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 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 for practitioners to assess MLIP utility 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.

Scientists use machine learning models to simulate atomic interactions for designing medicines and materials. However, these models sometimes create artificial "bumps" in the energy landscapes they predict, causing simulations to crash when atomic bonds stretch or break. Current detection methods are slow or miss these errors entirely. We introduce the Bond Smoothness Characterization Test (BSCT), a fast tool that checks for these artificial bumps by systematically stretching and compressing bonds. We used BSCT as a diagnostic to redesign a model called MinDScAIP. By adjusting its architecture with a differentiable neighbor search and temperature-controlled attention, we smoothed the energy landscape until it became physically realistic. BSCT correlates strongly with expensive evaluations like molecular dynamics but costs a fraction to run. Using BSCT during design yields highly accurate and physically stable models. BSCT is a valuable tool for building reliable models for chemical and materials discovery.