Symbolic Regression Based on Physics Informed Neural Network for Learning Interatomic Potentials

Molecular dynamics is a powerful technique for understanding system dynamics and relies on force-fields to describe the interatomic interactions. These force fields are trained to experimental or quantum mechanical data and over the years have evolved from simple pairwise potentials to the complex Neural Networks. There are two important aspects to evaluate quality of the force-fields - First, the accuracy of the models, and second the computational cost. While simple classical models can perform fast dynamics, they do so at the cost of accuracy. Neural Networks (NN) are more flexible and can capture a wide range of configurations, but that comes at a cost of interpretability. To address these challenges and bridge the gap between physics-based and ML models, we have developed a reinforcement learning workflow that trains Physics Informed Neural Networks to learn the symbolic relation between the atomic positions and energy. We compare the performance of our PINN models with state-of-the-art physics-based and ML models using a representative example of 10 metallic systems. This evaluation includes aspects like global structural characteristics, surface energies, elastic constants, and phonon dispersions. Compared to conventional NN models, we demonstrate a significant improvement in both speed of convergence and solution quality by integrating physics guided layers with NN.