   OPT_AVERAGED_SGD
 This is part of the ves module It is only available if you configure PLUMED with ./configure –enable-modules=ves . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Averaged stochastic gradient decent with fixed step size.

Algorithm

This optimizer updates the coefficients according to the averaged stochastic gradient decent algorithm described in ref . This algorithm considers two sets of coefficients, the so-called instantaneous coefficients that are updated according to the recursion formula given by

$\boldsymbol{\alpha}^{(n+1)} = \boldsymbol{\alpha}^{(n)} - \mu \left[ \nabla \Omega(\bar{\boldsymbol{\alpha}}^{(n)}) + \mathbf{H}(\bar{\boldsymbol{\alpha}}^{(n)}) [\boldsymbol{\alpha}^{(n)}-\bar{\boldsymbol{\alpha}}^{(n)}] \right],$

where $$\mu$$ is a fixed step size and the gradient $$\nabla\Omega(\bar{\boldsymbol{\alpha}}^{(n)})$$ and the Hessian $$\mathbf{H}(\bar{\boldsymbol{\alpha}}^{(n)})$$ depend on the averaged coefficients defined as

$\bar{\boldsymbol{\alpha}}^{(n)} = \frac{1}{n+1} \sum_{k=0}^{n} \boldsymbol{\alpha}^{(k)}.$

This means that the bias acting on the system depends on the averaged coefficients $$\bar{\boldsymbol{\alpha}}^{(n)}$$ which leads to a smooth convergence of the bias and the estimated free energy surface. Furthermore, this allows for a rather short sampling time for each iteration, for classical MD simulations typical sampling times are on the order of few ps (around 1000-4000 MD steps).

Currently it is only supported to employ the diagonal part of the Hessian which is generally sufficient. Support for employing the full Hessian will be added later on.

The VES bias that is to be optimized should be specified using the BIAS keyword. The fixed step size $$\mu$$ is given using the STEPSIZE keyword. The frequency of updating the coefficients is given using the STRIDE keyword where the value is given in the number of MD steps. For example, if the MD time step is 0.02 ps and STRIDE=2000 will the coefficients be updated every 4 ps. The coefficients will be outputted to the file given by the COEFFS_FILE keyword. How often the coefficients are written to this file is controlled by the COEFFS_OUTPUT keyword.

If the VES bias employs a dynamic target distribution that needs to be iteratively updated (e.g. TD_WELLTEMPERED) , you will need to specify the stride for updating the target distribution by using the TARGETDIST_STRIDE keyword where the stride is given in terms coefficient iterations. For example if the MD time step is 0.02 ps and STRIDE=1000, such that the coefficients are updated every 2 ps, will TARGETDIST_STRIDE=500 mean that the target distribution will be updated every 1000 ps.

The output of the free energy surfaces and biases is controlled by the FES_OUTPUT and the BIAS_OUTPUT keywords. It is also possible to output one-dimensional projections of the free energy surfaces by using the FES_PROJ_OUTPUT keyword but for that to work you will need to select for which argument to do the projections by using the numbered PROJ_ARG keyword in the VES bias that is optimized. You can also output dynamic target distributions by using the TARGETDIST_OUTPUT and TARGETDIST_PROJ_OUTPUT keywords.

It is possible to start the optimization from some initial set of coefficients that have been previously obtained by using the INITIAL_COEFFS keyword.

When restarting simulations it should be sufficient to put the RESTART action in the beginning of the input files (or some MD codes the PLUMED should automatically detect if it is a restart run) and keep the same input as before The restarting of the optimization should be automatic as the optimizer will then read in the coefficients from the file given in COEFFS_FILE. For dynamic target distribution the code will also read in the final target distribution from the previous run (which is always outputted even if the TARGETDIST_OUTPUT keyword is not used).

This optimizer supports the usage of multiple walkers where different copies of the system share the same bias potential (i.e. coefficients) and cooperatively sample the averages needed for the gradient and Hessian. This can significantly help with convergence in difficult cases. It is of course best to start the different copies from different positions in CV space. To activate this option you just need to add the MULTIPLE_WALKERS flag. Note that this is only supported if the MD code support running multiple replicas connected via MPI.

The optimizer supports the usage of a so-called mask file that can be used to employ different step sizes for different coefficients and/or deactivate the optimization of certain coefficients (by putting values of 0.0). The mask file is read in by using the MASK_FILE keyword and should be in the same format as the coefficient file. It is possible to generate a template mask file by using the OUTPUT_MASK_FILE keyword.

Examples

In the following input we employ an averaged stochastic gradient decent with a fixed step size of 1.0 and update the coefficient every 1000 MD steps (e.g. every 2 ps if the MD time step is 0.02 ps). The coefficient are outputted to the coefficients.data every 50 iterations while the FES and bias is outputted to files every 500 iterations (e.g. every 1000 ps).

Click on the labels of the actions for more information on what each action computes phi: TORSION ATOMSthe four atoms involved in the torsional angle =5,7,9,15
bf1: BF_FOURIER ORDERcompulsory keyword
The order of the basis function expansion. =5 MINIMUMcompulsory keyword
The minimum of the interval on which the basis functions are defined. =-pi MAXIMUMcompulsory keyword
The maximum of the interval on which the basis functions are defined. =pi
ves1: VES_LINEAR_EXPANSION ...
ARGthe input for this action is the scalar output from one or more other actions. =phi
BASIS_FUNCTIONScompulsory keyword
the label of the one dimensional basis functions that should be used. =bf1

TEMPthe system temperature - this is needed if the MD code does not pass the temperature
to PLUMED. =300.0
GRID_BINSthe number of bins used for the grid. =100
...
o1: OPT_AVERAGED_SGD ...
BIAScompulsory keyword
the label of the VES bias to be optimized =ves1
STRIDEcompulsory keyword
the frequency of updating the coefficients given in the number of MD steps. =1000

STEPSIZEcompulsory keyword
the step size used for the optimization =1.0
COEFFS_FILEcompulsory keyword ( default=coeffs.data )
the name of output file for the coefficients =coefficients.data
COEFFS_OUTPUTcompulsory keyword ( default=100 )
how often the coefficients should be written to file. =50
FES_OUTPUThow often the FES(s) should be written out to file. =500
BIAS_OUTPUThow often the bias(es) should be written out to file. =500
...


In the following example we employ a well-tempered target distribution that is updated every 500 iterations (e.g. every 1000 ps). The target distribution is also output to a file every 2000 iterations (the TARGETDIST_OUTPUT keyword). Here we also employ MULTIPLE_WALKERS flag to enable the usage of multiple walkers.

Click on the labels of the actions for more information on what each action computes #SETTINGS NREPLICAS=2
phi: TORSION ATOMSthe four atoms involved in the torsional angle =5,7,9,15
psi: TORSION ATOMSthe four atoms involved in the torsional angle =7,9,15,17
bf1: BF_FOURIER ORDERcompulsory keyword
The order of the basis function expansion. =5 MINIMUMcompulsory keyword
The minimum of the interval on which the basis functions are defined. =-pi MAXIMUMcompulsory keyword
The maximum of the interval on which the basis functions are defined. =pi
bf2: BF_FOURIER ORDERcompulsory keyword
The order of the basis function expansion. =4 MINIMUMcompulsory keyword
The minimum of the interval on which the basis functions are defined. =-pi MAXIMUMcompulsory keyword
The maximum of the interval on which the basis functions are defined. =pi
td1: TD_WELLTEMPERED BIASFACTORcompulsory keyword
The bias factor used for the well-tempered distribution. =10
ves1: VES_LINEAR_EXPANSION ...
ARGthe input for this action is the scalar output from one or more other actions. =phi,psi
BASIS_FUNCTIONScompulsory keyword
the label of the one dimensional basis functions that should be used. =bf1,bf2

TEMPthe system temperature - this is needed if the MD code does not pass the temperature
to PLUMED. =300.0
GRID_BINSthe number of bins used for the grid. =100,100
TARGET_DISTRIBUTIONthe label of the target distribution to be used. =td1
PROJ_ARG1arguments for doing projections of the FES or the target distribution. =phi
PROJ_ARG2arguments for doing projections of the FES or the target distribution. =psi
...
o1: OPT_AVERAGED_SGD ...
BIAScompulsory keyword
the label of the VES bias to be optimized =ves1
STRIDEcompulsory keyword
the frequency of updating the coefficients given in the number of MD steps. =1000

STEPSIZEcompulsory keyword
the step size used for the optimization =1.0
MULTIPLE_WALKERS( default=off ) if optimization is to be performed using multiple walkers connected
via MPI
COEFFS_FILEcompulsory keyword ( default=coeffs.data )
the name of output file for the coefficients =coefficients.data
COEFFS_OUTPUTcompulsory keyword ( default=100 )
how often the coefficients should be written to file. =50
FES_OUTPUThow often the FES(s) should be written out to file. =500
FES_PROJ_OUTPUThow often the projections of the FES(s) should be written out to file. =500
BIAS_OUTPUThow often the bias(es) should be written out to file. =500
TARGETDIST_STRIDEstride for updating a target distribution that is iteratively updated during the
optimization. =500
TARGETDIST_OUTPUThow often the dynamic target distribution(s) should be written out to file. =2000
...

Glossary of keywords and components
Description of components

By default the value of the calculated quantity can be referenced elsewhere in the input file by using the label of the action. Alternatively this Action can be used to calculate the following quantities by employing the keywords listed below. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.