Physics-Inspired Neural Graph ODE for Long-term Dynamical Simulation

Simulating and modeling the long-term dynamics of multi-object physical systems is an essential and challenging task. Current studies model the physical systems utilizing Graph Neural Networks (GNNs) with equivariant properties. Specifically, they model the dynamics as a sequence of discrete states with a fixed time interval and learn a direct mapping for all the two adjacent states. However, this direct mapping overlooks the continuous nature between the two states. Namely, we have verified that there are countless possible trajectories between two discrete dynamic states in current GNN-based direct mapping models. This issue greatly hinders the model generalization ability, leading to poor performance of the long-term simulation. In this paper, to better model the latent trajectory through discrete supervision signals, we propose a Physics-Inspired Neural Graph ODE (PINGO) algorithm. In PINGO, to ensure the uniqueness of the trajectory, we construct a Physics-Inspired Neural ODE framework to update the latent trajectory. Meanwhile, to effectively capture intricate interactions among objects, we use a GNN-based model to parameterize Neural ODE in a plug-and-play manner. Furthermore, we prove that the discrepancy between the learned trajectory of PIGNO and the true trajectory can be theoretically bounded. Extensive experiments verify our theoretical findings and demonstrate that our model yields an order-of-magnitude improvement over the state-of-the-art baselines, especially on long-term predictions and roll-out errors.