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:

t: TORSION ATOMS=1,2,3,4 md: METAD ARG=d SIGMA=0.2 HEIGHT=0.3 PACE=500 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
dist: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
# this is the squared of the distance
dist2: COMBINE ARGthe input for this action is the scalar output from one or more other actions. =dist POWERScompulsory keyword ( default=1.0 )
the powers to which you are raising each of the arguments in your function =2 PERIODICcompulsory 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 ARGthe input for this action is the scalar output from one or more other actions. =dist,dist2 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0,1.0 PERIODSteps over which to adjust bias for adaptive or ramping =100 TEMPThe system temperature. =1.0
PRINT ARGthe 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 FILEthe name of the file on which to output these quantities =colvars.dat STRIDEcompulsory 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
dist: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
dist2: COMBINE ARGthe input for this action is the scalar output from one or more other actions. =dist POWERScompulsory keyword ( default=1.0 )
the powers to which you are raising each of the arguments in your function =2 PERIODICcompulsory 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 ARGthe input for this action is the scalar output from one or more other actions. =dist,dist2 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0,1.0 FIXEDcompulsory keyword ( default=0 )
Fixed target values for coupling constant. =-1,1 RAMP( default=off ) Slowly increase bias constant to a fixed value  PERIODSteps over which to adjust bias for adaptive or ramping =50000 TEMPThe system temperature. =1.0
#same as above, except starting at -0.5,0.5 rather than default of 0,0
eds2: EDS ARGthe input for this action is the scalar output from one or more other actions. =dist,dist2 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0,1.0 FIXEDcompulsory keyword ( default=0 )
Fixed target values for coupling constant. =-1,1 INITcompulsory keyword ( default=0 )
Starting value for coupling constant =-0.5,0.5 RAMP( default=off ) Slowly increase bias constant to a fixed value  PERIODSteps over which to adjust bias for adaptive or ramping =50000 TEMPThe 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
dist: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
dist2: COMBINE ARGthe input for this action is the scalar output from one or more other actions. =dist POWERScompulsory keyword ( default=1.0 )
the powers to which you are raising each of the arguments in your function =2 PERIODICcompulsory 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 ARGthe input for this action is the scalar output from one or more other actions. =dist,dist2 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0,1.0 PERIODSteps over which to adjust bias for adaptive or ramping =100 TEMPThe system temperature. =1.0 OUT_RESTARTOutput 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 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
d1: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
eds: EDS ARGthe input for this action is the scalar output from one or more other actions. =d1 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0 PERIODSteps over which to adjust bias for adaptive or ramping =100 TEMPThe system temperature. =1.0 IN_RESTARTRead this file to continue an EDS simulation. =restart.eds RESTARTallows 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
d1: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
eds: EDS ARGthe input for this action is the scalar output from one or more other actions. =d1 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0 TEMPThe system temperature. =1.0 IN_RESTARTRead 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
d1: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
eds: EDS ARGthe input for this action is the scalar output from one or more other actions. =d1 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0 TEMPThe system temperature. =1.0 IN_RESTARTRead 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
d1: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. =1,2
eds: EDS ARGthe input for this action is the scalar output from one or more other actions. =d1 CENTERThe desired centers (equilibrium values) which will be sought during the adaptive
linear biasing. =2.0 PERIODSteps over which to adjust bias for adaptive or ramping =100 TEMPThe system temperature. =1.0 IN_RESTARTRead 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