{"ID":2843370,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08185","arxiv_id":"2511.08185","title":"Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics","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 that facilitates PDE matching, where the trajectory produced by integrating the port-Hamiltonian core aligns with the ground-truth trajectory, thereby reducing 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. Our project page: https://thobotics.github.io/neural_pde_matching.","short_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...","url_abs":"https://arxiv.org/abs/2511.08185","url_pdf":"https://arxiv.org/pdf/2511.08185v2","authors":"[\"Tai Hoang\",\"Alessandro Trenta\",\"Alessio Gravina\",\"Niklas Freymuth\",\"Philipp Becker\",\"Davide Bacciu\",\"Gerhard Neumann\"]","published":"2025-11-11T12:53:56Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}