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

Add a linear bias on a set of observables.

This force is the same as the linear part of the bias in RESTRAINT, but this bias has the ability to compute the prefactors adaptively using the scheme of White and Voth [123] in order to match target observable values for a set of CVs. Further updates to the algorithm are described in [57] and you can read a review on the method and its applications here: [2].

You can see a tutorial on EDS specifically for biasing coordination number at Andrew White's webpage.

The addition to the potential is of the form

\[ \sum_i \frac{\alpha_i}{s_i} x_i \]

where for CV \(x_i\), a coupling constant \({\alpha}_i\) is determined adaptively or set by the user to match a target value for \(x_i\). \(s_i\) is a scale parameter, which by default is set to the target value. It may also be set separately.

Warning
It is not possible to set the target value of the observable to zero with the default value of \(s_i\) as this will cause a divide-by-zero error. Instead, set \(s_i=1\) or modify the CV so the desired target value is no longer zero.

Notice that a similar method is available as MAXENT, although with different features and using a different optimization algorithm.

Virial

The bias forces modify the virial and this can change your simulation density if the bias is used in an NPT simulation. One way to avoid changing the virial contribution from the bias is to add the keyword VIRIAL=1.0, which changes how the bias is computed to minimize its contribution to the virial. This can also lead to smaller magnitude biases that are more robust if transferred to other systems. VIRIAL=1.0 can be a reasonable starting point and increasing the value changes the balance between matching the set-points and minimizing the virial. See [2] for details on the equations. Since the coupling constants are unique with a single CV, VIRIAL is not applicable with a single CV. When used with multiple CVs, the CVs should be correlated which is almost always the case.

Weighting

EDS computes means and variances as part of its algorithm. If you are also using a biasing method like metadynamics, you may wish to remove the effect of this bias in your EDS computations so that EDS works on the canonical values (reweighted). For example, you may be using metadynamics to bias a dihedral angle to enhance sampling and be using EDS to set the average distance between two particular atoms. Specifically:

plumedfile working DATADIR=example-check/EDS.tmp

set-up metadnyamics

t: TORSION ATOMS=1,2,3,4 md: METAD ARG=d SIGMA=0.2 HEIGHT=0.3 PACE=500 TEMP=300

compute bias weights

bias: REWEIGHT_METAD TEMP=300

now do EDS on distance while removing effect of metadynamics

d: DISTANCE ATOMS=4,7 eds: EDS ARG=d CENTER=3.0 PERIOD=100 TEMP=300 LOGWEIGHTS=bias

This is an approximation though because EDS uses a finte sample to get means/variances. At the end of a run, you should ensure this approach worked and indeed your reweighted CV matches the target value.

Examples

The following input for a harmonic oscillator of two beads will adaptively find a linear bias to change the mean and variance to the target values. The PRINT line shows how to access the value of the coupling constants.

Click on the labels of the actions for more information on what each action computes
tested on v2.7
dist: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 # this is the squared of the distance dist2: COMBINE
ARG
the input for this action is the scalar output from one or more other actions.
=dist
POWERS
compulsory keyword ( default=1.0 ) the powers to which you are raising each of the arguments in your function
=2
PERIODIC
compulsory keyword if the output of your function is periodic then you should specify the periodicity of the function.
=NO #bias mean and variance eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=dist,dist2
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0,1.0
PERIOD
Steps over which to adjust bias for adaptive or ramping
=100
TEMP
The system temperature.
=1.0 PRINT
ARG
the input for this action is the scalar output from one or more other actions.
=dist,dist2,eds.dist_coupling,eds.dist2_coupling,eds.bias,eds.force2
FILE
the name of the file on which to output these quantities
=colvars.dat
STRIDE
compulsory keyword ( default=1 ) the frequency with which the quantities of interest should be output
=100

Rather than trying to find the coupling constants adaptively, one can ramp up to a constant value.

Click on the labels of the actions for more information on what each action computes
tested on v2.7
dist: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 dist2: COMBINE
ARG
the input for this action is the scalar output from one or more other actions.
=dist
POWERS
compulsory keyword ( default=1.0 ) the powers to which you are raising each of the arguments in your function
=2
PERIODIC
compulsory keyword if the output of your function is periodic then you should specify the periodicity of the function.
=NO #ramp couplings from 0,0 to -1,1 over 50000 steps eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=dist,dist2
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0,1.0
FIXED
compulsory keyword ( default=0 ) Fixed target values for coupling constant.
=-1,1
RAMP
( default=off ) Slowly increase bias constant to a fixed value
PERIOD
Steps over which to adjust bias for adaptive or ramping
=50000
TEMP
The system temperature.
=1.0 #same as above, except starting at -0.5,0.5 rather than default of 0,0 eds2: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=dist,dist2
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0,1.0
FIXED
compulsory keyword ( default=0 ) Fixed target values for coupling constant.
=-1,1
INIT
compulsory keyword ( default=0 ) Starting value for coupling constant
=-0.5,0.5
RAMP
( default=off ) Slowly increase bias constant to a fixed value
PERIOD
Steps over which to adjust bias for adaptive or ramping
=50000
TEMP
The system temperature.
=1.0

A restart file can be added to dump information needed to restart/continue simulation using these parameters every PERIOD.

Click on the labels of the actions for more information on what each action computes
tested on v2.7
dist: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 dist2: COMBINE
ARG
the input for this action is the scalar output from one or more other actions.
=dist
POWERS
compulsory keyword ( default=1.0 ) the powers to which you are raising each of the arguments in your function
=2
PERIODIC
compulsory keyword if the output of your function is periodic then you should specify the periodicity of the function.
=NO #add the option to write to a restart file eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=dist,dist2
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0,1.0
PERIOD
Steps over which to adjust bias for adaptive or ramping
=100
TEMP
The system temperature.
=1.0
OUT_RESTART
Output file for all information needed to continue EDS simulation.
=checkpoint.eds

The first few lines of the restart file that is output if we run a calculation with one CV will look something like this:

#! FIELDS time d1_center d1_set d1_target d1_coupling d1_maxrange d1_maxgrad d1_accum d1_mean d1_std
#! SET adaptive  1
#! SET update_period  1
#! SET seed  0
#! SET kbt    2.4943
   0.0000   1.0000   0.0000   0.0000   0.0000   7.4830   0.1497   0.0000   0.0000   0.0000
   1.0000   1.0000   0.0000   0.0000   0.0000   7.4830   0.1497   0.0000   0.0000   0.0000
   2.0000   1.0000  -7.4830   0.0000   0.0000   7.4830   0.1497   0.0224   0.0000   0.0000
   3.0000   1.0000  -7.4830   0.0000  -7.4830   7.4830   0.1497   0.0224   0.0000   0.0000
   4.0000   1.0000  -7.4830   0.0000  -7.4830   7.4830   0.1497   0.0224   0.0000   0.0000

Read in a previous restart file. Adding RESTART flag makes output append

Click on the labels of the actions for more information on what each action computes
tested on v2.7
d1: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=d1
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0
PERIOD
Steps over which to adjust bias for adaptive or ramping
=100
TEMP
The system temperature.
=1.0
IN_RESTART
Read this file to continue an EDS simulation.
=restart.eds
RESTART
allows per-action setting of restart (YES/NO/AUTO)
=YES

Read in a previous restart file and freeze the bias at the final level from the previous simulation

Click on the labels of the actions for more information on what each action computes
tested on v2.7
d1: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=d1
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0
TEMP
The system temperature.
=1.0
IN_RESTART
Read this file to continue an EDS simulation.
=restart.eds
FREEZE
( default=off ) Fix bias at current level (only used for restarting).

Read in a previous restart file and freeze the bias at the mean from the previous simulation

Click on the labels of the actions for more information on what each action computes
tested on v2.7
d1: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=d1
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0
TEMP
The system temperature.
=1.0
IN_RESTART
Read this file to continue an EDS simulation.
=restart.eds
FREEZE
( default=off ) Fix bias at current level (only used for restarting).
MEAN
( default=off ) Instead of using final bias level from restart, use average.

Read in a previous restart file and continue the bias, but use the mean from the previous run as the starting point

Click on the labels of the actions for more information on what each action computes
tested on v2.7
d1: DISTANCE 
ATOMS
the pair of atom that we are calculating the distance between.
=1,2 eds: EDS
ARG
the input for this action is the scalar output from one or more other actions.
=d1
CENTER
The desired centers (equilibrium values) which will be sought during the adaptive linear biasing.
=2.0
PERIOD
Steps over which to adjust bias for adaptive or ramping
=100
TEMP
The system temperature.
=1.0
IN_RESTART
Read this file to continue an EDS simulation.
=restart.eds
MEAN
( default=off ) Instead of using final bias level from restart, use average.
Glossary of keywords and components
Description of components

By default this Action calculates the following quantities. 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.

Quantity Description
bias the instantaneous value of the bias potential
force2 squared value of force from the bias
pressure If using virial keyword, this is the current sum of virial terms. It is in units of pressure (energy / vol^3)
_coupling For each named CV biased, there will be a corresponding output CV_coupling storing the current linear bias prefactor.
Compulsory keywords
RANGE ( default=25.0 ) The (starting) maximum increase in coupling constant per PERIOD (in \(k_B T\)/[BIAS_SCALE unit]) for each CV based
SEED ( default=0 ) Seed for random order of changing bias
INIT ( default=0 ) Starting value for coupling constant
FIXED ( default=0 ) Fixed target values for coupling constant. Non-adaptive.
Options
NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically
LM ( default=off ) Use Levenberg-Marquadt algorithm along with simultaneous keyword. Otherwise use gradient descent.
LM_MIXING ( default=on ) Initial mixing parameter when using Levenberg-Marquadt minimization.
RAMP ( default=off ) Slowly increase bias constant to a fixed value
COVAR ( default=off ) Utilize the covariance matrix when updating the bias. Default Off, but may be enabled due to other options
FREEZE ( default=off ) Fix bias at current level (only used for restarting).
MEAN

( default=off ) Instead of using final bias level from restart, use average. Can only be used in conjunction with FREEZE

ARG the input for this action is the scalar output from one or more other actions. The particular scalars that you will use are referenced using the label of the action. If the label appears on its own then it is assumed that the Action calculates a single scalar value. The value of this scalar is thus used as the input to this new action. If * or *.* appears the scalars calculated by all the proceeding actions in the input file are taken. Some actions have multi-component outputs and each component of the output has a specific label. For example a DISTANCE action labelled dist may have three components x, y and z. To take just the x component you should use dist.x, if you wish to take all three components then use dist.*.More information on the referencing of Actions can be found in the section of the manual on the PLUMED Getting Started. Scalar values can also be referenced using POSIX regular expressions as detailed in the section on Regular Expressions. To use this feature you you must compile PLUMED with the appropriate flag. You can use multiple instances of this keyword i.e. ARG1, ARG2, ARG3...
CENTER The desired centers (equilibrium values) which will be sought during the adaptive linear biasing. This is for fixed centers
CENTER_ARG The desired centers (equilibrium values) which will be sought during the adaptive linear biasing. CENTER_ARG is for calculated centers, e.g. from a CV or analysis.
PERIOD Steps over which to adjust bias for adaptive or ramping
BIAS_SCALE A divisor to set the units of the bias. If not set, this will be the CENTER value by default (as is done in White and Voth 2014).
TEMP The system temperature. If not provided will be taken from MD code (if available)
MULTI_PROP What proportion of dimensions to update at each step. Must be in interval [1,0), where 1 indicates all and any other indicates a stochastic update. If not set, default is 1 / N, where N is the number of CVs.
VIRIAL Add an update penalty for having non-zero virial contributions. Only makes sense with multiple correlated CVs.
LOGWEIGHTS Add weights to use for computing statistics. For example, if biasing with metadynamics.
RESTART_FMT the format that should be used to output real numbers in EDS restarts
OUT_RESTART Output file for all information needed to continue EDS simulation. If you have the RESTART directive set (global or for EDS), this file will be appended to. Note that the header will be printed again if appending.
IN_RESTART Read this file to continue an EDS simulation. If same as OUT_RESTART and you have not set the RESTART directive, the file will be backed-up and overwritten with new output. If you do have the RESTART flag set and it is the same name as OUT_RESTART, this file will be appended.
RESTART allows per-action setting of restart (YES/NO/AUTO)