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Rethink GraphODE Generalization within Coupled Dynamical System

ICML 2025 · Probabilistic and scientific modeling › Dynamical systems · approach: Switching and law-discovery dynamics

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Proposes GREAT, a generalizable GraphODE that disentangles static and dynamic states via orthogonal subspace projections and applies variational causal mediation over coupling factors to improve ID and OOD generalization on coupled dynamical systems.

Problem

GraphODE models trained on partially observed, limited trajectories generalize poorly to unseen scenarios because static attributes entangle with dynamic initial states and context-specific coupling patterns bias the learned dynamics.

Approach

Uses a Structural Causal Model to identify two backdoor paths, then adds a Dynamic-Static Equilibrium Decoupler (orthogonal static/dynamic subspace projections with an orthogonality loss plus Hawkes-style augmentation) and Causal Mediation for Coupled Dynamics (Gumbel-Softmax coupling factor estimator with a KL regularizer against a uniform prior) to a GraphODE.

Key results

• On SPRING in-distribution, GREAT achieves RMSE 3.687 and MAPE 2.348 (x10^-1), beating the best baseline TREAT (3.892 / 2.748) per the paper's Table 1.
• GREAT is reported best across all three datasets in both ID and OOD settings, with the paper noting larger gains in OOD scenarios.
• Ablation on SPRING shows DyStaED and CMCD each improve performance, and combining both gives the lowest RMSE in ID and OOD settings.

Measured effects reported in the paper

Limitations

• Evaluated only on three simulated coupled-system benchmarks (SPRING, CHARGED, PENDULUM).
• Orthogonality between subspaces is enforced by a soft loss rather than guaranteed by construction.

Experimental setup

Datasets: SPRING CHARGED PENDULUM

Benchmarks: SPRING CHARGED PENDULUM

Metrics: RMSE MAPE

Baselines: VAR LSTM LatentODE HODEN TRS-ODEN LG-ODE SocialODE PGODE TREAT

Builds on: Neural ODE LG-ODE TREAT PGODE Gumbel-Softmax

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