Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics

The introduction of Information-preserving Graph Neural Simulators (IGNS) marks a significant advancement in the simulation of complex physical systems. Traditional numerical solvers often face prohibitive computational costs and struggle with long-range interactions, leading to error accumulation. IGNS, built on Hamiltonian dynamics, addresses these challenges by preserving information across the graph and capturing a broader class of dynamics, including non-conservative effects. This model incorporates a warmup phase for global context initialization, geometric encoding for irregular meshes, and a multi-step training objective to minimize rollout error. Systematic evaluations through new benchmarks targeting long-range dependencies demonstrate that IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under complex dynamical conditions. This development is crucial for various scientific and engineering applications, as it enhances the ability to…