Rethink GraphODE Generalization within Coupled Dynamical System

Guancheng Wan, Zijie Huang, Wanjia Zhao, Xiao Luo, Yizhou Sun, Wei Wang

TL;DR: We propose GREAT, a GraphODE framework that disentangles static and dynamic states, regularizes coupling dynamics, and significantly improves generalization across diverse dynamical systems.

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.

Lay Summary: Many phenomena in science and engineering, from interacting particles in physics to networks in biology, involve interconnected parts evolving together over time. We use powerful AI tools called Graph Ordinary Differential Equations (GraphODEs) to model these complex "coupled dynamical systems." However, these models often struggle to predict new situations accurately when they've only learned from limited data. We discovered two main reasons: First, the models tend to mix up unchanging properties (like an object's material) with changing states (like its movement). Second, they often learn interaction patterns that are specific only to the training data, rather than the universal underlying laws. To fix this, we developed "GREAT," a new GraphODE framework. Using causal reasoning, we designed two key components: one module carefully separates the static properties from the dynamic states, ensuring a clean start. The other helps the model learn the true, universal rules of interaction, ignoring misleading patterns from the training data. Our experiments show that GREAT significantly outperforms existing methods, especially when predicting unseen scenarios. This work offers a more robust way to understand and forecast the behavior of complex, interconnected systems in the real world.

Primary Area: Applications->Chemistry, Physics, and Earth Sciences

Keywords: Graph Machine Learning, GraphODE, Dynamical System

Submission Number: 9093