Dynamically training machine-learning-based force fields for strongly anharmonic materials

TL;DR

This paper introduces a dynamic training framework for machine learning force fields that adaptively improves accuracy and transferability in simulating strongly anharmonic materials by using Bayesian error estimation during molecular dynamics.

Contribution

The work presents a novel adaptive training method that employs Bayesian error estimates to guide data acquisition, enhancing ML force field robustness for anharmonic materials.

Findings

Trajectory-averaged Bayesian errors enable efficient exploration of configuration space.

The method improves force field transferability across different materials.

Bayesian error estimation helps determine training convergence without extra ab initio data.

Abstract

Machine learning (ML) force fields have emerged as a powerful tool for computing materials properties at finite temperatures, particularly in regimes where traditional phonon-based perturbation theories fail or cannot be extended beyond the harmonic approximation. These approaches offer accuracy comparable to ab initio molecular dynamics (MD), but at a fraction of the computational cost. However, their reliability critically depends on the quality and representativeness of the training data. In particular, static training datasets often lead to failure when the force field encounters previously unseen atomic configurations during MD simulations. In this work, we present a framework for dynamically training ML force fields and demonstrate its effectiveness across materials with varying degrees of anharmonicity, including cubic boron arsenide (c-BAs), silicon (Si), and tin selenide (SnSe). Our method builds on the conventional lattice dynamics expansion of total energy and incorporates Bayesian error estimation to guide adaptive data acquisition during simulation. Specifically, we show that trajectory-averaged Bayesian errors enable efficient and targeted exploration of the configuration space, significantly enhancing the robustness and transferability of the resulting force fields. We further demonstrate how Bayesian error estimation can be applied to determine the convergence of the dynamic training without requiring additional ab initio data. This proposed framework offers a practical and easily implementable scheme to improve the training process, which is the most critical step in developing reliable ML force fields.