Learning from the Future: Improve Long-term Mesh-based Simulation with Foresight

Xiao Luo, Junyu Luo, Huiyu Jiang, Wei Ju, Carl Yang, Ming Zhang, Yizhou Sun

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: Dynamical System, Neural ODE, Graph Neural Network, Physics Simulation

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Abstract: This paper studies the problem of learning mesh-based physical simulations, a crucial task with applications in fluid mechanics and aerodynamics. Recent works typically utilize graph neural networks 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 accumulation. 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 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, \method{} can generate accurate long-term trajectories, achieving an error reduction of up to 25.4% on benchmark datasets. Extensive ablation studies and visualization further validate the superiority of the proposed FAIR.

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Submission Number: 2108