Combining Physics and Machine Learning: Hybrid Models for Predicting Interatomic Potentials

Constructing accurate Potential Energy Surfaces (PES) is a central task in molecular modeling, as it determines the forces governing nuclear motion and enables reliable quantum dynamics simulations. While ab initio methods can provide accurate PES, they are computationally prohibitive for extensive applications. Alternatively, analytical physics-based models such as the Morse potential offer efficient solutions but are limited by their rigidity and poor generalization to excited states. In recent years, neural networks have emerged as powerful tools for determining PES, due to their universal function approximation capabilities, but they require large training datasets. In this work, we investigate hybrid-residual modeling approaches that combine physics-based potentials with neural network corrections, aiming to leverage both physical priors and data adaptability. Specifically, we compare three hybrid models—APHYNITY, Sequential Phy-ML, and PhysiNet—in their ability to reconstruct the potential energy curve of the ground and first excited states of the hydrogen molecule. Each model integrates a simplified physical representation with a neural component that learns the discrepancies from accurate reference data. Our findings reveal that hybrid models significantly outperform both standalone neural networks and pure physics-based models, especially in low-data regimes. Notably, APHYNITY and Sequential Phy-ML exhibit better generalization and maintain accurate estimation of physical parameters, underscoring the benefits of explicit physics incorporation.