Approximation of forces and torques from anisotropic pairwise interactions using multivariate polynomials

TL;DR

This paper presents a polynomial-based framework for accurately approximating forces and torques between anisotropic particles using limited data, improving simulation efficiency in complex particle systems.

Contribution

It extends a polynomial approximation framework to include forces and torques, enabling accurate modeling with less data than traditional methods.

Findings

Interpolation of potential energy yields the best force and torque approximation.

Force and torque regression is effective when potential energy data is unavailable.

The method performs well on model anisotropic nanoparticles in 2D and 3D.

Abstract

The dynamics of anisotropic particles are dictated by forces and torques that can be challenging to mathematically represent in computer simulations. Several data-driven approaches have been developed to approximate these interactions, but they often rely on having large amounts of training data that may be practically difficult to generate. Here, we extend a framework we recently developed for approximating anisotropic pair potentials to the approximation of pairwise forces and torques. The framework uses multivariate polynomials and physics-motivated coordinate transformations to produce accurate approximations using limited amounts of data. We first derive expressions relating the force and torque to partial derivatives of the potential energy with respect to the transformed coordinates used to represent the particle configuration. We then explore several options for approximating the forces and torques, and we critically assess their accuracy using model two- and three-dimensional shape-anisotropic nanoparticles as test cases. We find that interpolation of the pairwise potential energy produces the best result when it is known, but force and torque matching (regression) is a viable strategy when only the force and torque is available.