Energy Loss Functions for Physical Systems

TL;DR

This paper introduces a physics-informed loss function framework for machine learning models in scientific systems, improving alignment with physical principles and enhancing performance in molecular and spin system tasks.

Contribution

It proposes a novel energy-based loss function derived from physical principles, applicable across architectures, and demonstrates improved results in molecular and spin system modeling.

Findings

Significant performance improvements over baselines.

Physically grounded loss functions better respect symmetries.

Energy loss functions improve model alignment with physical configurations.

Abstract

Effectively leveraging prior knowledge of a system's physics is crucial for applications of machine learning to scientific domains. Previous approaches mostly focused on incorporating physical insights at the architectural level. In this paper, we propose a framework to leverage physical information directly into the loss function for prediction and generative modeling tasks on systems like molecules and spins. We derive energy loss functions assuming that each data sample is in thermal equilibrium with respect to an approximate energy landscape. By using the reverse KL divergence with a Boltzmann distribution around the data, we obtain the loss as an energy difference between the data and the model predictions. This perspective also recasts traditional objectives like MSE as energy-based, but with a physically meaningless energy. In contrast, our formulation yields physically grounded loss functions with gradients that better align with valid configurations, while being architecture-agnostic and computationally efficient. The energy loss functions also inherently respect physical symmetries. We demonstrate our approach on molecular generation and spin ground-state prediction and report significant improvements over baselines.