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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 theseinteractions, which are then captured by powerful graph neural networks (GNNs).However, predicting interacting dynamics in challenging scenarios such asout-of-distribution shift and complicated underlying rules remains unsolved. Inthis paper, we propose a new approach named Graph ODE with factorizedprototypes (GOAT) to address the problem. The core of GOAT is to incorporatefactorized prototypes from contextual knowledge into a continuous graph ODEframework. Specifically, GOAT employs representation disentanglement and systemparameters to extract both object-level and system-level contexts fromhistorical trajectories, which allows us to explicitly model their independentinfluence and thus enhances the generalization capability under system changes.Then, we integrate these disentangled latent representations into a graph ODEmodel, which determines a combination of various interacting prototypes forenhanced model expressivity. The entire model is optimized using an end-to-endvariational inference framework to maximize the likelihood. Extensiveexperiments in both in-distribution and out-of-distribution settings validatethe superiority of GOAT.

Graph ODE with Factorized Prototypes for Modeling Complicated Interacting Dynamics