Learning Interatomic Potentials from First Principles Data Using Symbolic Regression

Fast accurate and interpretable interatomic potentials are essential for molecular dynamics (MD) simulations, yet traditional methods—relying on predefined functional forms and manual tuning—are labor-intensive and limited in flexibility. Here, we introduce a symbolic regression approach driven by reinforcement learning (RL) framework to automate the discovery of interpretable interatomic potential models. We show that this approach offers a scalable, efficient solution across multiple materials and systems, reducing development time from months or years to hours or days. Our framework integrates equation learner networks with MCTS-based symbolic regression to systematically explore a vast function space, identifying closed-form expressions that encapsulate essential physical insights. MCTS guides this exploration by pruning suboptimal equations while refining promising candidates, resulting in interpretable models that retain the transparency of classical potentials. These models integrate seamlessly into MD workflows, boosting computational efficiency without sacrificing clarity—a key advantage over
black-box machine learning models. We validate this approach using transition metals, with copper as a case study. Trained on density functional theory (DFT) data, the RL-discovered potentials accurately predict essential material properties—including elastic coefficients, surface energies, equations of state, and melting points—critical for understanding material behavior. Moreover, these models main-
tain the computational speed required for large-scale MD simulations, meeting practical demands for performance. A key strength of our framework is its generality: unlike traditional approaches tailored to specific systems, our RL-based Symbolic regression adapts easily across diverse elements and compounds.
This adaptability facilitates rapid exploration of material properties, empowering researchers to discover new potentials efficiently and accelerating materials innovation. Our work represents a paradigm shift in interatomic potential development, blending the precision of machine learning with the interpretability
of symbolic expressions. By automating the discovery process, we enable faster, more reliable dynamical predictions of complex material behavior, enhancing the predictive power of MD simulations.