  This paper studies the problem of modeling multi-agent dynamical systems,
where agents could interact mutually to influence their behaviors. Recent
research predominantly uses geometric graphs to depict these mutual
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 Prototypical Graph ODE (PGODE) to
address the problem. The core of PGODE is to incorporate prototype
decomposition from contextual knowledge into a continuous graph ODE framework.
Specifically, PGODE 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 PGODE compared to various baselines.
