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CSG-ODE: ControlSynth Graph ODE For Modeling Complex Evolution of Dynamic Graphs
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Proposes CSG-ODE, a VAE-based graph neural ODE with information-propagation edge importance and nonlinear ODE sub-networks for irregular dynamic graphs, plus a stable variant SCSG-ODE with antisymmetric weights.
Problem
Graph neural ODE models for incomplete, irregularly sampled dynamic graphs struggle to capture time-varying inter-node relationships and nonlinear node state evolution.
Approach
Combines a communicability-derivative (Fréchet derivative) based edge importance weight with latent correlations to guide adaptive graph convolutional recurrent encoding, and decodes with an ODE that includes a control term from a GNN plus multiple nonlinear sub-networks; SCSG-ODE constrains the weight matrix to be antisymmetric for stability.
Key results
- On interpolation, CSG-ODE achieves MSE 0.1386e-2 on Springs at 80% observation vs 0.2313e-2 for LG-ODE (best prior listed).
- On extrapolation motion-walk at 40% ratio, CSG-ODE reaches 0.1791e-2 MSE vs 0.3835e-2 for LG-ODE.
- SCSG-ODE shows roughly half the standard deviation of CSG-ODE across subsampling ratios on motion-walk (e.g., 0.0056 vs 0.0092 at 40%), but with higher mean error (0.2304 vs 0.1883).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use CSG-ODE instead of LG-ODE | dynamic graph prediction · Motion-walk interpolation 40% | MSE ×10−2: 0.0823 -> 0.0439 | Helped |
| use CSG-ODE instead of LG-CSODE | dynamic graph prediction · Charged interpolation 40% | MSE ×10−2: 0.7794 -> 0.7947 | Hurt |
| use CSG-ODE instead of LG-ODE | dynamic graph prediction · Motion-jump extrapolation 40% | MSE ×10−2: 0.2743 -> 0.1393 | Helped |
| replace mean-observation node representations with adaptive node representation matrix Q (ablation) | CSG-ODE · Springs interpolation 40% | MSE ×10−2: 0.1550 -> 0.1520 | Hurt |
| add information propagation-based inter-node importance weights (ablation) | CSG-ODE · Springs interpolation 40% | MSE ×10−2: 0.1841 -> 0.1550 | Helped |
| add control function g(·) (ablation) | CSG-ODE · Springs interpolation 40% | MSE ×10−2: 0.1655 -> 0.1550 | Helped |
| add the nonlinear term (ablation) | CSG-ODE · Springs interpolation 40% | MSE ×10−2: 0.1913 -> 0.1550 | Helped |
| constrain weight matrices to learnable antisymmetric forms | SCSG-ODE · Motion-walk extrapolation 40% | MSE ×10−2 standard deviation: 0.0092 -> 0.0056 | Helped |
Surprising findings
- SCSG-ODE trades higher mean error for lower run-to-run variance, with CSG-ODE slightly better on mean MSE across tasks.
Limitations
- Assumes the underlying interaction graph is static over time, which does not hold in some physical systems.
- Ignores environmental changes, noise, and latent unmodeled dynamics; errors accumulate.
- Numerical error from ODE solving (Euler) is unavoidable; computational efficiency not addressed for large graphs.
Experimental setup
Datasets: Springs Charged CMU motion capture (walk subject 35, jump subject 118) PEMS08
Benchmarks: Springs Charged CMU motion capture walk CMU motion capture jump PEMS08
Metrics: MSE
Baselines: Latent-ODE Weight-Decay Edge-GNN NRI+RNN LG-ODE LG-CSODE
Builds on: LG-ODE ControlSynth ODE (CSODE) Latent ODE Graph ODE in VAE framework NRI
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