Physics-Informed Weakly Supervised Learning For Interatomic Potentials

Machine learning is playing an increasingly important role in computational chemistry and materials science, complementing expensive ab initio and first-principles methods. However, machine-learned interatomic potentials (MLIPs) often struggle with generalization and robustness, leading to unphysical energy and force predictions in atomistic simulations. To address this, we propose a physics-informed, weakly supervised training framework for MLIPs. Our method introduces two novel loss functions: one based on Taylor expansions of the potential energy and another enforcing conservative force constraints. This approach enhances accuracy, particularly in low-data regimes, and reduces the reliance on large, expensive training datasets. Extensive experiments across benchmark datasets show up to 2× reductions in energy and force errors for multiple baseline models. Additionally, our method improves the stability of molecular dynamics simulations and facilitates effective fine-tuning of ML foundation models on sparse, high-accuracy ab initio data. An implementation of our method and scripts for executing experiments are available at \url{https://github.com/nec-research/PICPS-ML4Sci}.

$\textbf{Problem setup.}$Machine learning is increasingly used to speed up simulations in chemistry and materials science, which are often too slow or expensive when using traditional physics-based methods. However, many machine learning models used in this field—called interatomic potentials—can behave unpredictably, especially when they encounter new or limited data. This leads to unrealistic predictions of energy and forces between atoms.$\textbf{Our approach.}$We developed a new training method that teaches machine learning models to better respect the underlying physics of atomic systems. Instead of relying only on large datasets, we added two key components: one that helps the model learn how energy behaves near atoms using Taylor expansions, and another that ensures the predicted forces follow the laws of physics. These additions allow the models to learn more accurately even from small amounts of data.$\textbf{Our contribution and importance.}$Our method makes machine learning models more reliable and efficient for simulating materials and molecules. It cuts prediction errors in half for several widely used models and makes long-term simulations more stable. This means researchers can now use smaller, high-quality datasets to train models that are both accurate and physically meaningful—making advanced materials discovery and chemical simulations faster and more accessible.