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

2025-11-11

AI Summary

Existing graph neural simulators (GNSs) struggle to model long-range physical interactions and suffer from severe error accumulation in autoregressive rollouts, limiting high-fidelity simulation of complex dynamical systems. To address this, we propose the Information-Preserving Graph Neural Simulator (IGNS), the first framework to embed Hamiltonian dynamics and port-Hamiltonian system principles into a graph neural architecture. IGNS integrates geometric positional encoding, global contextual initialization, and a multi-step rollout warmup training strategy to explicitly model non-conservative force fields and energy evolution on irregular meshes. Evaluated on a newly constructed benchmark featuring strong long-range dependencies and external forcing, IGNS achieves substantial improvements in simulation accuracy and long-term stability—reducing prediction error by 32%–47% compared to prior methods. This work establishes a new paradigm for interpretable, robust, and physically grounded modeling of complex physical systems.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Graph-based Machine Learning
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Addresses poor long-range interaction modeling in graph neural simulators
• Reduces error accumulation during autoregressive simulation rollouts
• Extends Hamiltonian dynamics to capture non-conservative physical effects

Innovation

• Uses Hamiltonian dynamics for information preservation
• Extends to port-Hamiltonian systems for broader dynamics
• Incorporates warmup phase and geometric encoding techniques