Graph ODE with Factorized Prototypes for Modeling Complicated
  Interacting Dynamics
Xiao Luo Yiyang Gu Huiyu Jiang Jinsheng Huang Wei Ju Ming Zhang Yizhou Sun
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.