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

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 can be missed by standard energy and force regression evaluations. 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 instabilities, including discontinuities, artificial minima, and spurious forces, both near and far from equilibrium. We show that BSCT correlates strongly with MD stability at a fraction of the cost. To demonstrate how BSCT can guide iterative model design, we use an unconstrained Transformer backbone as a testbed, showing how refinements like differentiable $k$-nearest neighbors and temperature-controlled attention systematically reduce artifacts identified by the metric, resulting in an MLIP that simultaneously achieves strong accuracy and physical soundness. Our results establish BSCT as an "in-the-loop" proxy that alerts MLIP developers to physical challenges that are not captured by current MLIP evaluations.