Graph ODE with Factorized Prototypes for Modeling Complicated Interacting Dynamics

This paper studies the problem of modeling interacting dynamical systems, which is critical for understanding physical dynamics and biological processes. Recent research predominantly uses geometric graphs to represent these interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Graph ODE with factorized prototypes (GOAT) to address the problem. The core of GOAT is to incorporate factorized prototypes from contextual knowledge into a continuous graph ODE framework. Specifically, GOAT employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of GOAT.