Action: OPES_METAD_EXPLORE

Module	opes
Description	Usage
On-the-fly probability enhanced sampling with well-tempered target distribution in exploreation mode.

Details and examples

On-the-fly probability enhanced sampling with well-tempered target distribution in exploreation mode.

On-the-fly probability enhanced sampling with well-tempered target distribution (OPES) with well-tempered target distribution, exploration mode as discussed in the paper cited below.

This OPES_METAD_EXPLORE action samples the well-tempered target distribution, that is defined via its marginal $p^{\text{WT}}(\mathbf{s})\propto [P(\mathbf{s})]^{1/\gamma}$ over some collective variables (CVs), $\mathbf{s}=\mathbf{s}(\mathbf{x})$. While OPES_METAD does so by estimating the unbiased distribution $P(\mathbf{s})$, OPES_METAD_EXPLORE instead estimates on-the-fly the target $p^{\text{WT}}(\mathbf{s})$ and uses it to define the bias. The bias at step $n$ is

$$V_n(\mathbf{s}) = (\gamma-1)\frac{1}{\beta}\log\left(\frac{p^{\text{WT}}_n(\mathbf{s})}{Z_n}+\epsilon\right)\, .$$

See the paper cited below for a complete description of the method.

Intuitively, while OPES_METAD aims at quickly converging the reweighted free energy, OPES_METAD_EXPLORE aims at quickly sampling the target well-tempered distribution. Given enough simulation time, both will converge to the same bias potential but they do so in a qualitatively different way. Compared to OPES_METAD, OPES_METAD_EXPLORE is more similar to METAD, because it allows the bias to vary significantly, thus enhancing exploration. This goes at the expenses of a typically slower convergence of the reweight estimate. OPES_METAD_EXPLORE can be useful e.g.~for simulating a new system with an unknown BARRIER, or for quickly testing the effectiveness of a new CV that might be degenerate.

Similarly to OPES_METAD, also OPES_METAD_EXPLORE uses a kernel density estimation with the same on-the-fly compression algorithm. The only difference is that the kernels are not weighted, since it estimates the sampled distribution and not the reweighted unbiased one.

All the options of OPES_METAD are also available in OPES_METAD_EXPLORE, except for those that modify the target distribution, since only a well-tempered target is allowed in this case.

Examples

The following is a minimal working example:

Click on the labels of the actions for more information on what each action computes

cvThe DISTANCE action with label cv calculates the following quantities:
 Quantity   
 Type   
 Description  
cv
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2
opesThe OPES_METAD_EXPLORE action with label opes calculates the following quantities:
 Quantity   
 Type   
 Description  
opes.bias
scalar
the instantaneous value of the bias potential
opes.rct
scalar
estimate of c(t). log(exp(beta V)/beta, should become flat as the simulation converges. Do NOT use for reweighting
opes.zed
scalar
estimate of Z_n. should become flat once no new CV-space region is explored
opes.neff
scalar
effective sample size
opes.nker
scalar
total number of compressed kernels used to represent the bias: OPES_METAD_EXPLOREOn-the-fly probability enhanced sampling with well-tempered target distribution in exploreation mode. This action has hidden defaults. More details ARGthe labels of the scalars on which the bias will act=cv PACEthe frequency for kernel deposition=500 BARRIERthe free energy barrier to be overcome=40
opes: OPES_METAD_EXPLOREOn-the-fly probability enhanced sampling with well-tempered target distribution in exploreation mode. This action uses the defaults shown here. More details ARGthe labels of the scalars on which the bias will act=cv PACEthe frequency for kernel deposition=500 BARRIERthe free energy barrier to be overcome=40  TEMP temperature=-1 SIGMA the initial widths of the kernels, divided by the square root of gamma=ADAPTIVE COMPRESSION_THRESHOLD merge kernels if closer than this threshold, in units of sigma=1 FILE a file in which the list of all deposited kernels is stored=KERNELS
PRINTPrint quantities to a file. More details STRIDE the frequency with which the quantities of interest should be output=100 FILEthe name of the file on which to output these quantities=COLVAR ARGthe labels of the values that you would like to print to the file=cv,opes.*

Input

The arguments that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
ARG	scalar	the labels of the scalars on which the bias will act
EXCLUDED_REGION	scalar	kernels are not deposited when the action provided here has a nonzero value, see example above

Output components

This action can calculate the values in the following table when the associated keyword is included in the input for the action. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Keyword	Description
bias	scalar	default	the instantaneous value of the bias potential
rct	scalar	default	estimate of c(t)
zed	scalar	default	estimate of Z_n
neff	scalar	default	effective sample size
nker	scalar	default	total number of compressed kernels used to represent the bias
work	scalar	CALC_WORK	total accumulated work done by the bias
nlker	scalar	NLIST	number of kernels in the neighbor list
nlsteps	scalar	NLIST	number of steps from last neighbor list update

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
ARG	input	none	the labels of the scalars on which the bias will act
EXCLUDED_REGIONThis keyword do not have examples	input	none	kernels are not deposited when the action provided here has a nonzero value, see example above
TEMP	compulsory	-1	temperature
PACE	compulsory	none	the frequency for kernel deposition
SIGMA	compulsory	ADAPTIVE	the initial widths of the kernels, divided by the square root of gamma
BARRIER	compulsory	none	the free energy barrier to be overcome
COMPRESSION_THRESHOLD	compulsory	1	merge kernels if closer than this threshold, in units of sigma
FILE	compulsory	KERNELS	a file in which the list of all deposited kernels is stored
NUMERICAL_DERIVATIVESThis keyword do not have examples	optional	false	calculate the derivatives for these quantities numerically
ADAPTIVE_SIGMA_STRIDEThis keyword do not have examples	optional	not used	number of steps for measuring adaptive sigma
SIGMA_MINThis keyword do not have examples	optional	not used	never reduce SIGMA below this value
BIASFACTORThis keyword do not have examples	optional	not used	the gamma bias factor used for the well-tempered target distribution
EPSILONThis keyword do not have examples	optional	not used	the value of the regularization constant for the probability
KERNEL_CUTOFFThis keyword do not have examples	optional	not used	truncate kernels at this distance, in units of sigma
NLIST_PARAMETERSThis keyword do not have examples	optional	not used	the two cutoff parameters for the kernels neighbor list
NLISTThis keyword do not have examples	optional	false	use neighbor list for kernels summation, faster but experimental
NLIST_PACE_RESETThis keyword do not have examples	optional	false	force the reset of the neighbor list at each PACE
FIXED_SIGMAThis keyword do not have examples	optional	false	do not decrease sigma as the simulation proceeds
RECURSIVE_MERGE_OFFThis keyword do not have examples	optional	false	do not recursively attempt kernel merging when a new one is added
NO_ZEDThis keyword do not have examples	optional	false	do not normalize over the explored CV space, Z_n=1
FMTThis keyword do not have examples	optional	not used	specify format for KERNELS file
STATE_RFILEThis keyword do not have examples	optional	not used	read from this file the compressed kernels and all the info needed to RESTART the simulation
STATE_WFILEThis keyword do not have examples	optional	not used	write to this file the compressed kernels and all the info needed to RESTART the simulation
STATE_WSTRIDEThis keyword do not have examples	optional	not used	number of MD steps between writing the STATE_WFILE
STORE_STATESThis keyword do not have examples	optional	false	append to STATE_WFILE instead of ovewriting it each time
CALC_WORKThis keyword do not have examples	optional	false	calculate the total accumulated work done by the bias since last restart
WALKERS_MPIThis keyword do not have examples	optional	false	switch on MPI version of multiple walkers
SERIALThis keyword do not have examples	optional	false	perform calculations in serial
RESTARTThis keyword do not have examples	optional	not used	allows per-action setting of restart (YES/NO/AUTO)
UPDATE_FROMThis keyword do not have examples	optional	not used	Only update this action from this time
UPDATE_UNTILThis keyword do not have examples	optional	not used	Only update this action until this time

References

More information about how this action can be used is available in the following articles:

• M. Invernizzi, M. Parrinello, Exploration vs Convergence Speed in Adaptive-Bias Enhanced Sampling. Journal of Chemical Theory and Computation. 18, 3988–3996 (2022)