Future Matters for Present: Towards Effective Physical Simulation over Meshes

This paper investigates the problem of learning mesh-based physical simulations, which is a crucial task with applications in fluid mechanics and aerodynamics. Recent works typically utilize graph neural networks (GNNs) to produce next-time states on irregular meshes by modeling interacting dynamics, and then adopt iterative rollouts for the whole trajectories. However, these methods cannot achieve satisfactory performance in long-term predictions due to the failure of capturing long-term dependency and potential error accumulations. To tackle this, we introduce a new future-to-present learning perspective, and further develop a simple yet effective approach named Foresight And Interpolation (FAIR) for long-term mesh-based simulations. The main idea of our FAIR is to first learn a graph ODE model for coarse long-term predictions and then refine short-term predictions via interpolation. Specifically, FAIR employs a continuous graph ODE model that incorporates past states into the evolution of interacting node representations, which is capable of learning coarse long-term trajectories under a multi-task learning framework. Then, we leverage a channel aggregation strategy to summarize the trajectories for refined short-term predictions, which can be illustrated using an interpolation process. Through pyramid-like alternative propagation between the foresight step and refinement step, our proposed framework FAIR can generate accurate long-term trajectories, achieving a significant error reduction compared with the best baseline on four benchmark datasets. Extensive ablation studies and visualization further validate the superiority of our proposed FAIR.