Hessian-informed machine learning interatomic potential towards bridging theory and experiments

TL;DR

This paper introduces a Hessian-informed machine learning interatomic potential that accurately captures potential energy surface curvature, improving predictions of thermodynamic and kinetic properties, and bridging the gap between theory and experiments.

Contribution

The authors develop a Hessian-informed training protocol (HINT) that drastically reduces the need for expensive Hessian labels, enabling efficient and accurate curvature-aware interatomic potentials.

Findings

Enhanced transition-state search accuracy

Gibbs free-energy predictions near chemical accuracy

Accurate modeling of anharmonic hydrides and superconducting temperatures

Abstract

Local curvature of potential energy surfaces is critical for predicting certain experimental observables of molecules and materials from first principles, yet it remains far beyond reach for complex systems. In this work, we introduce a Hessian-informed Machine Learning Interatomic Potential (Hi-MLIP) that captures such curvature reliably, thereby enabling accurate analysis of associated thermodynamic and kinetic phenomena. To make Hessian supervision practically viable, we develop a highly efficient training protocol, termed Hessian INformed Training (HINT), achieving two to four orders of magnitude reduction for the requirement of expensive Hessian labels. HINT integrates critical techniques, including Hessian pre-training, configuration sampling, curriculum learning and stochastic projection Hessian loss. Enabled by HINT, Hi-MLIP significantly improves transition-state search and brings Gibbs free-energy predictions close to chemical accuracy especially in data-scarce regimes. Our framework also enables accurate treatment of strongly anharmonic hydrides, reproducing phonon renormalization and superconducting critical temperatures in close agreement with experiment while bypassing the computational bottleneck of anharmonic calculations. These results establish a practical route to enhancing curvature awareness of machine learning interatomic potentials, bridging simulation and experimental observables across a wide range of systems.