POD - Proper Orthogonal Descriptors¶

Description¶

The POD potential writes the energy of an atom as a linear combination of orthogonal descriptors. The descriptors are built from two-body and three-body (and optionally higher-order) radial and angular basis functions, compressed by a proper orthogonal decomposition. POD also supports environment clustering: atoms are assigned to clusters of local environments, each with its own set of coefficients.

A POD potential is defined by two files:

a parameter file (.pod): species, cutoffs, basis sizes, body orders, number of environment clusters, ...
a coefficient file (.pod): the fitted coefficients.

Build

Configure exaStamp with -DEXASTAMP_MLIP_POD_BUILD=ON. POD requires BLAS and LAPACK. To force a given BLAS implementation, set -DEXASTAMP_MLIP_POD_BLAS_VENDOR=<vendor> (for instance OpenBLAS or Intel10_64lp). The value is passed to CMake's FindBLAS as BLA_VENDOR.

Operators¶

pod_init reads both files once, in init_parameters, and raises rcut_max to the POD cutoff. pod_force computes energies, forces and the virial in compute_force.

Syntax

init_parameters:
  - species
  - pod_init:
      parameters:
        pod_file: <string>
        coeff_file: <string>

compute_force:
  - pod_force

Parameters

parameters.pod_file:    string, required   # POD parameter file.
parameters.coeff_file:  string, required   # POD coefficient file.

pod_init needs the species operator to have run before it, so list species first in init_parameters.

Usage example

includes:
  - config_update_symmetric_forces.msp

species:
  - Ta: { mass: 180.95 Da, z: 73, charge: 0 e- }

init_parameters:
  - species
  - pod_init:
      parameters:
        pod_file: "Ta_param.pod"
        coeff_file: "Ta_coefficients.pod"

compute_force:
  - pod_force

Examples are in exaStamp/data/regression_new/mliaps/pod/: Ta_pod.msp, Ta_pod_nClusters_2.msp (two environment clusters) and Ta_enhanced_pod.msp (short-range options below).

Short-range options¶

The parameter file accepts optional keywords that control the radial basis at short distances:

Keyword	Default	Description
`rin`	0.5	Inner cutoff: the radial basis functions are evaluated on \(r = r_{ij} - r_{in}\).
`fadein_mu`, `fadein_delta`	0, 0	When both are positive, every radial basis function is multiplied by the fade-in function \(f_{in}(r_{ij}) = 1/\left(1+e^{2(\mu-r_{ij})/\delta}\right)\), which goes from 0 below \(\mu\) to 1 above it over a width of about \(\delta\).
`use_scaled_lj`	0	When set, the inverse-power radial functions use \((r_{ij}/r_{in})^{-k}\) instead of \(r_{ij}^{-k}\).

Short-range part of a parameter file (Ta_param_enhanced.pod)

rin 0.4
rcut 5.0
fadein_mu 0.4
fadein_delta 0.04
use_scaled_lj 1

The fade-in function enters both the projection of the descriptors and the radial basis used for energies, forces and descriptors. It only changes the results for pair distances within a few \(\delta\) of \(\mu\) or below.

Descriptors¶

POD descriptors, their derivatives and the global fitting matrix are computed by compute_descriptor_pod, compute_descriptor_pod_global and write_descriptor_pod_global. See Descriptors.