Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems

2026-06-08

AI Summary

Existing approaches to modeling interacting dynamical systems often suffer from long-term error accumulation due to spatiotemporal decoupling and autoregressive prediction, struggling to simultaneously capture spatial interactions and long-range temporal dependencies. This work proposes a latent-space simulator that, for the first time, unifies state space models and graph neural networks within a single recurrent framework. Leveraging the Mamba architecture, it enables linear state updates and introduces input-dependent dynamic coefficients to adaptively model both graph-based interactions and temporal evolution. By overcoming the limitations of local interaction assumptions and spatiotemporal disentanglement inherent in conventional methods, the proposed approach achieves significantly lower prediction errors on N-body systems, motion capture, and robotic datasets, with particularly pronounced improvements in long-horizon forecasting tasks.

Abstract

Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies. Graph neural networks (GNNs) provide a natural representation but typically rely on autoregressive rollouts and treat spatial and temporal dynamics separately, leading to error accumulation over long horizons. Existing approaches also focus on local interactions and short temporal contexts, limiting their ability to capture multi-hop dependencies and global structure. We introduce the Graph Mamba Operator (GraMO), a latent-space simulator that integrates state-space models with graph-based interaction learning. In contrast to prior work that sequences nodes or applies spatial and temporal updates in separate stages, GraMO couples graph-based interactions and temporal state updates within a single recurrence. The update is linear in the latent state, with input-dependent coefficients that adapt across regimes. We evaluate GraMO on N-body systems, motion capture, and robotics datasets, achieving the lowest error across benchmarks and the largest gains in long-horizon prediction.

Problem

• interacting dynamical systems
• spatial-temporal dependencies
• long-horizon prediction
• graph neural networks
• multi-hop dependencies

Innovation

• Graph Mamba Operator
• state-space models
• latent-space simulation
• long-horizon prediction
• graph neural networks