用状态空间模型融合图结构，提升粒子系统长期预测精度。
Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
- 图结构与时序更新在单一递归中耦合，避免误差累积。
- 在多体系统等数据集上，长期预测误差最低，提升显著。
- 适合需要建模复杂交互与长程依赖的物理仿真任务。
建模相互作用的动力系统需同时捕捉空间关联与长程时序依赖。图神经网络（GNN）虽提供自然表征，但通常依赖自回归推演，并将空间与时间动态分开处理，导致长时程预测中误差累积。现有方法也多关注局部交互与短时上下文，难以捕捉多跳依赖与全局结构。本文提出图态空间算子（GraMO），一种嵌入空间的模拟器，将状态空间模型与基于图的交互学习结合。与以往按节点序列化或分阶段处理空间与时间更新不同，GraMO在单次递归中耦合图交互与时序状态更新。更新过程对潜在状态为线性，系数随输入自适应变化，可跨不同动态模式调整。我们在多体系统、动作捕捉及机器人数据集上评估GraMO，结果表明其在各基准测试中误差最低，尤其在长时程预测中表现最优。
原文摘要 · Abstract (English)
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.
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