Molecular physics-informed neural network (mPINN) for solving the molecular dynamics equation of motion with energy conservation

Temoor Muther, Vuong Van Pham, Amirmasoud Kalantari Dahaghi

Abstract Machine learning is increasingly utilized in molecular dynamics simulations to investigate complex system properties across disciplines ranging from chemical and physical sciences to engineering. However, these methods often require large datasets for model training and may not fully adhere to physical principles, limiting their scientific explainability. Furthermore, the model training remains highly challenging under sparse data. To overcome these limitations, this paper introduces the Molecular Physics-Informed Neural Network (mPINN) framework, designed to solve Newton’s equations of motion for multi-body atomistic interactions without relying on prior observational time-series data. By directly embedding the governing principles of molecular dynamics into the neural network training process, the mPINN promotes physical consistency, ensuring that predicted trajectories adhere to conserved thermodynamic quantities. This methodology replaces unconstrained empirical data-fitting with mathematically bound physical relationships, yielding stable and physically valid performance across continuous temporal domains. Unlike traditional MD engines that rely on step-by-step discrete integration, the mPINN operates within a continuous time framework during each training iteration. This approach effectively alleviates issues related to timestep selection and stability commonly faced in discrete simulations. The results demonstrate that the mPINN architecture functions as a reliable, physics-constrained machine learning framework capable of delivering high-fidelity trajectory predictions for complex multi-body molecular systems.