An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields

TL;DR

This paper introduces DECAF, a robust and efficient atomistic fingerprint algorithm that uses density fields and canonical alignment to improve data-driven modeling of molecular force fields, especially in sparse or symmetric neighborhoods.

Contribution

The paper presents the DECAF fingerprint algorithm, which employs density fields and a kernel minisum optimization for rotational invariance, outperforming PCA-based methods in atomistic modeling.

Findings

DECAF provides superior rotational invariance, especially with sparse or symmetric neighborhoods.

The density field comparison using volume integrals is computationally efficient.

The method demonstrates improved accuracy in fitting interatomic potentials on benchmark problems.

Abstract

Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we present the Density-Encoded Canonically Aligned Fingerprint (DECAF) fingerprint algorithm, which is robust and efficient, for fitting per-atom scalar and vector quantities. The fingerprint is essentially a continuous density field formed through the superimposition of smoothing kernels centered on the atoms. Rotational invariance of the fingerprint is achieved by aligning, for each fingerprint instance, the neighboring atoms onto a local canonical coordinate frame computed from a kernel minisum optimization procedure. We show that this approach is superior over PCA-based methods especially when the atomistic neighborhood is sparse and/or contains symmetry. We propose that the `distance' between the density fields be measured using a volume integral of their pointwise difference. This can be efficiently computed using optimal quadrature rules, which only require discrete sampling at a small number of grid points. We also experiment on the choice of weight functions for constructing the density fields, and characterize their performance for fitting interatomic potentials. The applicability of the fingerprint is demonstrated through a set of benchmark problems.