Research map / Graph learning / Knowledge and temporal graphs
Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes GraMO, a latent graph state-space simulator that couples graph Laplacian propagation and selective SSM recurrence in one update, evaluated on N-body, MoCap, and robotics trajectory prediction.
Problem
Simulating interacting particle systems requires capturing spatial interactions and long-range temporal dependencies while avoiding error accumulation from autoregressive GNN rollouts over long horizons.
Approach
A single linear latent recurrence in which graph-Laplacian propagation over nodes, a state-dimension mixing matrix, HiPPO-initialized temporal decay, and input-dependent (selective) B, C, and step size are applied jointly to a persistent latent state H_t of shape V x D x N, avoiding node sequencing and separate spatial/temporal stages.
Key results
- On N-body Charged, GraMO reports AMSE 0.790 vs 1.090 for ESTAG (second best), and FMSE 2.410 vs 2.540 for GeoTDM.
- On MoCap Walk, average FMSE 0.117 vs 0.347 for NS-EGNN (second best); on Run, 0.161 vs 0.508.
- On Rope, GraMO FMSE 0.412 vs 0.538 for GeoTDM (second best), reported as the lowest error across all robotics settings.
Surprising findings
- Removing HiPPO initialization or selectivity hurts only moderately on Charged, but removing selectivity raises MoCap Run error to 5.92 from 3.87, a larger degradation than most other ablations on that dataset.
Limitations
- Scaling with graph size is a limitation due to repeated graph-state interactions.
- Theoretical claims rely on assumptions such as uniform per-step approximation error and L>1, and proofs are only partly tied to the implemented model.
Experimental setup
Datasets: Charged particles N-body Spring dynamics N-body Gravity N-body CMU Motion Capture Walk and Run Rope robotics Soft robot Swim soft robot
Benchmarks: N-body charged particles N-body spring dynamics N-body gravity Rope Soft robot Swim CMU MoCap Walk CMU MoCap Run
Metrics: AMSE FMSE
Baselines: ST-GNN ST-TFN ST-SE(3)TR ST-EGNN Koopman EqMotion SVAE GeoTDM GraphMamba ESTAG NS-EGNN STGCN
Builds on: Mamba HiPPO Koopman operator theory EqMotion GeoTDM
Closest papers by meaning
- Scalable Graph Networks for Particle Simulations (AAAI 2021 · similarity 0.88)
- Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics (ICLR 2026 · similarity 0.88)
- Neural Persistence Dynamics (NeurIPS 2024 · similarity 0.87)
- A Graph Dynamics Prior for Relational Inference (AAAI 2024 · similarity 0.86)
- PGODE: Towards High-quality System Dynamics Modeling (ICML 2024 · similarity 0.86)
- Benchmarking Structural Inference Methods for Interacting Dynamical Systems with Synthetic Data (NeurIPS 2024 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.