Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields

TL;DR

This paper introduces a novel approach using algorithmic differentiation to enhance the efficiency and flexibility of machine learning models for reconstructing force fields, enabling automatic use of complex descriptors and physical constraints.

Contribution

It presents a method that automates the integration of new descriptors and physical laws into ML force field models with significantly improved computational efficiency.

Findings

Enables automatic incorporation of complex descriptors.

Increases computational efficiency by an order of magnitude.

Facilitates inclusion of higher-order physical information.

Abstract

Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the underlying symmetry and conservation laws of physics. However, so far, every descriptor newly proposed for an ML model has required a cumbersome and mathematically tedious remodeling. We therefore propose using modern techniques from algorithmic differentiation within the ML modeling process -- effectively enabling the usage of novel descriptors or models fully automatically at an order of magnitude higher computational efficiency. This paradigmatic approach enables not only a versatile usage of novel representations and the efficient computation of larger systems -- all of high value to the FF community -- but also the simple inclusion of further physical knowledge such as higher-order information (e.g. Hessians, more complex partial differential equations constraints etc.), even beyond the presented FF domain.