Generalizable Physics Simulation through Compositional Energy Minimization

Learning the dynamics of interacting physical systems is a central challenge in machine learning for the physical sciences. Prevailing architectures such as Graph Neural Networks (GNNs) and feedforward models often fail to explicitly capture the compositional nature of physical laws. Instead of modeling the forces that govern a system, these networks learn to approximate aggregate state transitions. As a result, they lack a causal understanding of the underlying physics interactions, leading to poor generalization in out-of-distribution systems with varying numbers of entities or novel configurations. In this work, we introduce Compositional Potential Minimization (CPM), a framework that casts simulation as an energy minimization procedure over a composition of learned force potentials. Each force component is represented as a separate, interpretable energy landscape, and interaction dynamics emerge from their addition. Inference in CPM is framed as a global energy minimization problem over an arbitrary number of composed functions. Because CPM learns to disentangle separate forces during training, it enables seamless generalization during test time to larger-scale systems and unseen configurations through straightforward compositions of the learned energy components. Our experiments show that CPM significantly outperforms previous state-of-the-art GNN-based solutions in 2D, 3D, and particle-based simulations.