Rethink GraphODE Generalization Within Coupled Dynamical System

Abstract

Coupled dynamical systems govern essential phenomena across physics, biology, and engineering, where components interact through complex dependencies. While Graph Ordinary Differential Equations (GraphODE) offer a powerful framework to model these systems, their generalization capabilities degrade severely under limited observational training data due to two fundamental flaws: (i) the entanglement of static attributes and dynamic states in the initialization process, and (ii) the reliance on context-specific coupling patterns during training, which hinders performance in unseen scenarios. In this paper, we propose a Generalizable GraphODE with disentanglement and regularization (GREAT) to address these challenges. Through systematic analysis via the Structural Causal Model, we identify backdoor paths that undermine generalization and design two key modules to mitigate their effects. The Dynamic-Static Equilibrium Decoupler (DyStaED) disentangles static and dynamic states via orthogonal subspace projections, ensuring robust initialization. Furthermore, the Causal Mediation for Coupled Dynamics (CMCD) employs variational inference to estimate latent causal factors, reducing spurious correlations and enhancing universal coupling dynamics. Extensive experiments across diverse dynamical systems demonstrate that ours outperforms state-of-the-art methods within both in-distribution and out-of-distribution.