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

Tai Hoang, Alessandro Trenta, Alessio Gravina, Niklas Freymuth, Philipp Becker, Davide Bacciu, Gerhard Neumann

Keywords: Graph Neural Simulators, Long-range interactions, Learning Simulators, AI4Science

TL;DR: We propose a novel Graph Neural Simulator that preserves information during propagation, enabling it to model complex physical dynamical systems with long-range dependencies.

Abstract: Learning to simulate complex physical systems from data has emerged as a promising way to overcome the limitations of traditional numerical solvers, which often require prohibitive computational costs for high-fidelity solutions. Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data, yet often struggle to capture long-range interactions and suffer from error accumulation under autoregressive rollouts. To address these challenges, we propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics. This structure guarantees preservation of information across the graph, while extending to port-Hamiltonian systems allows the model to capture a broader class of dynamics, including non-conservative effects. IGNS further incorporates a warmup phase to initialize global context, geometric encoding to handle irregular meshes, and a multi-step training objective to reduce rollout error. To evaluate these properties systematically, we introduce new benchmarks that target long-range dependencies and challenging external forcing scenarios. Across all tasks, IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems.

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Submission Number: 5