From Evaluation to Design: Using Potential Energy Surface Smoothness Metrics to Guide Machine Learning Interatomic Potential Architectures

TL;DR

This paper introduces the Bond Smoothness Characterization Test (BSCT), an efficient metric for evaluating and guiding the design of Machine Learning Interatomic Potentials to better replicate the physical smoothness of quantum potential energy surfaces.

Contribution

The paper presents BSCT as a novel, computationally efficient benchmark that correlates with MD stability and guides iterative MLIP model improvements, including new algorithms and attention mechanisms.

Findings

BSCT effectively detects non-smoothness in PES.

Refinements guided by BSCT improve MD stability.

MLIPs optimized with BSCT achieve better physical fidelity.

Abstract

Machine Learning Interatomic Potentials (MLIPs) sometimes fail to reproduce the physical smoothness of the quantum potential energy surface (PES), leading to erroneous behavior in downstream simulations that standard energy and force regression evaluations can miss. Existing evaluations, such as microcanonical molecular dynamics (MD), are computationally expensive and primarily probe near-equilibrium states. To improve evaluation metrics for MLIPs, we introduce the Bond Smoothness Characterization Test (BSCT). This efficient benchmark probes the PES via controlled bond deformations and detects non-smoothness, including discontinuities, artificial minima, and spurious forces, both near and far from equilibrium. We show that BSCT correlates strongly with MD stability while requiring a fraction of the cost of MD. To demonstrate how BSCT can guide iterative model design, we utilize an unconstrained Transformer backbone as a testbed, illustrating how refinements such as a new differentiable $k$-nearest neighbors algorithm and temperature-controlled attention reduce artifacts identified by our metric. By optimizing model design systematically based on BSCT, the resulting MLIP simultaneously achieves a low conventional E/F regression error, stable MD simulations, and robust atomistic property predictions. Our results establish BSCT as both a validation metric and as an "in-the-loop" model design proxy that alerts MLIP developers to physical challenges that cannot be efficiently evaluated by current MLIP benchmarks.