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PGODE: Towards High-quality System Dynamics Modeling
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Proposes PGODE, a prototypical graph ODE that disentangles object-level and system-level contexts from historical trajectories and mixes learned GNN prototypes via context-derived weights, evaluated on physical (Springs, Charged) and molecular (5AWL, 2N5C) dynamics.
Problem
Modeling multi-agent interacting dynamical systems under out-of-distribution shifts in system parameters and complicated underlying rules, where autoregressive GNN rollouts accumulate error and generalize poorly.
Approach
Combine a continuous graph ODE with a mixture of learnable GNN prototypes whose per-object weights come from disentangled object-level and system-level context embeddings (mutual information minimization/maximization with known system parameters), trained with a variational ELBO.
Key results
- On Springs and Charged, PGODE reduces average MSE vs HOPE by 47.40% (ID) and 48.57% (OOD) per the authors.
- On 5AWL and 2N5C, PGODE achieves the lowest MSE across prediction lengths 12 and 24 in both ID and OOD settings.
- Ablations show removing the disentanglement loss or the multi-prototype design degrades performance on all datasets.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PGODE instead of SocialODE | interacting dynamics modeling · Springs ID, prediction length 24, q | MSE × 10^-2: 0.129 -> 0.070 | Helped |
| Use PGODE instead of SocialODE | interacting dynamics modeling · Charged ID, prediction length 24, q | MSE × 10^-2: 2.441 -> 2.037 | Helped |
| Use PGODE instead of HOPE | molecular dynamics modeling · 5AWL ID, prediction length 24, q_x | MSE × 10^-3: 3.495 -> 2.910 | Helped |
| Use PGODE instead of SocialODE | molecular dynamics modeling · 2N5C ID, prediction length 24, q_x | MSE × 10^-3: 2.575 -> 1.960 | Helped |
| Add object-level contexts (ablation) | PGODE · Springs, prediction length 24, q | MSE × 10^-2: 0.106 -> 0.070 | Helped |
| Add system-level contexts (ablation) | PGODE · Springs, prediction length 24, q | MSE × 10^-2: 0.089 -> 0.070 | Helped |
| Use multiple prototypes instead of one (ablation) | PGODE · Springs, prediction length 24, q | MSE × 10^-2: 0.164 -> 0.070 | Helped |
| Add disentanglement loss (ablation) | PGODE · Springs, prediction length 24, q | MSE × 10^-2: 0.073 -> 0.070 | Helped |
Limitations
- Does not model physical symmetry (equivariance)
- Computational cost increases with number of prototypes
Experimental setup
Datasets: Springs Charged 5AWL 2N5C
Benchmarks: Springs Charged 5AWL 2N5C
Metrics: MSE
Baselines: LSTM GRU NODE LG-ODE MPNODE SocialODE HOPE NRI AgentFormer I-GPODE
Builds on: neural ODE LG-ODE HOPE Jensen-Shannon mutual information estimator
Closest papers by meaning
- Rethink GraphODE Generalization within Coupled Dynamical System (ICML 2025 · similarity 0.88)
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- Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems (NeurIPS 2026 · similarity 0.86)
- A Graph Dynamics Prior for Relational Inference (AAAI 2024 · similarity 0.86)
- Prometheus: Out-of-distribution Fluid Dynamics Modeling with Disentangled Graph ODE (ICML 2024 · similarity 0.86)
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