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 [5]. 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) [103], 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.

Description of components

The names of the components in this action can be customized by the user in the actions input file. However, in addition to the components that can be customized the following quantities will always be output

Compulsory keywords
 BIAS the label of the VES bias to be optimized STRIDE the frequency of updating the coefficients given in the number of MD steps. COEFFS_FILE ( default=coeffs.data ) the name of output file for the coefficients COEFFS_OUTPUT ( default=100 ) how often the coefficients should be written to file. This parameter is given as the number of iterations. STEPSIZE the step size used for the optimization
Options
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).

phi:   TORSION ATOMS=5,7,9,15

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

OPT_AVERAGED_SGD ...
BIAS=ves1
STRIDE=1000
LABEL=o1
STEPSIZE=1.0
COEFFS_FILE=coefficients.data
COEFFS_OUTPUT=50
FES_OUTPUT=500
BIAS_OUTPUT=500
... OPT_AVERAGED_SGD

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.

#SETTINGS NREPLICAS=2
phi:   TORSION ATOMS=5,7,9,15
psi:   TORSION ATOMS=7,9,15,17

bf1: BF_FOURIER ORDER=5 MINIMUM=-pi MAXIMUM=pi
bf2: BF_FOURIER ORDER=4 MINIMUM=-pi MAXIMUM=pi

td1: TD_WELLTEMPERED BIASFACTOR=10

VES_LINEAR_EXPANSION ...
ARG=phi,psi
BASIS_FUNCTIONS=bf1,bf2
LABEL=ves1
TEMP=300.0
GRID_BINS=100,100
TARGET_DISTRIBUTION=td1
PROJ_ARG1=phi
PROJ_ARG2=psi
... VES_LINEAR_EXPANSION

OPT_AVERAGED_SGD ...
BIAS=ves1
STRIDE=1000
LABEL=o1
STEPSIZE=1.0
MULTIPLE_WALKERS
COEFFS_FILE=coefficients.data
COEFFS_OUTPUT=50
FES_OUTPUT=500
FES_PROJ_OUTPUT=500
BIAS_OUTPUT=500
TARGETDIST_STRIDE=500
TARGETDIST_OUTPUT=2000
... OPT_AVERAGED_SGD