592   -3.798619184   -5.051347997
+    1.947787445   -3.429696029   -6.576207401
+    2.010619298   -2.988390547   -7.332346000
+    2.073451151   -2.526367898   -7.228480223
+    2.136283004   -2.097961365   -6.271936183
+    2.199114858   -1.753908884   -4.568960171
+    2.261946711   -1.535415076   -2.314123056
+    2.324778564   -1.469197662    0.230153754
+    2.387610417   -1.564078476    2.761863469
+    2.450442270   -1.809520038    4.972532009
+    2.513274123   -2.176304947    6.581698361
+    2.576105976   -2.619327928    7.369072046
+    2.638937829   -3.082242736    7.200869631
+    2.701769682   -3.503501849    6.047385643
+    2.764601535   -3.823167726    3.989720592
+    2.827433388   -3.989777340    1.214684827
+    2.890265241   -3.966517945   -2.001887206
+    2.953097094   -3.736025222   -5.321964767
+    3.015928947   -3.303241013   -8.379756402
+    3.078760801   -2.695955240  -10.820370974
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/coeffs.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/coeffs.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..478cffec045c1a8bfd01d84cb123d22f99f8168b
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/coeffs.data.reference
@@ -0,0 +1,231 @@
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 0.000000
+#! SET iteration  0
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.000000     0.000000       1
+       2     0.000000     0.000000       2
+       3     0.000000     0.000000       3
+       4     0.000000     0.000000       4
+       5     0.000000     0.000000       5
+       6     0.000000     0.000000       6
+       7     0.000000     0.000000       7
+       8     0.000000     0.000000       8
+       9     0.000000     0.000000       9
+      10     0.000000     0.000000      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 2.000000
+#! SET iteration  1
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.219197     0.219197       1
+       2    -0.970366    -0.970366       2
+       3    -0.884094    -0.884094       3
+       4    -0.421298    -0.421298       4
+       5    -0.590820    -0.590820       5
+       6     0.748809     0.748809       6
+       7     0.576392     0.576392       7
+       8     0.715341     0.715341       8
+       9     0.786645     0.786645       9
+      10    -0.381816    -0.381816      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 4.000000
+#! SET iteration  2
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.305152     0.391107       1
+       2    -1.461895    -1.953423       2
+       3    -1.350614    -1.817134       3
+       4    -0.589608    -0.757918       4
+       5    -0.834473    -1.078125       5
+       6     1.174985     1.601160       6
+       7     0.948813     1.321234       7
+       8     1.024273     1.333206       8
+       9     1.148264     1.509884       9
+      10    -0.689625    -0.997434      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 6.000000
+#! SET iteration  3
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.421218     0.653351       1
+       2    -1.946133    -2.914610       2
+       3    -1.788707    -2.664892       3
+       4    -0.812257    -1.257555       4
+       5    -1.146186    -1.769612       5
+       6     1.540202     2.270638       6
+       7     1.220946     1.765213       7
+       8     1.401662     2.156440       8
+       9     1.564119     2.395830       9
+      10    -0.857540    -1.193370      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 8.000000
+#! SET iteration  4
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.448007     0.528372       1
+       2    -2.433590    -3.895961       2
+       3    -2.239120    -3.590362       3
+       4    -0.861012    -1.007276       4
+       5    -1.209573    -1.399733       5
+       6     1.931358     3.104824       6
+       7     1.535645     2.479741       7
+       8     1.472935     1.686754       8
+       9     1.639154     1.864258       9
+      10    -1.086629    -1.773897      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 10.000000
+#! SET iteration  5
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.441146     0.413704       1
+       2    -2.895058    -4.740930       2
+       3    -2.593087    -4.008954       3
+       4    -0.858951    -0.850710       4
+       5    -1.239599    -1.359702       5
+       6     2.140456     2.976852       6
+       7     1.611231     1.913575       7
+       8     1.562246     1.919487       8
+       9     1.789475     2.390761       9
+      10    -1.071904    -1.013004      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 12.000000
+#! SET iteration  6
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.441948     0.445955       1
+       2    -3.365271    -5.716337       2
+       3    -2.979506    -4.911603       3
+       4    -0.867479    -0.910117       4
+       5    -1.269466    -1.418805       5
+       6     2.410784     3.762420       6
+       7     1.766861     2.545012       7
+       8     1.621663     1.918750       8
+       9     1.870932     2.278215       9
+      10    -1.136982    -1.462370      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 14.000000
+#! SET iteration  7
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.383175     0.030542       1
+       2    -3.758763    -6.119715       2
+       3    -3.154779    -4.206413       3
+       4    -0.874583    -0.917208       4
+       5    -1.387569    -2.096189       5
+       6     2.602191     3.750634       6
+       7     1.994254     3.358610       7
+       8     1.747113     2.499816       8
+       9     1.915919     2.185842       9
+      10    -1.282146    -2.153134      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 16.000000
+#! SET iteration  8
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.296543    -0.309884       1
+       2    -4.141493    -6.820603       2
+       3    -3.290550    -4.240951       3
+       4    -0.837652    -0.579136       4
+       5    -1.491646    -2.220179       5
+       6     2.688068     3.289207       6
+       7     2.149365     3.235145       7
+       8     1.917967     3.113944       8
+       9     2.038602     2.897379       9
+      10    -1.468354    -2.771810      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 18.000000
+#! SET iteration  9
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.234442    -0.262361       1
+       2    -4.548948    -7.808582       2
+       3    -3.501952    -5.193167       3
+       4    -0.818965    -0.669467       4
+       5    -1.579418    -2.281596       5
+       6     2.854156     4.182861       6
+       7     2.360190     4.046783       7
+       8     2.050168     3.107779       8
+       9     2.134519     2.901856       9
+      10    -1.691816    -3.479514      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 20.000000
+#! SET iteration  10
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.205729    -0.052695       1
+       2    -4.971305    -8.772526       2
+       3    -3.756567    -6.048102       3
+       4    -0.842988    -1.059199       4
+       5    -1.697444    -2.759682       5
+       6     3.054607     4.858669       6
+       7     2.568698     4.445279       7
+       8     2.208072     3.629202       8
+       9     2.266734     3.456672       9
+      10    -1.877002    -3.543669      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/colvar.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/colvar.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..0670a8d28fbcbe20d416c9f1102922e4dc77d0b0
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/colvar.data.reference
@@ -0,0 +1,24 @@
+#! FIELDS time phi ves1.bias o1.avergradrms o1.avergradmax
+#! SET min_phi -pi
+#! SET max_phi pi
+ 0.000000 -1.238  0.000  0.000  0.000
+ 1.000000 -1.484  0.000  0.000  0.000
+ 2.000000 -1.324  0.000  0.637  0.970
+ 3.000000 -1.334  4.716  0.637  0.970
+ 4.000000 -1.461  4.403  0.659  0.983
+ 5.000000 -1.220  6.371  0.659  0.983
+ 6.000000 -1.388  7.123  0.649  0.961
+ 7.000000 -1.548  7.766  0.649  0.961
+ 8.000000 -1.843  1.066  0.599  0.981
+ 9.000000 -2.242 -3.365  0.599  0.981
+ 10.000000 -1.148  8.387  0.439  0.847
+ 11.000000 -1.758  5.325  0.439  0.847
+ 12.000000 -1.319 12.218  0.523  0.975
+ 13.000000 -2.991 -1.159  0.523  0.975
+ 14.000000 -1.411 13.737  0.475  0.814
+ 15.000000 -2.599 -0.714  0.475  0.814
+ 16.000000 -1.461 14.602  0.451  0.755
+ 17.000000 -1.379 15.945  0.451  0.755
+ 18.000000 -1.677 10.610  0.598  0.988
+ 19.000000 -1.524 16.005  0.598  0.988
+ 20.000000 -1.200 13.955  0.585  0.965
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/combined_gradient.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/combined_gradient.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..fd2741b6458ded2a3525e6ef0197241c4d2b8000
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/combined_gradient.data.reference
@@ -0,0 +1,210 @@
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 2.000000
+#! SET iteration  1
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.219197       1
+       2     0.970366       2
+       3     0.884094       3
+       4     0.421298       4
+       5     0.590820       5
+       6    -0.748809       6
+       7    -0.576392       7
+       8    -0.715341       8
+       9    -0.786645       9
+      10     0.381816      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 4.000000
+#! SET iteration  2
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.171909       1
+       2     0.983056       2
+       3     0.933040       3
+       4     0.336620       4
+       5     0.487305       5
+       6    -0.852350       6
+       7    -0.744842       7
+       8    -0.617866       8
+       9    -0.723239       9
+      10     0.615618      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 6.000000
+#! SET iteration  3
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.262244       1
+       2     0.961187       2
+       3     0.847758       3
+       4     0.499637       4
+       5     0.691487       5
+       6    -0.669478       6
+       7    -0.443979       7
+       8    -0.823233       8
+       9    -0.885946       9
+      10     0.195936      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 8.000000
+#! SET iteration  4
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.124979       1
+       2     0.981351       2
+       3     0.925470       3
+       4    -0.250280       4
+       5    -0.369879       5
+       6    -0.834186       6
+       7    -0.714529       7
+       8     0.469686       8
+       9     0.531572       9
+      10     0.580527      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 10.000000
+#! SET iteration  5
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.114667       1
+       2     0.844969       2
+       3     0.418592       3
+       4    -0.156566       4
+       5    -0.040031       5
+       6     0.127972       6
+       7     0.566166       7
+       8    -0.232733       8
+       9    -0.526503       9
+      10    -0.760892      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 12.000000
+#! SET iteration  6
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.032251       1
+       2     0.975407       2
+       3     0.902649       3
+       4     0.059408       4
+       5     0.059102       5
+       6    -0.785568       6
+       7    -0.631437       7
+       8     0.000738       8
+       9     0.112546       9
+      10     0.449365      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 14.000000
+#! SET iteration  7
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.415413       1
+       2     0.403378       2
+       3    -0.705190       3
+       4     0.007091       4
+       5     0.677384       5
+       6     0.011786       6
+       7    -0.813598       7
+       8    -0.581066       8
+       9     0.092373       9
+      10     0.690764      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 16.000000
+#! SET iteration  8
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.340425       1
+       2     0.700888       2
+       3     0.034538       3
+       4    -0.338072       4
+       5     0.123991       5
+       6     0.461427       6
+       7     0.123465       7
+       8    -0.614128       8
+       9    -0.711537       9
+      10     0.618677      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 18.000000
+#! SET iteration  9
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.047522       1
+       2     0.987979       2
+       3     0.952216       3
+       4     0.090331       4
+       5     0.061417       5
+       6    -0.893654       6
+       7    -0.811638       7
+       8     0.006164       8
+       9    -0.004477       9
+      10     0.707703      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 20.000000
+#! SET iteration  10
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.209666       1
+       2     0.963944       2
+       3     0.854935       3
+       4     0.389732       4
+       5     0.478086       5
+       6    -0.675807       6
+       7    -0.398496       7
+       8    -0.521422       8
+       9    -0.554816       9
+      10     0.064155      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/config b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/config
new file mode 100644
index 0000000000000000000000000000000000000000..d9b022c5f95c12fdf3de7e32807e196863eec343
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/config
@@ -0,0 +1,3 @@
+plumed_modules=ves
+type=driver
+arg="--plumed plumed.dat --trajectory-stride 500 --timestep 0.002 --igro traj.gro --dump-forces forces --dump-forces-fmt=%10.6f "
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/fes.ves1.iter-10.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/fes.ves1.iter-10.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..d50483ac34516d62eac2c7fd2592ae5ef72ba0af
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/fes.ves1.iter-10.data.reference
@@ -0,0 +1,105 @@
+#! FIELDS phi ves1.fes
+#! SET min_phi -pi
+#! SET max_phi pi
+#! SET nbins_phi  100
+#! SET periodic_phi true
+   -3.141592654   20.497536200
+   -3.078760801   19.704062923
+   -3.015928947   18.925946415
+   -2.953097094   18.241634172
+   -2.890265241   17.723868121
+   -2.827433388   17.431435858
+   -2.764601535   17.401912078
+   -2.701769682   17.646168907
+   -2.638937829   18.145285307
+   -2.576105976   18.850270868
+   -2.513274123   19.684757617
+   -2.450442270   20.550529614
+   -2.387610417   21.335481149
+   -2.324778564   21.923347445
+   -2.261946711   22.204361318
+   -2.199114858   22.085874739
+   -2.136283004   21.501958062
+   -2.073451151   20.421055959
+   -2.010619298   18.850933268
+   -1.947787445   16.840372909
+   -1.884955592   14.477371479
+   -1.822123739   11.883890368
+   -1.759291886    9.207532462
+   -1.696460033    6.610797784
+   -1.633628180    4.258799067
+   -1.570796327    2.306468659
+   -1.507964474    0.886346801
+   -1.445132621    0.098002001
+   -1.382300768    0.000000000
+   -1.319468915    0.605120352
+   -1.256637061    1.879238705
+   -1.193805208    3.743973689
+   -1.130973355    6.082869229
+   -1.068141502    8.750575807
+   -1.005309649   11.584235793
+   -0.942477796   14.416091724
+   -0.879645943   17.086239085
+   -0.816814090   19.454444982
+   -0.753982237   21.410050510
+   -0.691150384   22.879157907
+   -0.628318531   23.828556259
+   -0.565486678   24.266137588
+   -0.502654825   24.237870844
+   -0.439822972   23.821705285
+   -0.376991118   23.119039279
+   -0.314159265   22.244591720
+   -0.251327412   21.315633608
+   -0.188495559   20.441566950
+   -0.125663706   19.714776047
+   -0.062831853   19.203529863
+    0.000000000   18.947498997
+    0.062831853   18.956188434
+    0.125663706   19.210303564
+    0.188495559   19.665789288
+    0.251327412   20.260036806
+    0.314159265   20.919562617
+    0.376991118   21.568346457
+    0.439822972   22.135979202
+    0.502654825   22.564819678
+    0.565486678   22.815484466
+    0.628318531   22.870183117
+    0.691150384   22.733642841
+    0.753982237   22.431617795
+    0.816814090   22.007223380
+    0.879645943   21.515550884
+    0.942477796   21.017181692
+    1.005309649   20.571317381
+    1.068141502   20.229263897
+    1.130973355   20.028953661
+    1.193805208   19.991065692
+    1.256637061   20.117124372
+    1.319468915   20.389741461
+    1.382300768   20.774936136
+    1.445132621   21.226247968
+    1.507964474   21.690170517
+    1.570796327   22.112297643
+    1.633628180   22.443504384
+    1.696460033   22.645486094
+    1.759291886   22.695052917
+    1.822123739   22.586713543
+    1.884955592   22.333268044
+    1.947787445   21.964344888
+    2.010619298   21.523039407
+    2.073451151   21.061016758
+    2.136283004   20.632610225
+    2.199114858   20.288557744
+    2.261946711   20.070063935
+    2.324778564   20.003846521
+    2.387610417   20.098727335
+    2.450442270   20.344168898
+    2.513274123   20.710953806
+    2.576105976   21.153976788
+    2.638937829   21.616891596
+    2.701769682   22.038150709
+    2.764601535   22.357816586
+    2.827433388   22.524426200
+    2.890265241   22.501166805
+    2.953097094   22.270674081
+    3.015928947   21.837889873
+    3.078760801   21.230604100
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/forces.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/forces.reference
new file mode 100644
index 0000000000000000000000000000000000000000..75ae219e0f6736a9037c0c36631fa4ee84749782
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/forces.reference
@@ -0,0 +1,504 @@
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diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/plumed.dat b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/plumed.dat
new file mode 100644
index 0000000000000000000000000000000000000000..6f21242f9f709b22d3bfc11b921bd31ac16956d2
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/plumed.dat
@@ -0,0 +1,44 @@
+# vim:ft=plumed
+
+phi:   TORSION ATOMS=5,7,9,15     NOPBC
+
+bf1: BF_FOURIER ORDER=5 MINIMUM=-pi MAXIMUM=pi
+
+VES_LINEAR_EXPANSION ...
+ ARG=phi
+ BASIS_FUNCTIONS=bf1
+ LABEL=ves1
+ TEMP=300.0
+ GRID_BINS=100
+... VES_LINEAR_EXPANSION
+
+# NOTE: These parameters do not reflect parameters used in real simulations! 
+#       This is only for testing!
+#
+
+OPT_AVERAGED_SGD ...
+  BIAS=ves1
+  STRIDE=1000
+  LABEL=o1
+  STEPSIZE=1.0
+  COEFFS_FILE=coeffs.data
+  COEFFS_OUTPUT=1
+  COEFFS_FMT=%12.6f
+  FES_OUTPUT=10
+  BIAS_OUTPUT=10
+  TARGETDIST_AVERAGES_FMT=%12.6f
+  COMBINED_GRADIENT_FILE=combined_gradient.data
+  COMBINED_GRADIENT_OUTPUT=1
+  COMBINED_GRADIENT_FMT=%12.6f
+  MONITOR_AVERAGE_GRADIENT
+  MONITOR_AVERAGES_GRADIENT_EXP_DECAY=1
+... OPT_AVERAGED_SGD
+
+PRINT ...
+  STRIDE=500
+  ARG=phi,ves1.bias,o1.*
+  FILE=colvar.data FMT=%6.3f
+... PRINT
+
+ENDPLUMED
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/targetdist-averages.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/targetdist-averages.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..b6bf5b55ccca602f2814808f51085a0599e101ab
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/targetdist-averages.data.reference
@@ -0,0 +1,21 @@
+#! FIELDS idx_phi ves1.targetdist_averages index
+#! SET time 0.000000
+#! SET iteration  0
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     1.000000       0
+       1     0.000000       1
+       2     0.000000       2
+       3     0.000000       3
+       4     0.000000       4
+       5     0.000000       5
+       6     0.000000       6
+       7     0.000000       7
+       8     0.000000       8
+       9     0.000000       9
+      10     0.000000      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/traj.gro b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/traj.gro
new file mode 100644
index 0000000000000000000000000000000000000000..c1c387a0144ec8021b9e5b0453be534f2ca906e2
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad-exp-decay/traj.gro
@@ -0,0 +1,525 @@
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+    1ACE      C    5   1.364   1.422   1.284
+    1ACE      O    6   1.305   1.438   1.389
+    2ALA      N    7   1.347   1.326   1.187
+    2ALA      H    8   1.423   1.328   1.122
+    2ALA     CA    9   1.226   1.241   1.162
+    2ALA     HA   10   1.139   1.308   1.162
+    2ALA     CB   11   1.236   1.193   1.023
+    2ALA    HB1   12   1.314   1.117   1.012
+    2ALA    HB2   13   1.137   1.167   0.986
+    2ALA    HB3   14   1.273   1.278   0.966
+    2ALA      C   15   1.195   1.133   1.268
+    2ALA      O   16   1.173   1.016   1.239
+    3NME      N   17   1.204   1.175   1.393
+    3NME      H   18   1.211   1.275   1.403
+    3NME    CH3   19   1.188   1.090   1.513
+    3NME   HH31   20   1.089   1.044   1.509
+    3NME   HH32   21   1.267   1.014   1.509
+    3NME   HH33   22   1.189   1.145   1.607
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   6.00000
+   22
+    1ACE   HH31    1   1.517   1.511   1.181
+    1ACE    CH3    2   1.490   1.488   1.284
+    1ACE   HH32    3   1.482   1.582   1.339
+    1ACE   HH33    4   1.569   1.421   1.316
+    1ACE      C    5   1.359   1.414   1.282
+    1ACE      O    6   1.272   1.447   1.358
+    2ALA      N    7   1.351   1.320   1.186
+    2ALA      H    8   1.434   1.297   1.133
+    2ALA     CA    9   1.220   1.251   1.159
+    2ALA     HA   10   1.139   1.323   1.167
+    2ALA     CB   11   1.220   1.194   1.018
+    2ALA    HB1   12   1.298   1.120   1.003
+    2ALA    HB2   13   1.120   1.158   0.994
+    2ALA    HB3   14   1.224   1.286   0.960
+    2ALA      C   15   1.201   1.139   1.270
+    2ALA      O   16   1.190   1.022   1.239
+    3NME      N   17   1.203   1.178   1.393
+    3NME      H   18   1.207   1.277   1.409
+    3NME    CH3   19   1.211   1.102   1.515
+    3NME   HH31   20   1.111   1.064   1.534
+    3NME   HH32   21   1.275   1.017   1.492
+    3NME   HH33   22   1.264   1.151   1.597
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   7.00000
+   22
+    1ACE   HH31    1   1.483   1.590   1.185
+    1ACE    CH3    2   1.505   1.501   1.245
+    1ACE   HH32    3   1.538   1.533   1.344
+    1ACE   HH33    4   1.580   1.430   1.209
+    1ACE      C    5   1.379   1.418   1.267
+    1ACE      O    6   1.298   1.443   1.349
+    2ALA      N    7   1.360   1.320   1.187
+    2ALA      H    8   1.426   1.297   1.114
+    2ALA     CA    9   1.224   1.253   1.180
+    2ALA     HA   10   1.147   1.326   1.205
+    2ALA     CB   11   1.174   1.215   1.037
+    2ALA    HB1   12   1.245   1.152   0.983
+    2ALA    HB2   13   1.084   1.154   1.032
+    2ALA    HB3   14   1.153   1.311   0.992
+    2ALA      C   15   1.212   1.141   1.280
+    2ALA      O   16   1.219   1.022   1.244
+    3NME      N   17   1.191   1.176   1.408
+    3NME      H   18   1.207   1.275   1.423
+    3NME    CH3   19   1.162   1.068   1.509
+    3NME   HH31   20   1.229   0.982   1.503
+    3NME   HH32   21   1.162   1.109   1.610
+    3NME   HH33   22   1.056   1.044   1.499
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   8.00000
+   22
+    1ACE   HH31    1   1.576   1.425   1.169
+    1ACE    CH3    2   1.523   1.455   1.260
+    1ACE   HH32    3   1.547   1.556   1.294
+    1ACE   HH33    4   1.566   1.393   1.338
+    1ACE      C    5   1.385   1.422   1.255
+    1ACE      O    6   1.308   1.499   1.305
+    2ALA      N    7   1.346   1.311   1.189
+    2ALA      H    8   1.419   1.248   1.159
+    2ALA     CA    9   1.210   1.260   1.193
+    2ALA     HA   10   1.139   1.326   1.242
+    2ALA     CB   11   1.152   1.252   1.051
+    2ALA    HB1   12   1.230   1.210   0.987
+    2ALA    HB2   13   1.066   1.185   1.052
+    2ALA    HB3   14   1.127   1.354   1.024
+    2ALA      C   15   1.206   1.136   1.282
+    2ALA      O   16   1.195   1.023   1.229
+    3NME      N   17   1.210   1.152   1.420
+    3NME      H   18   1.221   1.243   1.463
+    3NME    CH3   19   1.185   1.048   1.518
+    3NME   HH31   20   1.195   0.948   1.475
+    3NME   HH32   21   1.261   1.070   1.593
+    3NME   HH33   22   1.088   1.064   1.565
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   9.00000
+   22
+    1ACE   HH31    1   1.515   1.474   1.040
+    1ACE    CH3    2   1.535   1.461   1.147
+    1ACE   HH32    3   1.561   1.560   1.184
+    1ACE   HH33    4   1.612   1.386   1.165
+    1ACE      C    5   1.406   1.430   1.217
+    1ACE      O    6   1.361   1.502   1.307
+    2ALA      N    7   1.345   1.316   1.190
+    2ALA      H    8   1.384   1.254   1.121
+    2ALA     CA    9   1.217   1.277   1.242
+    2ALA     HA   10   1.187   1.348   1.319
+    2ALA     CB   11   1.111   1.278   1.134
+    2ALA    HB1   12   1.129   1.198   1.062
+    2ALA    HB2   13   1.018   1.269   1.189
+    2ALA    HB3   14   1.121   1.372   1.079
+    2ALA      C   15   1.217   1.133   1.309
+    2ALA      O   16   1.293   1.044   1.265
+    3NME      N   17   1.132   1.116   1.408
+    3NME      H   18   1.076   1.195   1.437
+    3NME    CH3   19   1.112   1.003   1.490
+    3NME   HH31   20   1.156   0.910   1.456
+    3NME   HH32   21   1.153   1.026   1.588
+    3NME   HH33   22   1.005   0.985   1.500
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  10.00000
+   22
+    1ACE   HH31    1   1.536   1.485   1.135
+    1ACE    CH3    2   1.521   1.460   1.240
+    1ACE   HH32    3   1.528   1.557   1.289
+    1ACE   HH33    4   1.602   1.397   1.276
+    1ACE      C    5   1.385   1.401   1.261
+    1ACE      O    6   1.341   1.416   1.373
+    2ALA      N    7   1.322   1.332   1.167
+    2ALA      H    8   1.364   1.316   1.076
+    2ALA     CA    9   1.190   1.273   1.177
+    2ALA     HA   10   1.125   1.352   1.216
+    2ALA     CB   11   1.134   1.230   1.038
+    2ALA    HB1   12   1.167   1.128   1.016
+    2ALA    HB2   13   1.026   1.238   1.046
+    2ALA    HB3   14   1.174   1.287   0.953
+    2ALA      C   15   1.183   1.157   1.283
+    2ALA      O   16   1.111   1.061   1.259
+    3NME      N   17   1.264   1.157   1.396
+    3NME      H   18   1.320   1.241   1.405
+    3NME    CH3   19   1.264   1.070   1.510
+    3NME   HH31   20   1.163   1.057   1.548
+    3NME   HH32   21   1.311   0.974   1.487
+    3NME   HH33   22   1.326   1.109   1.592
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  11.00000
+   22
+    1ACE   HH31    1   1.607   1.359   1.178
+    1ACE    CH3    2   1.535   1.442   1.176
+    1ACE   HH32    3   1.521   1.470   1.072
+    1ACE   HH33    4   1.569   1.533   1.224
+    1ACE      C    5   1.402   1.412   1.242
+    1ACE      O    6   1.368   1.454   1.350
+    2ALA      N    7   1.319   1.332   1.177
+    2ALA      H    8   1.363   1.279   1.103
+    2ALA     CA    9   1.194   1.289   1.231
+    2ALA     HA   10   1.153   1.355   1.308
+    2ALA     CB   11   1.092   1.300   1.113
+    2ALA    HB1   12   1.137   1.243   1.032
+    2ALA    HB2   13   1.001   1.243   1.131
+    2ALA    HB3   14   1.070   1.405   1.095
+    2ALA      C   15   1.198   1.143   1.290
+    2ALA      O   16   1.237   1.057   1.213
+    3NME      N   17   1.171   1.126   1.422
+    3NME      H   18   1.164   1.213   1.472
+    3NME    CH3   19   1.200   1.009   1.496
+    3NME   HH31   20   1.118   0.938   1.493
+    3NME   HH32   21   1.284   0.953   1.454
+    3NME   HH33   22   1.230   1.031   1.598
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  12.00000
+   22
+    1ACE   HH31    1   1.491   1.569   1.138
+    1ACE    CH3    2   1.511   1.462   1.134
+    1ACE   HH32    3   1.614   1.449   1.166
+    1ACE   HH33    4   1.495   1.444   1.028
+    1ACE      C    5   1.416   1.394   1.229
+    1ACE      O    6   1.445   1.392   1.345
+    2ALA      N    7   1.299   1.357   1.181
+    2ALA      H    8   1.278   1.358   1.082
+    2ALA     CA    9   1.196   1.301   1.267
+    2ALA     HA   10   1.185   1.364   1.355
+    2ALA     CB   11   1.063   1.319   1.182
+    2ALA    HB1   12   1.057   1.248   1.100
+    2ALA    HB2   13   0.976   1.288   1.240
+    2ALA    HB3   14   1.037   1.423   1.161
+    2ALA      C   15   1.226   1.161   1.304
+    2ALA      O   16   1.317   1.094   1.258
+    3NME      N   17   1.135   1.110   1.387
+    3NME      H   18   1.064   1.174   1.419
+    3NME    CH3   19   1.121   0.972   1.429
+    3NME   HH31   20   1.163   0.900   1.358
+    3NME   HH32   21   1.177   0.954   1.520
+    3NME   HH33   22   1.016   0.942   1.428
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  13.00000
+   22
+    1ACE   HH31    1   1.528   1.537   1.077
+    1ACE    CH3    2   1.543   1.448   1.137
+    1ACE   HH32    3   1.634   1.463   1.195
+    1ACE   HH33    4   1.560   1.362   1.072
+    1ACE      C    5   1.421   1.428   1.229
+    1ACE      O    6   1.396   1.520   1.301
+    2ALA      N    7   1.355   1.314   1.219
+    2ALA      H    8   1.385   1.241   1.156
+    2ALA     CA    9   1.249   1.276   1.311
+    2ALA     HA   10   1.297   1.288   1.409
+    2ALA     CB   11   1.122   1.359   1.284
+    2ALA    HB1   12   1.072   1.325   1.193
+    2ALA    HB2   13   1.053   1.352   1.367
+    2ALA    HB3   14   1.153   1.463   1.275
+    2ALA      C   15   1.204   1.131   1.290
+    2ALA      O   16   1.225   1.070   1.185
+    3NME      N   17   1.131   1.077   1.382
+    3NME      H   18   1.104   1.132   1.463
+    3NME    CH3   19   1.083   0.939   1.380
+    3NME   HH31   20   1.012   0.925   1.298
+    3NME   HH32   21   1.168   0.871   1.372
+    3NME   HH33   22   1.036   0.915   1.475
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  14.00000
+   22
+    1ACE   HH31    1   1.543   1.468   1.123
+    1ACE    CH3    2   1.548   1.443   1.229
+    1ACE   HH32    3   1.566   1.540   1.276
+    1ACE   HH33    4   1.634   1.382   1.257
+    1ACE      C    5   1.420   1.385   1.285
+    1ACE      O    6   1.412   1.375   1.404
+    2ALA      N    7   1.324   1.361   1.200
+    2ALA      H    8   1.345   1.354   1.101
+    2ALA     CA    9   1.189   1.323   1.244
+    2ALA     HA   10   1.163   1.394   1.323
+    2ALA     CB   11   1.094   1.344   1.125
+    2ALA    HB1   12   1.098   1.270   1.045
+    2ALA    HB2   13   0.995   1.352   1.170
+    2ALA    HB3   14   1.120   1.440   1.079
+    2ALA      C   15   1.166   1.169   1.284
+    2ALA      O   16   1.055   1.145   1.330
+    3NME      N   17   1.263   1.077   1.279
+    3NME      H   18   1.356   1.102   1.247
+    3NME    CH3   19   1.246   0.942   1.335
+    3NME   HH31   20   1.142   0.911   1.345
+    3NME   HH32   21   1.293   0.868   1.270
+    3NME   HH33   22   1.292   0.934   1.434
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  15.00000
+   22
+    1ACE   HH31    1   1.508   1.417   1.043
+    1ACE    CH3    2   1.539   1.448   1.143
+    1ACE   HH32    3   1.565   1.553   1.146
+    1ACE   HH33    4   1.630   1.395   1.169
+    1ACE      C    5   1.438   1.410   1.253
+    1ACE      O    6   1.429   1.471   1.356
+    2ALA      N    7   1.348   1.327   1.217
+    2ALA      H    8   1.362   1.285   1.126
+    2ALA     CA    9   1.233   1.289   1.298
+    2ALA     HA   10   1.269   1.295   1.401
+    2ALA     CB   11   1.107   1.379   1.286
+    2ALA    HB1   12   1.057   1.360   1.191
+    2ALA    HB2   13   1.034   1.369   1.366
+    2ALA    HB3   14   1.141   1.482   1.282
+    2ALA      C   15   1.192   1.141   1.266
+    2ALA      O   16   1.220   1.089   1.156
+    3NME      N   17   1.131   1.075   1.364
+    3NME      H   18   1.117   1.126   1.450
+    3NME    CH3   19   1.090   0.931   1.376
+    3NME   HH31   20   1.156   0.880   1.446
+    3NME   HH32   21   0.996   0.929   1.431
+    3NME   HH33   22   1.090   0.874   1.283
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  16.00000
+   22
+    1ACE   HH31    1   1.587   1.386   1.166
+    1ACE    CH3    2   1.554   1.425   1.262
+    1ACE   HH32    3   1.559   1.534   1.266
+    1ACE   HH33    4   1.627   1.390   1.335
+    1ACE      C    5   1.417   1.372   1.300
+    1ACE      O    6   1.390   1.364   1.421
+    2ALA      N    7   1.334   1.344   1.205
+    2ALA      H    8   1.365   1.367   1.111
+    2ALA     CA    9   1.190   1.324   1.235
+    2ALA     HA   10   1.160   1.386   1.319
+    2ALA     CB   11   1.105   1.363   1.112
+    2ALA    HB1   12   1.129   1.297   1.029
+    2ALA    HB2   13   0.999   1.351   1.131
+    2ALA    HB3   14   1.125   1.467   1.088
+    2ALA      C   15   1.162   1.180   1.282
+    2ALA      O   16   1.054   1.128   1.258
+    3NME      N   17   1.261   1.106   1.318
+    3NME      H   18   1.349   1.152   1.336
+    3NME    CH3   19   1.250   0.960   1.324
+    3NME   HH31   20   1.264   0.908   1.229
+    3NME   HH32   21   1.322   0.926   1.399
+    3NME   HH33   22   1.153   0.923   1.357
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  17.00000
+   22
+    1ACE   HH31    1   1.614   1.382   1.173
+    1ACE    CH3    2   1.559   1.432   1.253
+    1ACE   HH32    3   1.547   1.532   1.213
+    1ACE   HH33    4   1.625   1.444   1.339
+    1ACE      C    5   1.426   1.380   1.288
+    1ACE      O    6   1.411   1.348   1.406
+    2ALA      N    7   1.325   1.370   1.200
+    2ALA      H    8   1.341   1.388   1.102
+    2ALA     CA    9   1.189   1.318   1.239
+    2ALA     HA   10   1.170   1.358   1.338
+    2ALA     CB   11   1.084   1.388   1.158
+    2ALA    HB1   12   1.113   1.369   1.055
+    2ALA    HB2   13   0.994   1.336   1.189
+    2ALA    HB3   14   1.075   1.493   1.186
+    2ALA      C   15   1.170   1.163   1.252
+    2ALA      O   16   1.097   1.103   1.171
+    3NME      N   17   1.235   1.099   1.349
+    3NME      H   18   1.305   1.153   1.399
+    3NME    CH3   19   1.220   0.964   1.393
+    3NME   HH31   20   1.315   0.912   1.406
+    3NME   HH32   21   1.168   0.953   1.489
+    3NME   HH33   22   1.178   0.897   1.318
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  18.00000
+   22
+    1ACE   HH31    1   1.555   1.419   1.126
+    1ACE    CH3    2   1.554   1.431   1.235
+    1ACE   HH32    3   1.554   1.535   1.267
+    1ACE   HH33    4   1.638   1.381   1.283
+    1ACE      C    5   1.423   1.378   1.292
+    1ACE      O    6   1.416   1.347   1.409
+    2ALA      N    7   1.322   1.351   1.211
+    2ALA      H    8   1.350   1.370   1.115
+    2ALA     CA    9   1.185   1.318   1.251
+    2ALA     HA   10   1.171   1.358   1.352
+    2ALA     CB   11   1.091   1.400   1.149
+    2ALA    HB1   12   1.059   1.346   1.060
+    2ALA    HB2   13   1.008   1.443   1.205
+    2ALA    HB3   14   1.154   1.480   1.109
+    2ALA      C   15   1.163   1.166   1.255
+    2ALA      O   16   1.060   1.108   1.214
+    3NME      N   17   1.255   1.102   1.328
+    3NME      H   18   1.335   1.159   1.354
+    3NME    CH3   19   1.246   0.964   1.369
+    3NME   HH31   20   1.154   0.913   1.344
+    3NME   HH32   21   1.323   0.899   1.327
+    3NME   HH33   22   1.251   0.953   1.477
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  19.00000
+   22
+    1ACE   HH31    1   1.559   1.326   1.133
+    1ACE    CH3    2   1.552   1.413   1.200
+    1ACE   HH32    3   1.538   1.504   1.142
+    1ACE   HH33    4   1.631   1.428   1.273
+    1ACE      C    5   1.426   1.375   1.280
+    1ACE      O    6   1.428   1.345   1.398
+    2ALA      N    7   1.319   1.363   1.209
+    2ALA      H    8   1.322   1.382   1.110
+    2ALA     CA    9   1.191   1.329   1.265
+    2ALA     HA   10   1.186   1.364   1.368
+    2ALA     CB   11   1.075   1.391   1.178
+    2ALA    HB1   12   1.098   1.383   1.072
+    2ALA    HB2   13   0.980   1.348   1.211
+    2ALA    HB3   14   1.066   1.499   1.192
+    2ALA      C   15   1.169   1.174   1.275
+    2ALA      O   16   1.086   1.118   1.203
+    3NME      N   17   1.233   1.105   1.363
+    3NME      H   18   1.312   1.150   1.405
+    3NME    CH3   19   1.242   0.956   1.350
+    3NME   HH31   20   1.219   0.899   1.440
+    3NME   HH32   21   1.165   0.918   1.284
+    3NME   HH33   22   1.333   0.921   1.301
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  20.00000
+   22
+    1ACE   HH31    1   1.622   1.459   1.287
+    1ACE    CH3    2   1.546   1.434   1.214
+    1ACE   HH32    3   1.578   1.365   1.135
+    1ACE   HH33    4   1.509   1.531   1.180
+    1ACE      C    5   1.430   1.358   1.283
+    1ACE      O    6   1.444   1.310   1.394
+    2ALA      N    7   1.315   1.370   1.215
+    2ALA      H    8   1.323   1.427   1.132
+    2ALA     CA    9   1.178   1.334   1.258
+    2ALA     HA   10   1.163   1.376   1.357
+    2ALA     CB   11   1.079   1.393   1.158
+    2ALA    HB1   12   1.096   1.348   1.060
+    2ALA    HB2   13   0.979   1.367   1.192
+    2ALA    HB3   14   1.087   1.501   1.165
+    2ALA      C   15   1.163   1.177   1.270
+    2ALA      O   16   1.073   1.114   1.216
+    3NME      N   17   1.249   1.110   1.347
+    3NME      H   18   1.324   1.165   1.388
+    3NME    CH3   19   1.242   0.964   1.360
+    3NME   HH31   20   1.325   0.920   1.416
+    3NME   HH32   21   1.151   0.938   1.414
+    3NME   HH33   22   1.221   0.913   1.266
+  10.00000  10.00000  10.00000
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/Makefile b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..3703b27cea227aa053fb6d1d73f861e4384dbcee
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/bias.ves1.iter-10.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/bias.ves1.iter-10.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..55fc4b90e0bb8e0a74059ba4d1ad0bc14e44ef67
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/bias.ves1.iter-10.data.reference
@@ -0,0 +1,105 @@
+#! FIELDS phi ves1.bias der_phi
+#! SET min_phi -pi
+#! SET max_phi pi
+#! SET nbins_phi  100
+#! SET periodic_phi true
+   -3.141592654   -1.962887340  -12.338802116
+   -3.078760801   -1.169414064  -12.715200498
+   -3.015928947   -0.391297555  -11.842670932
+   -2.953097094    0.293014687   -9.744489584
+   -2.890265241    0.810780738   -6.578621340
+   -2.827433388    1.103213002   -2.628636251
+   -2.764601535    1.132736781    1.718540218
+   -2.701769682    0.888479952    6.006285748
+   -2.638937829    0.389363553    9.750412598
+   -2.576105976   -0.315622008   12.485919949
+   -2.513274123   -1.150108758   13.813956198
+   -2.450442270   -2.015880754   13.444439030
+   -2.387610417   -2.800832289   11.230078693
+   -2.324778564   -3.388698586    7.188264732
+   -2.261946711   -3.669712459    1.508346390
+   -2.199114858   -3.551225879   -5.456835497
+   -2.136283004   -2.967309202  -13.214845369
+   -2.073451151   -1.886407100  -21.171200499
+   -2.010619298   -0.316284409  -28.677475468
+   -1.947787445    1.694275951  -35.085823711
+   -1.884955592    4.057277381  -39.805102330
+   -1.822123739    6.650758491  -42.353552663
+   -1.759291886    9.327116398  -42.403222481
+   -1.696460033   11.923851076  -39.811998967
+   -1.633628180   14.275849793  -34.640194909
+   -1.570796327   16.228180200  -27.149996573
+   -1.507964474   17.648302059  -17.787615275
+   -1.445132621   18.436646858   -7.149543685
+   -1.382300768   18.534648860    4.064242212
+   -1.319468915   17.929528507   15.106108250
+   -1.256637061   16.655410154   25.240764953
+   -1.193805208   14.790675170   33.804217774
+   -1.130973355   12.451779631   40.256530152
+   -1.068141502    9.784073053   44.223828351
+   -1.005309649    6.950413066   45.525955652
+   -0.942477796    4.118557135   44.187485578
+   -0.879645943    1.448409775   40.431307959
+   -0.816814090   -0.919796122   34.655567695
+   -0.753982237   -2.875401651   27.396218871
+   -0.691150384   -4.344509048   19.278719545
+   -0.628318531   -5.293907399   10.963319829
+   -0.565486678   -5.731488729    3.088904596
+   -0.502654825   -5.703221985   -3.779600964
+   -0.439822972   -5.287056426   -9.195669122
+   -0.376991118   -4.584390419  -12.863688798
+   -0.314159265   -3.709942861  -14.656970625
+   -0.251327412   -2.780984749  -14.620029905
+   -0.188495559   -1.906918090  -12.955414618
+   -0.125663706   -1.180127187   -9.996768596
+   -0.062831853   -0.668881003   -6.171056989
+    0.000000000   -0.412850137   -1.953818247
+    0.062831853   -0.421539575    2.178140178
+    0.125663706   -0.675654705    5.792062628
+    0.188495559   -1.131140428    8.538354992
+    0.251327412   -1.725387947   10.179965544
+    0.314159265   -2.384913757   10.609550868
+    0.376991118   -3.033697597    9.853189732
+    0.439822972   -3.601330342    8.060748792
+    0.502654825   -4.030170819    5.484305244
+    0.565486678   -4.280835606    2.447166697
+    0.628318531   -4.335534258   -0.693110509
+    0.691150384   -4.198993981   -3.583796504
+    0.753982237   -3.896968936   -5.914139727
+    0.816814090   -3.472574521   -7.446871847
+    0.879645943   -2.980902025   -8.041001900
+    0.942477796   -2.482532833   -7.663790383
+    1.005309649   -2.036668522   -6.390943538
+    1.068141502   -1.694615038   -4.395294320
+    1.130973355   -1.494304801   -1.925415089
+    1.193805208   -1.456416832    0.723380390
+    1.256637061   -1.582475512    3.242441860
+    1.319468915   -1.855092601    5.343983442
+    1.382300768   -2.240287277    6.792439000
+    1.445132621   -2.691599109    7.429676026
+    1.507964474   -3.155521657    7.191454953
+    1.570796327   -3.577648783    6.113468227
+    1.633628180   -3.908855525    4.326406440
+    1.696460033   -4.110837235    2.040661900
+    1.759291886   -4.160404057   -0.477626840
+    1.822123739   -4.052064683   -2.936575167
+    1.884955592   -3.798619184   -5.051347997
+    1.947787445   -3.429696029   -6.576207401
+    2.010619298   -2.988390547   -7.332346000
+    2.073451151   -2.526367898   -7.228480223
+    2.136283004   -2.097961365   -6.271936183
+    2.199114858   -1.753908884   -4.568960171
+    2.261946711   -1.535415076   -2.314123056
+    2.324778564   -1.469197662    0.230153754
+    2.387610417   -1.564078476    2.761863469
+    2.450442270   -1.809520038    4.972532009
+    2.513274123   -2.176304947    6.581698361
+    2.576105976   -2.619327928    7.369072046
+    2.638937829   -3.082242736    7.200869631
+    2.701769682   -3.503501849    6.047385643
+    2.764601535   -3.823167726    3.989720592
+    2.827433388   -3.989777340    1.214684827
+    2.890265241   -3.966517945   -2.001887206
+    2.953097094   -3.736025222   -5.321964767
+    3.015928947   -3.303241013   -8.379756402
+    3.078760801   -2.695955240  -10.820370974
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/coeffs.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/coeffs.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..478cffec045c1a8bfd01d84cb123d22f99f8168b
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/coeffs.data.reference
@@ -0,0 +1,231 @@
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 0.000000
+#! SET iteration  0
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.000000     0.000000       1
+       2     0.000000     0.000000       2
+       3     0.000000     0.000000       3
+       4     0.000000     0.000000       4
+       5     0.000000     0.000000       5
+       6     0.000000     0.000000       6
+       7     0.000000     0.000000       7
+       8     0.000000     0.000000       8
+       9     0.000000     0.000000       9
+      10     0.000000     0.000000      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 2.000000
+#! SET iteration  1
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.219197     0.219197       1
+       2    -0.970366    -0.970366       2
+       3    -0.884094    -0.884094       3
+       4    -0.421298    -0.421298       4
+       5    -0.590820    -0.590820       5
+       6     0.748809     0.748809       6
+       7     0.576392     0.576392       7
+       8     0.715341     0.715341       8
+       9     0.786645     0.786645       9
+      10    -0.381816    -0.381816      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 4.000000
+#! SET iteration  2
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.305152     0.391107       1
+       2    -1.461895    -1.953423       2
+       3    -1.350614    -1.817134       3
+       4    -0.589608    -0.757918       4
+       5    -0.834473    -1.078125       5
+       6     1.174985     1.601160       6
+       7     0.948813     1.321234       7
+       8     1.024273     1.333206       8
+       9     1.148264     1.509884       9
+      10    -0.689625    -0.997434      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 6.000000
+#! SET iteration  3
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.421218     0.653351       1
+       2    -1.946133    -2.914610       2
+       3    -1.788707    -2.664892       3
+       4    -0.812257    -1.257555       4
+       5    -1.146186    -1.769612       5
+       6     1.540202     2.270638       6
+       7     1.220946     1.765213       7
+       8     1.401662     2.156440       8
+       9     1.564119     2.395830       9
+      10    -0.857540    -1.193370      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 8.000000
+#! SET iteration  4
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.448007     0.528372       1
+       2    -2.433590    -3.895961       2
+       3    -2.239120    -3.590362       3
+       4    -0.861012    -1.007276       4
+       5    -1.209573    -1.399733       5
+       6     1.931358     3.104824       6
+       7     1.535645     2.479741       7
+       8     1.472935     1.686754       8
+       9     1.639154     1.864258       9
+      10    -1.086629    -1.773897      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 10.000000
+#! SET iteration  5
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.441146     0.413704       1
+       2    -2.895058    -4.740930       2
+       3    -2.593087    -4.008954       3
+       4    -0.858951    -0.850710       4
+       5    -1.239599    -1.359702       5
+       6     2.140456     2.976852       6
+       7     1.611231     1.913575       7
+       8     1.562246     1.919487       8
+       9     1.789475     2.390761       9
+      10    -1.071904    -1.013004      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 12.000000
+#! SET iteration  6
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.441948     0.445955       1
+       2    -3.365271    -5.716337       2
+       3    -2.979506    -4.911603       3
+       4    -0.867479    -0.910117       4
+       5    -1.269466    -1.418805       5
+       6     2.410784     3.762420       6
+       7     1.766861     2.545012       7
+       8     1.621663     1.918750       8
+       9     1.870932     2.278215       9
+      10    -1.136982    -1.462370      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 14.000000
+#! SET iteration  7
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.383175     0.030542       1
+       2    -3.758763    -6.119715       2
+       3    -3.154779    -4.206413       3
+       4    -0.874583    -0.917208       4
+       5    -1.387569    -2.096189       5
+       6     2.602191     3.750634       6
+       7     1.994254     3.358610       7
+       8     1.747113     2.499816       8
+       9     1.915919     2.185842       9
+      10    -1.282146    -2.153134      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 16.000000
+#! SET iteration  8
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.296543    -0.309884       1
+       2    -4.141493    -6.820603       2
+       3    -3.290550    -4.240951       3
+       4    -0.837652    -0.579136       4
+       5    -1.491646    -2.220179       5
+       6     2.688068     3.289207       6
+       7     2.149365     3.235145       7
+       8     1.917967     3.113944       8
+       9     2.038602     2.897379       9
+      10    -1.468354    -2.771810      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 18.000000
+#! SET iteration  9
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.234442    -0.262361       1
+       2    -4.548948    -7.808582       2
+       3    -3.501952    -5.193167       3
+       4    -0.818965    -0.669467       4
+       5    -1.579418    -2.281596       5
+       6     2.854156     4.182861       6
+       7     2.360190     4.046783       7
+       8     2.050168     3.107779       8
+       9     2.134519     2.901856       9
+      10    -1.691816    -3.479514      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 20.000000
+#! SET iteration  10
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.205729    -0.052695       1
+       2    -4.971305    -8.772526       2
+       3    -3.756567    -6.048102       3
+       4    -0.842988    -1.059199       4
+       5    -1.697444    -2.759682       5
+       6     3.054607     4.858669       6
+       7     2.568698     4.445279       7
+       8     2.208072     3.629202       8
+       9     2.266734     3.456672       9
+      10    -1.877002    -3.543669      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/colvar.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/colvar.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..7bea698e93ba38c1b40ba7d43f179a7fd123e164
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/colvar.data.reference
@@ -0,0 +1,24 @@
+#! FIELDS time phi ves1.bias o1.avergradrms o1.avergradmax
+#! SET min_phi -pi
+#! SET max_phi pi
+ 0.000000 -1.238  0.000  0.000  0.000
+ 1.000000 -1.484  0.000  0.000  0.000
+ 2.000000 -1.324  0.000  0.637  0.970
+ 3.000000 -1.334  4.716  0.637  0.970
+ 4.000000 -1.461  4.403  0.646  0.977
+ 5.000000 -1.220  6.371  0.646  0.977
+ 6.000000 -1.388  7.123  0.643  0.972
+ 7.000000 -1.548  7.766  0.643  0.972
+ 8.000000 -1.843  1.066  0.573  0.974
+ 9.000000 -2.242 -3.365  0.573  0.974
+ 10.000000 -1.148  8.387  0.493  0.949
+ 11.000000 -1.758  5.325  0.493  0.949
+ 12.000000 -1.319 12.218  0.492  0.953
+ 13.000000 -2.991 -1.159  0.492  0.953
+ 14.000000 -1.411 13.737  0.466  0.898
+ 15.000000 -2.599 -0.714  0.466  0.898
+ 16.000000 -1.461 14.602  0.449  0.880
+ 17.000000 -1.379 15.945  0.449  0.880
+ 18.000000 -1.677 10.610  0.461  0.892
+ 19.000000 -1.524 16.005  0.461  0.892
+ 20.000000 -1.200 13.955  0.472  0.900
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/combined_gradient.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/combined_gradient.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..fd2741b6458ded2a3525e6ef0197241c4d2b8000
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/combined_gradient.data.reference
@@ -0,0 +1,210 @@
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 2.000000
+#! SET iteration  1
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.219197       1
+       2     0.970366       2
+       3     0.884094       3
+       4     0.421298       4
+       5     0.590820       5
+       6    -0.748809       6
+       7    -0.576392       7
+       8    -0.715341       8
+       9    -0.786645       9
+      10     0.381816      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 4.000000
+#! SET iteration  2
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.171909       1
+       2     0.983056       2
+       3     0.933040       3
+       4     0.336620       4
+       5     0.487305       5
+       6    -0.852350       6
+       7    -0.744842       7
+       8    -0.617866       8
+       9    -0.723239       9
+      10     0.615618      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 6.000000
+#! SET iteration  3
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.262244       1
+       2     0.961187       2
+       3     0.847758       3
+       4     0.499637       4
+       5     0.691487       5
+       6    -0.669478       6
+       7    -0.443979       7
+       8    -0.823233       8
+       9    -0.885946       9
+      10     0.195936      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 8.000000
+#! SET iteration  4
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.124979       1
+       2     0.981351       2
+       3     0.925470       3
+       4    -0.250280       4
+       5    -0.369879       5
+       6    -0.834186       6
+       7    -0.714529       7
+       8     0.469686       8
+       9     0.531572       9
+      10     0.580527      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 10.000000
+#! SET iteration  5
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.114667       1
+       2     0.844969       2
+       3     0.418592       3
+       4    -0.156566       4
+       5    -0.040031       5
+       6     0.127972       6
+       7     0.566166       7
+       8    -0.232733       8
+       9    -0.526503       9
+      10    -0.760892      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 12.000000
+#! SET iteration  6
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.032251       1
+       2     0.975407       2
+       3     0.902649       3
+       4     0.059408       4
+       5     0.059102       5
+       6    -0.785568       6
+       7    -0.631437       7
+       8     0.000738       8
+       9     0.112546       9
+      10     0.449365      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 14.000000
+#! SET iteration  7
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.415413       1
+       2     0.403378       2
+       3    -0.705190       3
+       4     0.007091       4
+       5     0.677384       5
+       6     0.011786       6
+       7    -0.813598       7
+       8    -0.581066       8
+       9     0.092373       9
+      10     0.690764      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 16.000000
+#! SET iteration  8
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.340425       1
+       2     0.700888       2
+       3     0.034538       3
+       4    -0.338072       4
+       5     0.123991       5
+       6     0.461427       6
+       7     0.123465       7
+       8    -0.614128       8
+       9    -0.711537       9
+      10     0.618677      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 18.000000
+#! SET iteration  9
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.047522       1
+       2     0.987979       2
+       3     0.952216       3
+       4     0.090331       4
+       5     0.061417       5
+       6    -0.893654       6
+       7    -0.811638       7
+       8     0.006164       8
+       9    -0.004477       9
+      10     0.707703      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 20.000000
+#! SET iteration  10
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.209666       1
+       2     0.963944       2
+       3     0.854935       3
+       4     0.389732       4
+       5     0.478086       5
+       6    -0.675807       6
+       7    -0.398496       7
+       8    -0.521422       8
+       9    -0.554816       9
+      10     0.064155      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/config b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/config
new file mode 100644
index 0000000000000000000000000000000000000000..d9b022c5f95c12fdf3de7e32807e196863eec343
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/config
@@ -0,0 +1,3 @@
+plumed_modules=ves
+type=driver
+arg="--plumed plumed.dat --trajectory-stride 500 --timestep 0.002 --igro traj.gro --dump-forces forces --dump-forces-fmt=%10.6f "
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/fes.ves1.iter-10.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/fes.ves1.iter-10.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..d50483ac34516d62eac2c7fd2592ae5ef72ba0af
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/fes.ves1.iter-10.data.reference
@@ -0,0 +1,105 @@
+#! FIELDS phi ves1.fes
+#! SET min_phi -pi
+#! SET max_phi pi
+#! SET nbins_phi  100
+#! SET periodic_phi true
+   -3.141592654   20.497536200
+   -3.078760801   19.704062923
+   -3.015928947   18.925946415
+   -2.953097094   18.241634172
+   -2.890265241   17.723868121
+   -2.827433388   17.431435858
+   -2.764601535   17.401912078
+   -2.701769682   17.646168907
+   -2.638937829   18.145285307
+   -2.576105976   18.850270868
+   -2.513274123   19.684757617
+   -2.450442270   20.550529614
+   -2.387610417   21.335481149
+   -2.324778564   21.923347445
+   -2.261946711   22.204361318
+   -2.199114858   22.085874739
+   -2.136283004   21.501958062
+   -2.073451151   20.421055959
+   -2.010619298   18.850933268
+   -1.947787445   16.840372909
+   -1.884955592   14.477371479
+   -1.822123739   11.883890368
+   -1.759291886    9.207532462
+   -1.696460033    6.610797784
+   -1.633628180    4.258799067
+   -1.570796327    2.306468659
+   -1.507964474    0.886346801
+   -1.445132621    0.098002001
+   -1.382300768    0.000000000
+   -1.319468915    0.605120352
+   -1.256637061    1.879238705
+   -1.193805208    3.743973689
+   -1.130973355    6.082869229
+   -1.068141502    8.750575807
+   -1.005309649   11.584235793
+   -0.942477796   14.416091724
+   -0.879645943   17.086239085
+   -0.816814090   19.454444982
+   -0.753982237   21.410050510
+   -0.691150384   22.879157907
+   -0.628318531   23.828556259
+   -0.565486678   24.266137588
+   -0.502654825   24.237870844
+   -0.439822972   23.821705285
+   -0.376991118   23.119039279
+   -0.314159265   22.244591720
+   -0.251327412   21.315633608
+   -0.188495559   20.441566950
+   -0.125663706   19.714776047
+   -0.062831853   19.203529863
+    0.000000000   18.947498997
+    0.062831853   18.956188434
+    0.125663706   19.210303564
+    0.188495559   19.665789288
+    0.251327412   20.260036806
+    0.314159265   20.919562617
+    0.376991118   21.568346457
+    0.439822972   22.135979202
+    0.502654825   22.564819678
+    0.565486678   22.815484466
+    0.628318531   22.870183117
+    0.691150384   22.733642841
+    0.753982237   22.431617795
+    0.816814090   22.007223380
+    0.879645943   21.515550884
+    0.942477796   21.017181692
+    1.005309649   20.571317381
+    1.068141502   20.229263897
+    1.130973355   20.028953661
+    1.193805208   19.991065692
+    1.256637061   20.117124372
+    1.319468915   20.389741461
+    1.382300768   20.774936136
+    1.445132621   21.226247968
+    1.507964474   21.690170517
+    1.570796327   22.112297643
+    1.633628180   22.443504384
+    1.696460033   22.645486094
+    1.759291886   22.695052917
+    1.822123739   22.586713543
+    1.884955592   22.333268044
+    1.947787445   21.964344888
+    2.010619298   21.523039407
+    2.073451151   21.061016758
+    2.136283004   20.632610225
+    2.199114858   20.288557744
+    2.261946711   20.070063935
+    2.324778564   20.003846521
+    2.387610417   20.098727335
+    2.450442270   20.344168898
+    2.513274123   20.710953806
+    2.576105976   21.153976788
+    2.638937829   21.616891596
+    2.701769682   22.038150709
+    2.764601535   22.357816586
+    2.827433388   22.524426200
+    2.890265241   22.501166805
+    2.953097094   22.270674081
+    3.015928947   21.837889873
+    3.078760801   21.230604100
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/forces.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/forces.reference
new file mode 100644
index 0000000000000000000000000000000000000000..75ae219e0f6736a9037c0c36631fa4ee84749782
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/forces.reference
@@ -0,0 +1,504 @@
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diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/plumed.dat b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/plumed.dat
new file mode 100644
index 0000000000000000000000000000000000000000..71a804221f69fa4bfe898ffbc814bfa51352eeea
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/plumed.dat
@@ -0,0 +1,43 @@
+# vim:ft=plumed
+
+phi:   TORSION ATOMS=5,7,9,15     NOPBC
+
+bf1: BF_FOURIER ORDER=5 MINIMUM=-pi MAXIMUM=pi
+
+VES_LINEAR_EXPANSION ...
+ ARG=phi
+ BASIS_FUNCTIONS=bf1
+ LABEL=ves1
+ TEMP=300.0
+ GRID_BINS=100
+... VES_LINEAR_EXPANSION
+
+# NOTE: These parameters do not reflect parameters used in real simulations! 
+#       This is only for testing!
+#
+
+OPT_AVERAGED_SGD ...
+  BIAS=ves1
+  STRIDE=1000
+  LABEL=o1
+  STEPSIZE=1.0
+  COEFFS_FILE=coeffs.data
+  COEFFS_OUTPUT=1
+  COEFFS_FMT=%12.6f
+  FES_OUTPUT=10
+  BIAS_OUTPUT=10
+  TARGETDIST_AVERAGES_FMT=%12.6f
+  COMBINED_GRADIENT_FILE=combined_gradient.data
+  COMBINED_GRADIENT_OUTPUT=1
+  COMBINED_GRADIENT_FMT=%12.6f
+  MONITOR_AVERAGE_GRADIENT
+... OPT_AVERAGED_SGD
+
+PRINT ...
+  STRIDE=500
+  ARG=phi,ves1.bias,o1.*
+  FILE=colvar.data FMT=%6.3f
+... PRINT
+
+ENDPLUMED
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/targetdist-averages.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/targetdist-averages.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..b6bf5b55ccca602f2814808f51085a0599e101ab
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/targetdist-averages.data.reference
@@ -0,0 +1,21 @@
+#! FIELDS idx_phi ves1.targetdist_averages index
+#! SET time 0.000000
+#! SET iteration  0
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     1.000000       0
+       1     0.000000       1
+       2     0.000000       2
+       3     0.000000       3
+       4     0.000000       4
+       5     0.000000       5
+       6     0.000000       6
+       7     0.000000       7
+       8     0.000000       8
+       9     0.000000       9
+      10     0.000000      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/traj.gro b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/traj.gro
new file mode 100644
index 0000000000000000000000000000000000000000..c1c387a0144ec8021b9e5b0453be534f2ca906e2
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-aver-grad/traj.gro
@@ -0,0 +1,525 @@
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+    2ALA      N    7   1.349   1.324   1.182
+    2ALA      H    8   1.432   1.287   1.138
+    2ALA     CA    9   1.221   1.249   1.168
+    2ALA     HA   10   1.138   1.318   1.184
+    2ALA     CB   11   1.201   1.194   1.025
+    2ALA    HB1   12   1.276   1.117   1.005
+    2ALA    HB2   13   1.096   1.165   1.014
+    2ALA    HB3   14   1.229   1.265   0.947
+    2ALA      C   15   1.217   1.141   1.275
+    2ALA      O   16   1.234   1.024   1.243
+    3NME      N   17   1.183   1.174   1.400
+    3NME      H   18   1.184   1.274   1.412
+    3NME    CH3   19   1.187   1.078   1.509
+    3NME   HH31   20   1.248   0.990   1.490
+    3NME   HH32   21   1.220   1.120   1.604
+    3NME   HH33   22   1.088   1.035   1.527
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   5.00000
+   22
+    1ACE   HH31    1   1.449   1.585   1.168
+    1ACE    CH3    2   1.479   1.518   1.248
+    1ACE   HH32    3   1.523   1.577   1.328
+    1ACE   HH33    4   1.565   1.461   1.213
+    1ACE      C    5   1.364   1.422   1.284
+    1ACE      O    6   1.305   1.438   1.389
+    2ALA      N    7   1.347   1.326   1.187
+    2ALA      H    8   1.423   1.328   1.122
+    2ALA     CA    9   1.226   1.241   1.162
+    2ALA     HA   10   1.139   1.308   1.162
+    2ALA     CB   11   1.236   1.193   1.023
+    2ALA    HB1   12   1.314   1.117   1.012
+    2ALA    HB2   13   1.137   1.167   0.986
+    2ALA    HB3   14   1.273   1.278   0.966
+    2ALA      C   15   1.195   1.133   1.268
+    2ALA      O   16   1.173   1.016   1.239
+    3NME      N   17   1.204   1.175   1.393
+    3NME      H   18   1.211   1.275   1.403
+    3NME    CH3   19   1.188   1.090   1.513
+    3NME   HH31   20   1.089   1.044   1.509
+    3NME   HH32   21   1.267   1.014   1.509
+    3NME   HH33   22   1.189   1.145   1.607
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   6.00000
+   22
+    1ACE   HH31    1   1.517   1.511   1.181
+    1ACE    CH3    2   1.490   1.488   1.284
+    1ACE   HH32    3   1.482   1.582   1.339
+    1ACE   HH33    4   1.569   1.421   1.316
+    1ACE      C    5   1.359   1.414   1.282
+    1ACE      O    6   1.272   1.447   1.358
+    2ALA      N    7   1.351   1.320   1.186
+    2ALA      H    8   1.434   1.297   1.133
+    2ALA     CA    9   1.220   1.251   1.159
+    2ALA     HA   10   1.139   1.323   1.167
+    2ALA     CB   11   1.220   1.194   1.018
+    2ALA    HB1   12   1.298   1.120   1.003
+    2ALA    HB2   13   1.120   1.158   0.994
+    2ALA    HB3   14   1.224   1.286   0.960
+    2ALA      C   15   1.201   1.139   1.270
+    2ALA      O   16   1.190   1.022   1.239
+    3NME      N   17   1.203   1.178   1.393
+    3NME      H   18   1.207   1.277   1.409
+    3NME    CH3   19   1.211   1.102   1.515
+    3NME   HH31   20   1.111   1.064   1.534
+    3NME   HH32   21   1.275   1.017   1.492
+    3NME   HH33   22   1.264   1.151   1.597
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   7.00000
+   22
+    1ACE   HH31    1   1.483   1.590   1.185
+    1ACE    CH3    2   1.505   1.501   1.245
+    1ACE   HH32    3   1.538   1.533   1.344
+    1ACE   HH33    4   1.580   1.430   1.209
+    1ACE      C    5   1.379   1.418   1.267
+    1ACE      O    6   1.298   1.443   1.349
+    2ALA      N    7   1.360   1.320   1.187
+    2ALA      H    8   1.426   1.297   1.114
+    2ALA     CA    9   1.224   1.253   1.180
+    2ALA     HA   10   1.147   1.326   1.205
+    2ALA     CB   11   1.174   1.215   1.037
+    2ALA    HB1   12   1.245   1.152   0.983
+    2ALA    HB2   13   1.084   1.154   1.032
+    2ALA    HB3   14   1.153   1.311   0.992
+    2ALA      C   15   1.212   1.141   1.280
+    2ALA      O   16   1.219   1.022   1.244
+    3NME      N   17   1.191   1.176   1.408
+    3NME      H   18   1.207   1.275   1.423
+    3NME    CH3   19   1.162   1.068   1.509
+    3NME   HH31   20   1.229   0.982   1.503
+    3NME   HH32   21   1.162   1.109   1.610
+    3NME   HH33   22   1.056   1.044   1.499
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   8.00000
+   22
+    1ACE   HH31    1   1.576   1.425   1.169
+    1ACE    CH3    2   1.523   1.455   1.260
+    1ACE   HH32    3   1.547   1.556   1.294
+    1ACE   HH33    4   1.566   1.393   1.338
+    1ACE      C    5   1.385   1.422   1.255
+    1ACE      O    6   1.308   1.499   1.305
+    2ALA      N    7   1.346   1.311   1.189
+    2ALA      H    8   1.419   1.248   1.159
+    2ALA     CA    9   1.210   1.260   1.193
+    2ALA     HA   10   1.139   1.326   1.242
+    2ALA     CB   11   1.152   1.252   1.051
+    2ALA    HB1   12   1.230   1.210   0.987
+    2ALA    HB2   13   1.066   1.185   1.052
+    2ALA    HB3   14   1.127   1.354   1.024
+    2ALA      C   15   1.206   1.136   1.282
+    2ALA      O   16   1.195   1.023   1.229
+    3NME      N   17   1.210   1.152   1.420
+    3NME      H   18   1.221   1.243   1.463
+    3NME    CH3   19   1.185   1.048   1.518
+    3NME   HH31   20   1.195   0.948   1.475
+    3NME   HH32   21   1.261   1.070   1.593
+    3NME   HH33   22   1.088   1.064   1.565
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   9.00000
+   22
+    1ACE   HH31    1   1.515   1.474   1.040
+    1ACE    CH3    2   1.535   1.461   1.147
+    1ACE   HH32    3   1.561   1.560   1.184
+    1ACE   HH33    4   1.612   1.386   1.165
+    1ACE      C    5   1.406   1.430   1.217
+    1ACE      O    6   1.361   1.502   1.307
+    2ALA      N    7   1.345   1.316   1.190
+    2ALA      H    8   1.384   1.254   1.121
+    2ALA     CA    9   1.217   1.277   1.242
+    2ALA     HA   10   1.187   1.348   1.319
+    2ALA     CB   11   1.111   1.278   1.134
+    2ALA    HB1   12   1.129   1.198   1.062
+    2ALA    HB2   13   1.018   1.269   1.189
+    2ALA    HB3   14   1.121   1.372   1.079
+    2ALA      C   15   1.217   1.133   1.309
+    2ALA      O   16   1.293   1.044   1.265
+    3NME      N   17   1.132   1.116   1.408
+    3NME      H   18   1.076   1.195   1.437
+    3NME    CH3   19   1.112   1.003   1.490
+    3NME   HH31   20   1.156   0.910   1.456
+    3NME   HH32   21   1.153   1.026   1.588
+    3NME   HH33   22   1.005   0.985   1.500
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  10.00000
+   22
+    1ACE   HH31    1   1.536   1.485   1.135
+    1ACE    CH3    2   1.521   1.460   1.240
+    1ACE   HH32    3   1.528   1.557   1.289
+    1ACE   HH33    4   1.602   1.397   1.276
+    1ACE      C    5   1.385   1.401   1.261
+    1ACE      O    6   1.341   1.416   1.373
+    2ALA      N    7   1.322   1.332   1.167
+    2ALA      H    8   1.364   1.316   1.076
+    2ALA     CA    9   1.190   1.273   1.177
+    2ALA     HA   10   1.125   1.352   1.216
+    2ALA     CB   11   1.134   1.230   1.038
+    2ALA    HB1   12   1.167   1.128   1.016
+    2ALA    HB2   13   1.026   1.238   1.046
+    2ALA    HB3   14   1.174   1.287   0.953
+    2ALA      C   15   1.183   1.157   1.283
+    2ALA      O   16   1.111   1.061   1.259
+    3NME      N   17   1.264   1.157   1.396
+    3NME      H   18   1.320   1.241   1.405
+    3NME    CH3   19   1.264   1.070   1.510
+    3NME   HH31   20   1.163   1.057   1.548
+    3NME   HH32   21   1.311   0.974   1.487
+    3NME   HH33   22   1.326   1.109   1.592
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  11.00000
+   22
+    1ACE   HH31    1   1.607   1.359   1.178
+    1ACE    CH3    2   1.535   1.442   1.176
+    1ACE   HH32    3   1.521   1.470   1.072
+    1ACE   HH33    4   1.569   1.533   1.224
+    1ACE      C    5   1.402   1.412   1.242
+    1ACE      O    6   1.368   1.454   1.350
+    2ALA      N    7   1.319   1.332   1.177
+    2ALA      H    8   1.363   1.279   1.103
+    2ALA     CA    9   1.194   1.289   1.231
+    2ALA     HA   10   1.153   1.355   1.308
+    2ALA     CB   11   1.092   1.300   1.113
+    2ALA    HB1   12   1.137   1.243   1.032
+    2ALA    HB2   13   1.001   1.243   1.131
+    2ALA    HB3   14   1.070   1.405   1.095
+    2ALA      C   15   1.198   1.143   1.290
+    2ALA      O   16   1.237   1.057   1.213
+    3NME      N   17   1.171   1.126   1.422
+    3NME      H   18   1.164   1.213   1.472
+    3NME    CH3   19   1.200   1.009   1.496
+    3NME   HH31   20   1.118   0.938   1.493
+    3NME   HH32   21   1.284   0.953   1.454
+    3NME   HH33   22   1.230   1.031   1.598
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  12.00000
+   22
+    1ACE   HH31    1   1.491   1.569   1.138
+    1ACE    CH3    2   1.511   1.462   1.134
+    1ACE   HH32    3   1.614   1.449   1.166
+    1ACE   HH33    4   1.495   1.444   1.028
+    1ACE      C    5   1.416   1.394   1.229
+    1ACE      O    6   1.445   1.392   1.345
+    2ALA      N    7   1.299   1.357   1.181
+    2ALA      H    8   1.278   1.358   1.082
+    2ALA     CA    9   1.196   1.301   1.267
+    2ALA     HA   10   1.185   1.364   1.355
+    2ALA     CB   11   1.063   1.319   1.182
+    2ALA    HB1   12   1.057   1.248   1.100
+    2ALA    HB2   13   0.976   1.288   1.240
+    2ALA    HB3   14   1.037   1.423   1.161
+    2ALA      C   15   1.226   1.161   1.304
+    2ALA      O   16   1.317   1.094   1.258
+    3NME      N   17   1.135   1.110   1.387
+    3NME      H   18   1.064   1.174   1.419
+    3NME    CH3   19   1.121   0.972   1.429
+    3NME   HH31   20   1.163   0.900   1.358
+    3NME   HH32   21   1.177   0.954   1.520
+    3NME   HH33   22   1.016   0.942   1.428
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  13.00000
+   22
+    1ACE   HH31    1   1.528   1.537   1.077
+    1ACE    CH3    2   1.543   1.448   1.137
+    1ACE   HH32    3   1.634   1.463   1.195
+    1ACE   HH33    4   1.560   1.362   1.072
+    1ACE      C    5   1.421   1.428   1.229
+    1ACE      O    6   1.396   1.520   1.301
+    2ALA      N    7   1.355   1.314   1.219
+    2ALA      H    8   1.385   1.241   1.156
+    2ALA     CA    9   1.249   1.276   1.311
+    2ALA     HA   10   1.297   1.288   1.409
+    2ALA     CB   11   1.122   1.359   1.284
+    2ALA    HB1   12   1.072   1.325   1.193
+    2ALA    HB2   13   1.053   1.352   1.367
+    2ALA    HB3   14   1.153   1.463   1.275
+    2ALA      C   15   1.204   1.131   1.290
+    2ALA      O   16   1.225   1.070   1.185
+    3NME      N   17   1.131   1.077   1.382
+    3NME      H   18   1.104   1.132   1.463
+    3NME    CH3   19   1.083   0.939   1.380
+    3NME   HH31   20   1.012   0.925   1.298
+    3NME   HH32   21   1.168   0.871   1.372
+    3NME   HH33   22   1.036   0.915   1.475
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  14.00000
+   22
+    1ACE   HH31    1   1.543   1.468   1.123
+    1ACE    CH3    2   1.548   1.443   1.229
+    1ACE   HH32    3   1.566   1.540   1.276
+    1ACE   HH33    4   1.634   1.382   1.257
+    1ACE      C    5   1.420   1.385   1.285
+    1ACE      O    6   1.412   1.375   1.404
+    2ALA      N    7   1.324   1.361   1.200
+    2ALA      H    8   1.345   1.354   1.101
+    2ALA     CA    9   1.189   1.323   1.244
+    2ALA     HA   10   1.163   1.394   1.323
+    2ALA     CB   11   1.094   1.344   1.125
+    2ALA    HB1   12   1.098   1.270   1.045
+    2ALA    HB2   13   0.995   1.352   1.170
+    2ALA    HB3   14   1.120   1.440   1.079
+    2ALA      C   15   1.166   1.169   1.284
+    2ALA      O   16   1.055   1.145   1.330
+    3NME      N   17   1.263   1.077   1.279
+    3NME      H   18   1.356   1.102   1.247
+    3NME    CH3   19   1.246   0.942   1.335
+    3NME   HH31   20   1.142   0.911   1.345
+    3NME   HH32   21   1.293   0.868   1.270
+    3NME   HH33   22   1.292   0.934   1.434
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  15.00000
+   22
+    1ACE   HH31    1   1.508   1.417   1.043
+    1ACE    CH3    2   1.539   1.448   1.143
+    1ACE   HH32    3   1.565   1.553   1.146
+    1ACE   HH33    4   1.630   1.395   1.169
+    1ACE      C    5   1.438   1.410   1.253
+    1ACE      O    6   1.429   1.471   1.356
+    2ALA      N    7   1.348   1.327   1.217
+    2ALA      H    8   1.362   1.285   1.126
+    2ALA     CA    9   1.233   1.289   1.298
+    2ALA     HA   10   1.269   1.295   1.401
+    2ALA     CB   11   1.107   1.379   1.286
+    2ALA    HB1   12   1.057   1.360   1.191
+    2ALA    HB2   13   1.034   1.369   1.366
+    2ALA    HB3   14   1.141   1.482   1.282
+    2ALA      C   15   1.192   1.141   1.266
+    2ALA      O   16   1.220   1.089   1.156
+    3NME      N   17   1.131   1.075   1.364
+    3NME      H   18   1.117   1.126   1.450
+    3NME    CH3   19   1.090   0.931   1.376
+    3NME   HH31   20   1.156   0.880   1.446
+    3NME   HH32   21   0.996   0.929   1.431
+    3NME   HH33   22   1.090   0.874   1.283
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  16.00000
+   22
+    1ACE   HH31    1   1.587   1.386   1.166
+    1ACE    CH3    2   1.554   1.425   1.262
+    1ACE   HH32    3   1.559   1.534   1.266
+    1ACE   HH33    4   1.627   1.390   1.335
+    1ACE      C    5   1.417   1.372   1.300
+    1ACE      O    6   1.390   1.364   1.421
+    2ALA      N    7   1.334   1.344   1.205
+    2ALA      H    8   1.365   1.367   1.111
+    2ALA     CA    9   1.190   1.324   1.235
+    2ALA     HA   10   1.160   1.386   1.319
+    2ALA     CB   11   1.105   1.363   1.112
+    2ALA    HB1   12   1.129   1.297   1.029
+    2ALA    HB2   13   0.999   1.351   1.131
+    2ALA    HB3   14   1.125   1.467   1.088
+    2ALA      C   15   1.162   1.180   1.282
+    2ALA      O   16   1.054   1.128   1.258
+    3NME      N   17   1.261   1.106   1.318
+    3NME      H   18   1.349   1.152   1.336
+    3NME    CH3   19   1.250   0.960   1.324
+    3NME   HH31   20   1.264   0.908   1.229
+    3NME   HH32   21   1.322   0.926   1.399
+    3NME   HH33   22   1.153   0.923   1.357
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  17.00000
+   22
+    1ACE   HH31    1   1.614   1.382   1.173
+    1ACE    CH3    2   1.559   1.432   1.253
+    1ACE   HH32    3   1.547   1.532   1.213
+    1ACE   HH33    4   1.625   1.444   1.339
+    1ACE      C    5   1.426   1.380   1.288
+    1ACE      O    6   1.411   1.348   1.406
+    2ALA      N    7   1.325   1.370   1.200
+    2ALA      H    8   1.341   1.388   1.102
+    2ALA     CA    9   1.189   1.318   1.239
+    2ALA     HA   10   1.170   1.358   1.338
+    2ALA     CB   11   1.084   1.388   1.158
+    2ALA    HB1   12   1.113   1.369   1.055
+    2ALA    HB2   13   0.994   1.336   1.189
+    2ALA    HB3   14   1.075   1.493   1.186
+    2ALA      C   15   1.170   1.163   1.252
+    2ALA      O   16   1.097   1.103   1.171
+    3NME      N   17   1.235   1.099   1.349
+    3NME      H   18   1.305   1.153   1.399
+    3NME    CH3   19   1.220   0.964   1.393
+    3NME   HH31   20   1.315   0.912   1.406
+    3NME   HH32   21   1.168   0.953   1.489
+    3NME   HH33   22   1.178   0.897   1.318
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  18.00000
+   22
+    1ACE   HH31    1   1.555   1.419   1.126
+    1ACE    CH3    2   1.554   1.431   1.235
+    1ACE   HH32    3   1.554   1.535   1.267
+    1ACE   HH33    4   1.638   1.381   1.283
+    1ACE      C    5   1.423   1.378   1.292
+    1ACE      O    6   1.416   1.347   1.409
+    2ALA      N    7   1.322   1.351   1.211
+    2ALA      H    8   1.350   1.370   1.115
+    2ALA     CA    9   1.185   1.318   1.251
+    2ALA     HA   10   1.171   1.358   1.352
+    2ALA     CB   11   1.091   1.400   1.149
+    2ALA    HB1   12   1.059   1.346   1.060
+    2ALA    HB2   13   1.008   1.443   1.205
+    2ALA    HB3   14   1.154   1.480   1.109
+    2ALA      C   15   1.163   1.166   1.255
+    2ALA      O   16   1.060   1.108   1.214
+    3NME      N   17   1.255   1.102   1.328
+    3NME      H   18   1.335   1.159   1.354
+    3NME    CH3   19   1.246   0.964   1.369
+    3NME   HH31   20   1.154   0.913   1.344
+    3NME   HH32   21   1.323   0.899   1.327
+    3NME   HH33   22   1.251   0.953   1.477
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  19.00000
+   22
+    1ACE   HH31    1   1.559   1.326   1.133
+    1ACE    CH3    2   1.552   1.413   1.200
+    1ACE   HH32    3   1.538   1.504   1.142
+    1ACE   HH33    4   1.631   1.428   1.273
+    1ACE      C    5   1.426   1.375   1.280
+    1ACE      O    6   1.428   1.345   1.398
+    2ALA      N    7   1.319   1.363   1.209
+    2ALA      H    8   1.322   1.382   1.110
+    2ALA     CA    9   1.191   1.329   1.265
+    2ALA     HA   10   1.186   1.364   1.368
+    2ALA     CB   11   1.075   1.391   1.178
+    2ALA    HB1   12   1.098   1.383   1.072
+    2ALA    HB2   13   0.980   1.348   1.211
+    2ALA    HB3   14   1.066   1.499   1.192
+    2ALA      C   15   1.169   1.174   1.275
+    2ALA      O   16   1.086   1.118   1.203
+    3NME      N   17   1.233   1.105   1.363
+    3NME      H   18   1.312   1.150   1.405
+    3NME    CH3   19   1.242   0.956   1.350
+    3NME   HH31   20   1.219   0.899   1.440
+    3NME   HH32   21   1.165   0.918   1.284
+    3NME   HH33   22   1.333   0.921   1.301
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  20.00000
+   22
+    1ACE   HH31    1   1.622   1.459   1.287
+    1ACE    CH3    2   1.546   1.434   1.214
+    1ACE   HH32    3   1.578   1.365   1.135
+    1ACE   HH33    4   1.509   1.531   1.180
+    1ACE      C    5   1.430   1.358   1.283
+    1ACE      O    6   1.444   1.310   1.394
+    2ALA      N    7   1.315   1.370   1.215
+    2ALA      H    8   1.323   1.427   1.132
+    2ALA     CA    9   1.178   1.334   1.258
+    2ALA     HA   10   1.163   1.376   1.357
+    2ALA     CB   11   1.079   1.393   1.158
+    2ALA    HB1   12   1.096   1.348   1.060
+    2ALA    HB2   13   0.979   1.367   1.192
+    2ALA    HB3   14   1.087   1.501   1.165
+    2ALA      C   15   1.163   1.177   1.270
+    2ALA      O   16   1.073   1.114   1.216
+    3NME      N   17   1.249   1.110   1.347
+    3NME      H   18   1.324   1.165   1.388
+    3NME    CH3   19   1.242   0.964   1.360
+    3NME   HH31   20   1.325   0.920   1.416
+    3NME   HH32   21   1.151   0.938   1.414
+    3NME   HH33   22   1.221   0.913   1.266
+  10.00000  10.00000  10.00000
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/Makefile b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..3703b27cea227aa053fb6d1d73f861e4384dbcee
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/Makefile
@@ -0,0 +1 @@
+include ../../scripts/test.make
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/bias.ves1.iter-10.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/bias.ves1.iter-10.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..55fc4b90e0bb8e0a74059ba4d1ad0bc14e44ef67
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/bias.ves1.iter-10.data.reference
@@ -0,0 +1,105 @@
+#! FIELDS phi ves1.bias der_phi
+#! SET min_phi -pi
+#! SET max_phi pi
+#! SET nbins_phi  100
+#! SET periodic_phi true
+   -3.141592654   -1.962887340  -12.338802116
+   -3.078760801   -1.169414064  -12.715200498
+   -3.015928947   -0.391297555  -11.842670932
+   -2.953097094    0.293014687   -9.744489584
+   -2.890265241    0.810780738   -6.578621340
+   -2.827433388    1.103213002   -2.628636251
+   -2.764601535    1.132736781    1.718540218
+   -2.701769682    0.888479952    6.006285748
+   -2.638937829    0.389363553    9.750412598
+   -2.576105976   -0.315622008   12.485919949
+   -2.513274123   -1.150108758   13.813956198
+   -2.450442270   -2.015880754   13.444439030
+   -2.387610417   -2.800832289   11.230078693
+   -2.324778564   -3.388698586    7.188264732
+   -2.261946711   -3.669712459    1.508346390
+   -2.199114858   -3.551225879   -5.456835497
+   -2.136283004   -2.967309202  -13.214845369
+   -2.073451151   -1.886407100  -21.171200499
+   -2.010619298   -0.316284409  -28.677475468
+   -1.947787445    1.694275951  -35.085823711
+   -1.884955592    4.057277381  -39.805102330
+   -1.822123739    6.650758491  -42.353552663
+   -1.759291886    9.327116398  -42.403222481
+   -1.696460033   11.923851076  -39.811998967
+   -1.633628180   14.275849793  -34.640194909
+   -1.570796327   16.228180200  -27.149996573
+   -1.507964474   17.648302059  -17.787615275
+   -1.445132621   18.436646858   -7.149543685
+   -1.382300768   18.534648860    4.064242212
+   -1.319468915   17.929528507   15.106108250
+   -1.256637061   16.655410154   25.240764953
+   -1.193805208   14.790675170   33.804217774
+   -1.130973355   12.451779631   40.256530152
+   -1.068141502    9.784073053   44.223828351
+   -1.005309649    6.950413066   45.525955652
+   -0.942477796    4.118557135   44.187485578
+   -0.879645943    1.448409775   40.431307959
+   -0.816814090   -0.919796122   34.655567695
+   -0.753982237   -2.875401651   27.396218871
+   -0.691150384   -4.344509048   19.278719545
+   -0.628318531   -5.293907399   10.963319829
+   -0.565486678   -5.731488729    3.088904596
+   -0.502654825   -5.703221985   -3.779600964
+   -0.439822972   -5.287056426   -9.195669122
+   -0.376991118   -4.584390419  -12.863688798
+   -0.314159265   -3.709942861  -14.656970625
+   -0.251327412   -2.780984749  -14.620029905
+   -0.188495559   -1.906918090  -12.955414618
+   -0.125663706   -1.180127187   -9.996768596
+   -0.062831853   -0.668881003   -6.171056989
+    0.000000000   -0.412850137   -1.953818247
+    0.062831853   -0.421539575    2.178140178
+    0.125663706   -0.675654705    5.792062628
+    0.188495559   -1.131140428    8.538354992
+    0.251327412   -1.725387947   10.179965544
+    0.314159265   -2.384913757   10.609550868
+    0.376991118   -3.033697597    9.853189732
+    0.439822972   -3.601330342    8.060748792
+    0.502654825   -4.030170819    5.484305244
+    0.565486678   -4.280835606    2.447166697
+    0.628318531   -4.335534258   -0.693110509
+    0.691150384   -4.198993981   -3.583796504
+    0.753982237   -3.896968936   -5.914139727
+    0.816814090   -3.472574521   -7.446871847
+    0.879645943   -2.980902025   -8.041001900
+    0.942477796   -2.482532833   -7.663790383
+    1.005309649   -2.036668522   -6.390943538
+    1.068141502   -1.694615038   -4.395294320
+    1.130973355   -1.494304801   -1.925415089
+    1.193805208   -1.456416832    0.723380390
+    1.256637061   -1.582475512    3.242441860
+    1.319468915   -1.855092601    5.343983442
+    1.382300768   -2.240287277    6.792439000
+    1.445132621   -2.691599109    7.429676026
+    1.507964474   -3.155521657    7.191454953
+    1.570796327   -3.577648783    6.113468227
+    1.633628180   -3.908855525    4.326406440
+    1.696460033   -4.110837235    2.040661900
+    1.759291886   -4.160404057   -0.477626840
+    1.822123739   -4.052064683   -2.936575167
+    1.884955592   -3.798619184   -5.051347997
+    1.947787445   -3.429696029   -6.576207401
+    2.010619298   -2.988390547   -7.332346000
+    2.073451151   -2.526367898   -7.228480223
+    2.136283004   -2.097961365   -6.271936183
+    2.199114858   -1.753908884   -4.568960171
+    2.261946711   -1.535415076   -2.314123056
+    2.324778564   -1.469197662    0.230153754
+    2.387610417   -1.564078476    2.761863469
+    2.450442270   -1.809520038    4.972532009
+    2.513274123   -2.176304947    6.581698361
+    2.576105976   -2.619327928    7.369072046
+    2.638937829   -3.082242736    7.200869631
+    2.701769682   -3.503501849    6.047385643
+    2.764601535   -3.823167726    3.989720592
+    2.827433388   -3.989777340    1.214684827
+    2.890265241   -3.966517945   -2.001887206
+    2.953097094   -3.736025222   -5.321964767
+    3.015928947   -3.303241013   -8.379756402
+    3.078760801   -2.695955240  -10.820370974
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/coeffs.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/coeffs.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..478cffec045c1a8bfd01d84cb123d22f99f8168b
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/coeffs.data.reference
@@ -0,0 +1,231 @@
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 0.000000
+#! SET iteration  0
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.000000     0.000000       1
+       2     0.000000     0.000000       2
+       3     0.000000     0.000000       3
+       4     0.000000     0.000000       4
+       5     0.000000     0.000000       5
+       6     0.000000     0.000000       6
+       7     0.000000     0.000000       7
+       8     0.000000     0.000000       8
+       9     0.000000     0.000000       9
+      10     0.000000     0.000000      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 2.000000
+#! SET iteration  1
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.219197     0.219197       1
+       2    -0.970366    -0.970366       2
+       3    -0.884094    -0.884094       3
+       4    -0.421298    -0.421298       4
+       5    -0.590820    -0.590820       5
+       6     0.748809     0.748809       6
+       7     0.576392     0.576392       7
+       8     0.715341     0.715341       8
+       9     0.786645     0.786645       9
+      10    -0.381816    -0.381816      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 4.000000
+#! SET iteration  2
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.305152     0.391107       1
+       2    -1.461895    -1.953423       2
+       3    -1.350614    -1.817134       3
+       4    -0.589608    -0.757918       4
+       5    -0.834473    -1.078125       5
+       6     1.174985     1.601160       6
+       7     0.948813     1.321234       7
+       8     1.024273     1.333206       8
+       9     1.148264     1.509884       9
+      10    -0.689625    -0.997434      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 6.000000
+#! SET iteration  3
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.421218     0.653351       1
+       2    -1.946133    -2.914610       2
+       3    -1.788707    -2.664892       3
+       4    -0.812257    -1.257555       4
+       5    -1.146186    -1.769612       5
+       6     1.540202     2.270638       6
+       7     1.220946     1.765213       7
+       8     1.401662     2.156440       8
+       9     1.564119     2.395830       9
+      10    -0.857540    -1.193370      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 8.000000
+#! SET iteration  4
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.448007     0.528372       1
+       2    -2.433590    -3.895961       2
+       3    -2.239120    -3.590362       3
+       4    -0.861012    -1.007276       4
+       5    -1.209573    -1.399733       5
+       6     1.931358     3.104824       6
+       7     1.535645     2.479741       7
+       8     1.472935     1.686754       8
+       9     1.639154     1.864258       9
+      10    -1.086629    -1.773897      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 10.000000
+#! SET iteration  5
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.441146     0.413704       1
+       2    -2.895058    -4.740930       2
+       3    -2.593087    -4.008954       3
+       4    -0.858951    -0.850710       4
+       5    -1.239599    -1.359702       5
+       6     2.140456     2.976852       6
+       7     1.611231     1.913575       7
+       8     1.562246     1.919487       8
+       9     1.789475     2.390761       9
+      10    -1.071904    -1.013004      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 12.000000
+#! SET iteration  6
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.441948     0.445955       1
+       2    -3.365271    -5.716337       2
+       3    -2.979506    -4.911603       3
+       4    -0.867479    -0.910117       4
+       5    -1.269466    -1.418805       5
+       6     2.410784     3.762420       6
+       7     1.766861     2.545012       7
+       8     1.621663     1.918750       8
+       9     1.870932     2.278215       9
+      10    -1.136982    -1.462370      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 14.000000
+#! SET iteration  7
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.383175     0.030542       1
+       2    -3.758763    -6.119715       2
+       3    -3.154779    -4.206413       3
+       4    -0.874583    -0.917208       4
+       5    -1.387569    -2.096189       5
+       6     2.602191     3.750634       6
+       7     1.994254     3.358610       7
+       8     1.747113     2.499816       8
+       9     1.915919     2.185842       9
+      10    -1.282146    -2.153134      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 16.000000
+#! SET iteration  8
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.296543    -0.309884       1
+       2    -4.141493    -6.820603       2
+       3    -3.290550    -4.240951       3
+       4    -0.837652    -0.579136       4
+       5    -1.491646    -2.220179       5
+       6     2.688068     3.289207       6
+       7     2.149365     3.235145       7
+       8     1.917967     3.113944       8
+       9     2.038602     2.897379       9
+      10    -1.468354    -2.771810      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 18.000000
+#! SET iteration  9
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.234442    -0.262361       1
+       2    -4.548948    -7.808582       2
+       3    -3.501952    -5.193167       3
+       4    -0.818965    -0.669467       4
+       5    -1.579418    -2.281596       5
+       6     2.854156     4.182861       6
+       7     2.360190     4.046783       7
+       8     2.050168     3.107779       8
+       9     2.134519     2.901856       9
+      10    -1.691816    -3.479514      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.coeffs ves1.aux_coeffs index
+#! SET time 20.000000
+#! SET iteration  10
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000     0.000000       0
+       1     0.205729    -0.052695       1
+       2    -4.971305    -8.772526       2
+       3    -3.756567    -6.048102       3
+       4    -0.842988    -1.059199       4
+       5    -1.697444    -2.759682       5
+       6     3.054607     4.858669       6
+       7     2.568698     4.445279       7
+       8     2.208072     3.629202       8
+       9     2.266734     3.456672       9
+      10    -1.877002    -3.543669      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/colvar.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/colvar.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..d1d516bcc2d66523125a380459cf3cee3988f789
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/colvar.data.reference
@@ -0,0 +1,24 @@
+#! FIELDS time phi ves1.bias o1.gradrms o1.gradmax
+#! SET min_phi -pi
+#! SET max_phi pi
+ 0.000000 -1.238  0.000  0.000  0.000
+ 1.000000 -1.484  0.000  0.000  0.000
+ 2.000000 -1.324  0.000  0.637  0.970
+ 3.000000 -1.334  4.716  0.637  0.970
+ 4.000000 -1.461  4.403  0.659  0.983
+ 5.000000 -1.220  6.371  0.659  0.983
+ 6.000000 -1.388  7.123  0.649  0.961
+ 7.000000 -1.548  7.766  0.649  0.961
+ 8.000000 -1.843  1.066  0.599  0.981
+ 9.000000 -2.242 -3.365  0.599  0.981
+ 10.000000 -1.148  8.387  0.439  0.847
+ 11.000000 -1.758  5.325  0.439  0.847
+ 12.000000 -1.319 12.218  0.523  0.975
+ 13.000000 -2.991 -1.159  0.523  0.975
+ 14.000000 -1.411 13.737  0.475  0.814
+ 15.000000 -2.599 -0.714  0.475  0.814
+ 16.000000 -1.461 14.602  0.451  0.755
+ 17.000000 -1.379 15.945  0.451  0.755
+ 18.000000 -1.677 10.610  0.598  0.988
+ 19.000000 -1.524 16.005  0.598  0.988
+ 20.000000 -1.200 13.955  0.585  0.965
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/combined_gradient.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/combined_gradient.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..fd2741b6458ded2a3525e6ef0197241c4d2b8000
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/combined_gradient.data.reference
@@ -0,0 +1,210 @@
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 2.000000
+#! SET iteration  1
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.219197       1
+       2     0.970366       2
+       3     0.884094       3
+       4     0.421298       4
+       5     0.590820       5
+       6    -0.748809       6
+       7    -0.576392       7
+       8    -0.715341       8
+       9    -0.786645       9
+      10     0.381816      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 4.000000
+#! SET iteration  2
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.171909       1
+       2     0.983056       2
+       3     0.933040       3
+       4     0.336620       4
+       5     0.487305       5
+       6    -0.852350       6
+       7    -0.744842       7
+       8    -0.617866       8
+       9    -0.723239       9
+      10     0.615618      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 6.000000
+#! SET iteration  3
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.262244       1
+       2     0.961187       2
+       3     0.847758       3
+       4     0.499637       4
+       5     0.691487       5
+       6    -0.669478       6
+       7    -0.443979       7
+       8    -0.823233       8
+       9    -0.885946       9
+      10     0.195936      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 8.000000
+#! SET iteration  4
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.124979       1
+       2     0.981351       2
+       3     0.925470       3
+       4    -0.250280       4
+       5    -0.369879       5
+       6    -0.834186       6
+       7    -0.714529       7
+       8     0.469686       8
+       9     0.531572       9
+      10     0.580527      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 10.000000
+#! SET iteration  5
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.114667       1
+       2     0.844969       2
+       3     0.418592       3
+       4    -0.156566       4
+       5    -0.040031       5
+       6     0.127972       6
+       7     0.566166       7
+       8    -0.232733       8
+       9    -0.526503       9
+      10    -0.760892      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 12.000000
+#! SET iteration  6
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.032251       1
+       2     0.975407       2
+       3     0.902649       3
+       4     0.059408       4
+       5     0.059102       5
+       6    -0.785568       6
+       7    -0.631437       7
+       8     0.000738       8
+       9     0.112546       9
+      10     0.449365      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 14.000000
+#! SET iteration  7
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.415413       1
+       2     0.403378       2
+       3    -0.705190       3
+       4     0.007091       4
+       5     0.677384       5
+       6     0.011786       6
+       7    -0.813598       7
+       8    -0.581066       8
+       9     0.092373       9
+      10     0.690764      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 16.000000
+#! SET iteration  8
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1     0.340425       1
+       2     0.700888       2
+       3     0.034538       3
+       4    -0.338072       4
+       5     0.123991       5
+       6     0.461427       6
+       7     0.123465       7
+       8    -0.614128       8
+       9    -0.711537       9
+      10     0.618677      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 18.000000
+#! SET iteration  9
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.047522       1
+       2     0.987979       2
+       3     0.952216       3
+       4     0.090331       4
+       5     0.061417       5
+       6    -0.893654       6
+       7    -0.811638       7
+       8     0.006164       8
+       9    -0.004477       9
+      10     0.707703      10
+#!-------------------
+
+
+#! FIELDS idx_phi ves1.combined_gradient index
+#! SET time 20.000000
+#! SET iteration  10
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     0.000000       0
+       1    -0.209666       1
+       2     0.963944       2
+       3     0.854935       3
+       4     0.389732       4
+       5     0.478086       5
+       6    -0.675807       6
+       7    -0.398496       7
+       8    -0.521422       8
+       9    -0.554816       9
+      10     0.064155      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/config b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/config
new file mode 100644
index 0000000000000000000000000000000000000000..d9b022c5f95c12fdf3de7e32807e196863eec343
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/config
@@ -0,0 +1,3 @@
+plumed_modules=ves
+type=driver
+arg="--plumed plumed.dat --trajectory-stride 500 --timestep 0.002 --igro traj.gro --dump-forces forces --dump-forces-fmt=%10.6f "
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/fes.ves1.iter-10.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/fes.ves1.iter-10.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..d50483ac34516d62eac2c7fd2592ae5ef72ba0af
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/fes.ves1.iter-10.data.reference
@@ -0,0 +1,105 @@
+#! FIELDS phi ves1.fes
+#! SET min_phi -pi
+#! SET max_phi pi
+#! SET nbins_phi  100
+#! SET periodic_phi true
+   -3.141592654   20.497536200
+   -3.078760801   19.704062923
+   -3.015928947   18.925946415
+   -2.953097094   18.241634172
+   -2.890265241   17.723868121
+   -2.827433388   17.431435858
+   -2.764601535   17.401912078
+   -2.701769682   17.646168907
+   -2.638937829   18.145285307
+   -2.576105976   18.850270868
+   -2.513274123   19.684757617
+   -2.450442270   20.550529614
+   -2.387610417   21.335481149
+   -2.324778564   21.923347445
+   -2.261946711   22.204361318
+   -2.199114858   22.085874739
+   -2.136283004   21.501958062
+   -2.073451151   20.421055959
+   -2.010619298   18.850933268
+   -1.947787445   16.840372909
+   -1.884955592   14.477371479
+   -1.822123739   11.883890368
+   -1.759291886    9.207532462
+   -1.696460033    6.610797784
+   -1.633628180    4.258799067
+   -1.570796327    2.306468659
+   -1.507964474    0.886346801
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+   -1.382300768    0.000000000
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+   -1.256637061    1.879238705
+   -1.193805208    3.743973689
+   -1.130973355    6.082869229
+   -1.068141502    8.750575807
+   -1.005309649   11.584235793
+   -0.942477796   14.416091724
+   -0.879645943   17.086239085
+   -0.816814090   19.454444982
+   -0.753982237   21.410050510
+   -0.691150384   22.879157907
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+   -0.565486678   24.266137588
+   -0.502654825   24.237870844
+   -0.439822972   23.821705285
+   -0.376991118   23.119039279
+   -0.314159265   22.244591720
+   -0.251327412   21.315633608
+   -0.188495559   20.441566950
+   -0.125663706   19.714776047
+   -0.062831853   19.203529863
+    0.000000000   18.947498997
+    0.062831853   18.956188434
+    0.125663706   19.210303564
+    0.188495559   19.665789288
+    0.251327412   20.260036806
+    0.314159265   20.919562617
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+    0.439822972   22.135979202
+    0.502654825   22.564819678
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+    0.753982237   22.431617795
+    0.816814090   22.007223380
+    0.879645943   21.515550884
+    0.942477796   21.017181692
+    1.005309649   20.571317381
+    1.068141502   20.229263897
+    1.130973355   20.028953661
+    1.193805208   19.991065692
+    1.256637061   20.117124372
+    1.319468915   20.389741461
+    1.382300768   20.774936136
+    1.445132621   21.226247968
+    1.507964474   21.690170517
+    1.570796327   22.112297643
+    1.633628180   22.443504384
+    1.696460033   22.645486094
+    1.759291886   22.695052917
+    1.822123739   22.586713543
+    1.884955592   22.333268044
+    1.947787445   21.964344888
+    2.010619298   21.523039407
+    2.073451151   21.061016758
+    2.136283004   20.632610225
+    2.199114858   20.288557744
+    2.261946711   20.070063935
+    2.324778564   20.003846521
+    2.387610417   20.098727335
+    2.450442270   20.344168898
+    2.513274123   20.710953806
+    2.576105976   21.153976788
+    2.638937829   21.616891596
+    2.701769682   22.038150709
+    2.764601535   22.357816586
+    2.827433388   22.524426200
+    2.890265241   22.501166805
+    2.953097094   22.270674081
+    3.015928947   21.837889873
+    3.078760801   21.230604100
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/forces.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/forces.reference
new file mode 100644
index 0000000000000000000000000000000000000000..75ae219e0f6736a9037c0c36631fa4ee84749782
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/forces.reference
@@ -0,0 +1,504 @@
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diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/plumed.dat b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/plumed.dat
new file mode 100644
index 0000000000000000000000000000000000000000..dc1819aeededff7bccd844a2538ba4d9dd273ef6
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/plumed.dat
@@ -0,0 +1,43 @@
+# vim:ft=plumed
+
+phi:   TORSION ATOMS=5,7,9,15     NOPBC
+
+bf1: BF_FOURIER ORDER=5 MINIMUM=-pi MAXIMUM=pi
+
+VES_LINEAR_EXPANSION ...
+ ARG=phi
+ BASIS_FUNCTIONS=bf1
+ LABEL=ves1
+ TEMP=300.0
+ GRID_BINS=100
+... VES_LINEAR_EXPANSION
+
+# NOTE: These parameters do not reflect parameters used in real simulations! 
+#       This is only for testing!
+#
+
+OPT_AVERAGED_SGD ...
+  BIAS=ves1
+  STRIDE=1000
+  LABEL=o1
+  STEPSIZE=1.0
+  COEFFS_FILE=coeffs.data
+  COEFFS_OUTPUT=1
+  COEFFS_FMT=%12.6f
+  FES_OUTPUT=10
+  BIAS_OUTPUT=10
+  TARGETDIST_AVERAGES_FMT=%12.6f
+  COMBINED_GRADIENT_FILE=combined_gradient.data
+  COMBINED_GRADIENT_OUTPUT=1
+  COMBINED_GRADIENT_FMT=%12.6f
+  MONITOR_INSTANTANEOUS_GRADIENT
+... OPT_AVERAGED_SGD
+
+PRINT ...
+  STRIDE=500
+  ARG=phi,ves1.bias,o1.*
+  FILE=colvar.data FMT=%6.3f
+... PRINT
+
+ENDPLUMED
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/targetdist-averages.data.reference b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/targetdist-averages.data.reference
new file mode 100644
index 0000000000000000000000000000000000000000..b6bf5b55ccca602f2814808f51085a0599e101ab
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/targetdist-averages.data.reference
@@ -0,0 +1,21 @@
+#! FIELDS idx_phi ves1.targetdist_averages index
+#! SET time 0.000000
+#! SET iteration  0
+#! SET type LinearBasisSet
+#! SET ndimensions  1
+#! SET ncoeffs_total  11
+#! SET shape_phi  11
+       0     1.000000       0
+       1     0.000000       1
+       2     0.000000       2
+       3     0.000000       3
+       4     0.000000       4
+       5     0.000000       5
+       6     0.000000       6
+       7     0.000000       7
+       8     0.000000       8
+       9     0.000000       9
+      10     0.000000      10
+#!-------------------
+
+
diff --git a/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/traj.gro b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/traj.gro
new file mode 100644
index 0000000000000000000000000000000000000000..c1c387a0144ec8021b9e5b0453be534f2ca906e2
--- /dev/null
+++ b/regtest/ves/rt-opt-averaged-sgd-monitor-inst-grad/traj.gro
@@ -0,0 +1,525 @@
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+    2ALA      N    7   1.358   1.323   1.194
+    2ALA      H    8   1.443   1.313   1.140
+    2ALA     CA    9   1.235   1.243   1.164
+    2ALA     HA   10   1.150   1.310   1.170
+    2ALA     CB   11   1.240   1.197   1.019
+    2ALA    HB1   12   1.316   1.119   1.016
+    2ALA    HB2   13   1.145   1.157   0.982
+    2ALA    HB3   14   1.279   1.276   0.955
+    2ALA      C   15   1.201   1.137   1.272
+    2ALA      O   16   1.172   1.021   1.232
+    3NME      N   17   1.218   1.166   1.402
+    3NME      H   18   1.240   1.259   1.434
+    3NME    CH3   19   1.186   1.086   1.518
+    3NME   HH31   20   1.225   0.984   1.527
+    3NME   HH32   21   1.193   1.134   1.616
+    3NME   HH33   22   1.081   1.058   1.509
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   4.00000
+   22
+    1ACE   HH31    1   1.549   1.508   1.196
+    1ACE    CH3    2   1.500   1.486   1.290
+    1ACE   HH32    3   1.487   1.571   1.357
+    1ACE   HH33    4   1.563   1.415   1.343
+    1ACE      C    5   1.362   1.425   1.270
+    1ACE      O    6   1.265   1.465   1.340
+    2ALA      N    7   1.349   1.324   1.182
+    2ALA      H    8   1.432   1.287   1.138
+    2ALA     CA    9   1.221   1.249   1.168
+    2ALA     HA   10   1.138   1.318   1.184
+    2ALA     CB   11   1.201   1.194   1.025
+    2ALA    HB1   12   1.276   1.117   1.005
+    2ALA    HB2   13   1.096   1.165   1.014
+    2ALA    HB3   14   1.229   1.265   0.947
+    2ALA      C   15   1.217   1.141   1.275
+    2ALA      O   16   1.234   1.024   1.243
+    3NME      N   17   1.183   1.174   1.400
+    3NME      H   18   1.184   1.274   1.412
+    3NME    CH3   19   1.187   1.078   1.509
+    3NME   HH31   20   1.248   0.990   1.490
+    3NME   HH32   21   1.220   1.120   1.604
+    3NME   HH33   22   1.088   1.035   1.527
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   5.00000
+   22
+    1ACE   HH31    1   1.449   1.585   1.168
+    1ACE    CH3    2   1.479   1.518   1.248
+    1ACE   HH32    3   1.523   1.577   1.328
+    1ACE   HH33    4   1.565   1.461   1.213
+    1ACE      C    5   1.364   1.422   1.284
+    1ACE      O    6   1.305   1.438   1.389
+    2ALA      N    7   1.347   1.326   1.187
+    2ALA      H    8   1.423   1.328   1.122
+    2ALA     CA    9   1.226   1.241   1.162
+    2ALA     HA   10   1.139   1.308   1.162
+    2ALA     CB   11   1.236   1.193   1.023
+    2ALA    HB1   12   1.314   1.117   1.012
+    2ALA    HB2   13   1.137   1.167   0.986
+    2ALA    HB3   14   1.273   1.278   0.966
+    2ALA      C   15   1.195   1.133   1.268
+    2ALA      O   16   1.173   1.016   1.239
+    3NME      N   17   1.204   1.175   1.393
+    3NME      H   18   1.211   1.275   1.403
+    3NME    CH3   19   1.188   1.090   1.513
+    3NME   HH31   20   1.089   1.044   1.509
+    3NME   HH32   21   1.267   1.014   1.509
+    3NME   HH33   22   1.189   1.145   1.607
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   6.00000
+   22
+    1ACE   HH31    1   1.517   1.511   1.181
+    1ACE    CH3    2   1.490   1.488   1.284
+    1ACE   HH32    3   1.482   1.582   1.339
+    1ACE   HH33    4   1.569   1.421   1.316
+    1ACE      C    5   1.359   1.414   1.282
+    1ACE      O    6   1.272   1.447   1.358
+    2ALA      N    7   1.351   1.320   1.186
+    2ALA      H    8   1.434   1.297   1.133
+    2ALA     CA    9   1.220   1.251   1.159
+    2ALA     HA   10   1.139   1.323   1.167
+    2ALA     CB   11   1.220   1.194   1.018
+    2ALA    HB1   12   1.298   1.120   1.003
+    2ALA    HB2   13   1.120   1.158   0.994
+    2ALA    HB3   14   1.224   1.286   0.960
+    2ALA      C   15   1.201   1.139   1.270
+    2ALA      O   16   1.190   1.022   1.239
+    3NME      N   17   1.203   1.178   1.393
+    3NME      H   18   1.207   1.277   1.409
+    3NME    CH3   19   1.211   1.102   1.515
+    3NME   HH31   20   1.111   1.064   1.534
+    3NME   HH32   21   1.275   1.017   1.492
+    3NME   HH33   22   1.264   1.151   1.597
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   7.00000
+   22
+    1ACE   HH31    1   1.483   1.590   1.185
+    1ACE    CH3    2   1.505   1.501   1.245
+    1ACE   HH32    3   1.538   1.533   1.344
+    1ACE   HH33    4   1.580   1.430   1.209
+    1ACE      C    5   1.379   1.418   1.267
+    1ACE      O    6   1.298   1.443   1.349
+    2ALA      N    7   1.360   1.320   1.187
+    2ALA      H    8   1.426   1.297   1.114
+    2ALA     CA    9   1.224   1.253   1.180
+    2ALA     HA   10   1.147   1.326   1.205
+    2ALA     CB   11   1.174   1.215   1.037
+    2ALA    HB1   12   1.245   1.152   0.983
+    2ALA    HB2   13   1.084   1.154   1.032
+    2ALA    HB3   14   1.153   1.311   0.992
+    2ALA      C   15   1.212   1.141   1.280
+    2ALA      O   16   1.219   1.022   1.244
+    3NME      N   17   1.191   1.176   1.408
+    3NME      H   18   1.207   1.275   1.423
+    3NME    CH3   19   1.162   1.068   1.509
+    3NME   HH31   20   1.229   0.982   1.503
+    3NME   HH32   21   1.162   1.109   1.610
+    3NME   HH33   22   1.056   1.044   1.499
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   8.00000
+   22
+    1ACE   HH31    1   1.576   1.425   1.169
+    1ACE    CH3    2   1.523   1.455   1.260
+    1ACE   HH32    3   1.547   1.556   1.294
+    1ACE   HH33    4   1.566   1.393   1.338
+    1ACE      C    5   1.385   1.422   1.255
+    1ACE      O    6   1.308   1.499   1.305
+    2ALA      N    7   1.346   1.311   1.189
+    2ALA      H    8   1.419   1.248   1.159
+    2ALA     CA    9   1.210   1.260   1.193
+    2ALA     HA   10   1.139   1.326   1.242
+    2ALA     CB   11   1.152   1.252   1.051
+    2ALA    HB1   12   1.230   1.210   0.987
+    2ALA    HB2   13   1.066   1.185   1.052
+    2ALA    HB3   14   1.127   1.354   1.024
+    2ALA      C   15   1.206   1.136   1.282
+    2ALA      O   16   1.195   1.023   1.229
+    3NME      N   17   1.210   1.152   1.420
+    3NME      H   18   1.221   1.243   1.463
+    3NME    CH3   19   1.185   1.048   1.518
+    3NME   HH31   20   1.195   0.948   1.475
+    3NME   HH32   21   1.261   1.070   1.593
+    3NME   HH33   22   1.088   1.064   1.565
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=   9.00000
+   22
+    1ACE   HH31    1   1.515   1.474   1.040
+    1ACE    CH3    2   1.535   1.461   1.147
+    1ACE   HH32    3   1.561   1.560   1.184
+    1ACE   HH33    4   1.612   1.386   1.165
+    1ACE      C    5   1.406   1.430   1.217
+    1ACE      O    6   1.361   1.502   1.307
+    2ALA      N    7   1.345   1.316   1.190
+    2ALA      H    8   1.384   1.254   1.121
+    2ALA     CA    9   1.217   1.277   1.242
+    2ALA     HA   10   1.187   1.348   1.319
+    2ALA     CB   11   1.111   1.278   1.134
+    2ALA    HB1   12   1.129   1.198   1.062
+    2ALA    HB2   13   1.018   1.269   1.189
+    2ALA    HB3   14   1.121   1.372   1.079
+    2ALA      C   15   1.217   1.133   1.309
+    2ALA      O   16   1.293   1.044   1.265
+    3NME      N   17   1.132   1.116   1.408
+    3NME      H   18   1.076   1.195   1.437
+    3NME    CH3   19   1.112   1.003   1.490
+    3NME   HH31   20   1.156   0.910   1.456
+    3NME   HH32   21   1.153   1.026   1.588
+    3NME   HH33   22   1.005   0.985   1.500
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  10.00000
+   22
+    1ACE   HH31    1   1.536   1.485   1.135
+    1ACE    CH3    2   1.521   1.460   1.240
+    1ACE   HH32    3   1.528   1.557   1.289
+    1ACE   HH33    4   1.602   1.397   1.276
+    1ACE      C    5   1.385   1.401   1.261
+    1ACE      O    6   1.341   1.416   1.373
+    2ALA      N    7   1.322   1.332   1.167
+    2ALA      H    8   1.364   1.316   1.076
+    2ALA     CA    9   1.190   1.273   1.177
+    2ALA     HA   10   1.125   1.352   1.216
+    2ALA     CB   11   1.134   1.230   1.038
+    2ALA    HB1   12   1.167   1.128   1.016
+    2ALA    HB2   13   1.026   1.238   1.046
+    2ALA    HB3   14   1.174   1.287   0.953
+    2ALA      C   15   1.183   1.157   1.283
+    2ALA      O   16   1.111   1.061   1.259
+    3NME      N   17   1.264   1.157   1.396
+    3NME      H   18   1.320   1.241   1.405
+    3NME    CH3   19   1.264   1.070   1.510
+    3NME   HH31   20   1.163   1.057   1.548
+    3NME   HH32   21   1.311   0.974   1.487
+    3NME   HH33   22   1.326   1.109   1.592
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  11.00000
+   22
+    1ACE   HH31    1   1.607   1.359   1.178
+    1ACE    CH3    2   1.535   1.442   1.176
+    1ACE   HH32    3   1.521   1.470   1.072
+    1ACE   HH33    4   1.569   1.533   1.224
+    1ACE      C    5   1.402   1.412   1.242
+    1ACE      O    6   1.368   1.454   1.350
+    2ALA      N    7   1.319   1.332   1.177
+    2ALA      H    8   1.363   1.279   1.103
+    2ALA     CA    9   1.194   1.289   1.231
+    2ALA     HA   10   1.153   1.355   1.308
+    2ALA     CB   11   1.092   1.300   1.113
+    2ALA    HB1   12   1.137   1.243   1.032
+    2ALA    HB2   13   1.001   1.243   1.131
+    2ALA    HB3   14   1.070   1.405   1.095
+    2ALA      C   15   1.198   1.143   1.290
+    2ALA      O   16   1.237   1.057   1.213
+    3NME      N   17   1.171   1.126   1.422
+    3NME      H   18   1.164   1.213   1.472
+    3NME    CH3   19   1.200   1.009   1.496
+    3NME   HH31   20   1.118   0.938   1.493
+    3NME   HH32   21   1.284   0.953   1.454
+    3NME   HH33   22   1.230   1.031   1.598
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  12.00000
+   22
+    1ACE   HH31    1   1.491   1.569   1.138
+    1ACE    CH3    2   1.511   1.462   1.134
+    1ACE   HH32    3   1.614   1.449   1.166
+    1ACE   HH33    4   1.495   1.444   1.028
+    1ACE      C    5   1.416   1.394   1.229
+    1ACE      O    6   1.445   1.392   1.345
+    2ALA      N    7   1.299   1.357   1.181
+    2ALA      H    8   1.278   1.358   1.082
+    2ALA     CA    9   1.196   1.301   1.267
+    2ALA     HA   10   1.185   1.364   1.355
+    2ALA     CB   11   1.063   1.319   1.182
+    2ALA    HB1   12   1.057   1.248   1.100
+    2ALA    HB2   13   0.976   1.288   1.240
+    2ALA    HB3   14   1.037   1.423   1.161
+    2ALA      C   15   1.226   1.161   1.304
+    2ALA      O   16   1.317   1.094   1.258
+    3NME      N   17   1.135   1.110   1.387
+    3NME      H   18   1.064   1.174   1.419
+    3NME    CH3   19   1.121   0.972   1.429
+    3NME   HH31   20   1.163   0.900   1.358
+    3NME   HH32   21   1.177   0.954   1.520
+    3NME   HH33   22   1.016   0.942   1.428
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  13.00000
+   22
+    1ACE   HH31    1   1.528   1.537   1.077
+    1ACE    CH3    2   1.543   1.448   1.137
+    1ACE   HH32    3   1.634   1.463   1.195
+    1ACE   HH33    4   1.560   1.362   1.072
+    1ACE      C    5   1.421   1.428   1.229
+    1ACE      O    6   1.396   1.520   1.301
+    2ALA      N    7   1.355   1.314   1.219
+    2ALA      H    8   1.385   1.241   1.156
+    2ALA     CA    9   1.249   1.276   1.311
+    2ALA     HA   10   1.297   1.288   1.409
+    2ALA     CB   11   1.122   1.359   1.284
+    2ALA    HB1   12   1.072   1.325   1.193
+    2ALA    HB2   13   1.053   1.352   1.367
+    2ALA    HB3   14   1.153   1.463   1.275
+    2ALA      C   15   1.204   1.131   1.290
+    2ALA      O   16   1.225   1.070   1.185
+    3NME      N   17   1.131   1.077   1.382
+    3NME      H   18   1.104   1.132   1.463
+    3NME    CH3   19   1.083   0.939   1.380
+    3NME   HH31   20   1.012   0.925   1.298
+    3NME   HH32   21   1.168   0.871   1.372
+    3NME   HH33   22   1.036   0.915   1.475
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  14.00000
+   22
+    1ACE   HH31    1   1.543   1.468   1.123
+    1ACE    CH3    2   1.548   1.443   1.229
+    1ACE   HH32    3   1.566   1.540   1.276
+    1ACE   HH33    4   1.634   1.382   1.257
+    1ACE      C    5   1.420   1.385   1.285
+    1ACE      O    6   1.412   1.375   1.404
+    2ALA      N    7   1.324   1.361   1.200
+    2ALA      H    8   1.345   1.354   1.101
+    2ALA     CA    9   1.189   1.323   1.244
+    2ALA     HA   10   1.163   1.394   1.323
+    2ALA     CB   11   1.094   1.344   1.125
+    2ALA    HB1   12   1.098   1.270   1.045
+    2ALA    HB2   13   0.995   1.352   1.170
+    2ALA    HB3   14   1.120   1.440   1.079
+    2ALA      C   15   1.166   1.169   1.284
+    2ALA      O   16   1.055   1.145   1.330
+    3NME      N   17   1.263   1.077   1.279
+    3NME      H   18   1.356   1.102   1.247
+    3NME    CH3   19   1.246   0.942   1.335
+    3NME   HH31   20   1.142   0.911   1.345
+    3NME   HH32   21   1.293   0.868   1.270
+    3NME   HH33   22   1.292   0.934   1.434
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  15.00000
+   22
+    1ACE   HH31    1   1.508   1.417   1.043
+    1ACE    CH3    2   1.539   1.448   1.143
+    1ACE   HH32    3   1.565   1.553   1.146
+    1ACE   HH33    4   1.630   1.395   1.169
+    1ACE      C    5   1.438   1.410   1.253
+    1ACE      O    6   1.429   1.471   1.356
+    2ALA      N    7   1.348   1.327   1.217
+    2ALA      H    8   1.362   1.285   1.126
+    2ALA     CA    9   1.233   1.289   1.298
+    2ALA     HA   10   1.269   1.295   1.401
+    2ALA     CB   11   1.107   1.379   1.286
+    2ALA    HB1   12   1.057   1.360   1.191
+    2ALA    HB2   13   1.034   1.369   1.366
+    2ALA    HB3   14   1.141   1.482   1.282
+    2ALA      C   15   1.192   1.141   1.266
+    2ALA      O   16   1.220   1.089   1.156
+    3NME      N   17   1.131   1.075   1.364
+    3NME      H   18   1.117   1.126   1.450
+    3NME    CH3   19   1.090   0.931   1.376
+    3NME   HH31   20   1.156   0.880   1.446
+    3NME   HH32   21   0.996   0.929   1.431
+    3NME   HH33   22   1.090   0.874   1.283
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  16.00000
+   22
+    1ACE   HH31    1   1.587   1.386   1.166
+    1ACE    CH3    2   1.554   1.425   1.262
+    1ACE   HH32    3   1.559   1.534   1.266
+    1ACE   HH33    4   1.627   1.390   1.335
+    1ACE      C    5   1.417   1.372   1.300
+    1ACE      O    6   1.390   1.364   1.421
+    2ALA      N    7   1.334   1.344   1.205
+    2ALA      H    8   1.365   1.367   1.111
+    2ALA     CA    9   1.190   1.324   1.235
+    2ALA     HA   10   1.160   1.386   1.319
+    2ALA     CB   11   1.105   1.363   1.112
+    2ALA    HB1   12   1.129   1.297   1.029
+    2ALA    HB2   13   0.999   1.351   1.131
+    2ALA    HB3   14   1.125   1.467   1.088
+    2ALA      C   15   1.162   1.180   1.282
+    2ALA      O   16   1.054   1.128   1.258
+    3NME      N   17   1.261   1.106   1.318
+    3NME      H   18   1.349   1.152   1.336
+    3NME    CH3   19   1.250   0.960   1.324
+    3NME   HH31   20   1.264   0.908   1.229
+    3NME   HH32   21   1.322   0.926   1.399
+    3NME   HH33   22   1.153   0.923   1.357
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  17.00000
+   22
+    1ACE   HH31    1   1.614   1.382   1.173
+    1ACE    CH3    2   1.559   1.432   1.253
+    1ACE   HH32    3   1.547   1.532   1.213
+    1ACE   HH33    4   1.625   1.444   1.339
+    1ACE      C    5   1.426   1.380   1.288
+    1ACE      O    6   1.411   1.348   1.406
+    2ALA      N    7   1.325   1.370   1.200
+    2ALA      H    8   1.341   1.388   1.102
+    2ALA     CA    9   1.189   1.318   1.239
+    2ALA     HA   10   1.170   1.358   1.338
+    2ALA     CB   11   1.084   1.388   1.158
+    2ALA    HB1   12   1.113   1.369   1.055
+    2ALA    HB2   13   0.994   1.336   1.189
+    2ALA    HB3   14   1.075   1.493   1.186
+    2ALA      C   15   1.170   1.163   1.252
+    2ALA      O   16   1.097   1.103   1.171
+    3NME      N   17   1.235   1.099   1.349
+    3NME      H   18   1.305   1.153   1.399
+    3NME    CH3   19   1.220   0.964   1.393
+    3NME   HH31   20   1.315   0.912   1.406
+    3NME   HH32   21   1.168   0.953   1.489
+    3NME   HH33   22   1.178   0.897   1.318
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  18.00000
+   22
+    1ACE   HH31    1   1.555   1.419   1.126
+    1ACE    CH3    2   1.554   1.431   1.235
+    1ACE   HH32    3   1.554   1.535   1.267
+    1ACE   HH33    4   1.638   1.381   1.283
+    1ACE      C    5   1.423   1.378   1.292
+    1ACE      O    6   1.416   1.347   1.409
+    2ALA      N    7   1.322   1.351   1.211
+    2ALA      H    8   1.350   1.370   1.115
+    2ALA     CA    9   1.185   1.318   1.251
+    2ALA     HA   10   1.171   1.358   1.352
+    2ALA     CB   11   1.091   1.400   1.149
+    2ALA    HB1   12   1.059   1.346   1.060
+    2ALA    HB2   13   1.008   1.443   1.205
+    2ALA    HB3   14   1.154   1.480   1.109
+    2ALA      C   15   1.163   1.166   1.255
+    2ALA      O   16   1.060   1.108   1.214
+    3NME      N   17   1.255   1.102   1.328
+    3NME      H   18   1.335   1.159   1.354
+    3NME    CH3   19   1.246   0.964   1.369
+    3NME   HH31   20   1.154   0.913   1.344
+    3NME   HH32   21   1.323   0.899   1.327
+    3NME   HH33   22   1.251   0.953   1.477
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  19.00000
+   22
+    1ACE   HH31    1   1.559   1.326   1.133
+    1ACE    CH3    2   1.552   1.413   1.200
+    1ACE   HH32    3   1.538   1.504   1.142
+    1ACE   HH33    4   1.631   1.428   1.273
+    1ACE      C    5   1.426   1.375   1.280
+    1ACE      O    6   1.428   1.345   1.398
+    2ALA      N    7   1.319   1.363   1.209
+    2ALA      H    8   1.322   1.382   1.110
+    2ALA     CA    9   1.191   1.329   1.265
+    2ALA     HA   10   1.186   1.364   1.368
+    2ALA     CB   11   1.075   1.391   1.178
+    2ALA    HB1   12   1.098   1.383   1.072
+    2ALA    HB2   13   0.980   1.348   1.211
+    2ALA    HB3   14   1.066   1.499   1.192
+    2ALA      C   15   1.169   1.174   1.275
+    2ALA      O   16   1.086   1.118   1.203
+    3NME      N   17   1.233   1.105   1.363
+    3NME      H   18   1.312   1.150   1.405
+    3NME    CH3   19   1.242   0.956   1.350
+    3NME   HH31   20   1.219   0.899   1.440
+    3NME   HH32   21   1.165   0.918   1.284
+    3NME   HH33   22   1.333   0.921   1.301
+  10.00000  10.00000  10.00000
+Generated by trjconv : Gromacs Runs One Microsecond At Cannonball Speeds t=  20.00000
+   22
+    1ACE   HH31    1   1.622   1.459   1.287
+    1ACE    CH3    2   1.546   1.434   1.214
+    1ACE   HH32    3   1.578   1.365   1.135
+    1ACE   HH33    4   1.509   1.531   1.180
+    1ACE      C    5   1.430   1.358   1.283
+    1ACE      O    6   1.444   1.310   1.394
+    2ALA      N    7   1.315   1.370   1.215
+    2ALA      H    8   1.323   1.427   1.132
+    2ALA     CA    9   1.178   1.334   1.258
+    2ALA     HA   10   1.163   1.376   1.357
+    2ALA     CB   11   1.079   1.393   1.158
+    2ALA    HB1   12   1.096   1.348   1.060
+    2ALA    HB2   13   0.979   1.367   1.192
+    2ALA    HB3   14   1.087   1.501   1.165
+    2ALA      C   15   1.163   1.177   1.270
+    2ALA      O   16   1.073   1.114   1.216
+    3NME      N   17   1.249   1.110   1.347
+    3NME      H   18   1.324   1.165   1.388
+    3NME    CH3   19   1.242   0.964   1.360
+    3NME   HH31   20   1.325   0.920   1.416
+    3NME   HH32   21   1.151   0.938   1.414
+    3NME   HH33   22   1.221   0.913   1.266
+  10.00000  10.00000  10.00000