HelmSim: Learning Helmholtz Dynamics for Interpretable Fluid Simulation

Lanxiang Xing, Haixu Wu, Yuezhou Ma, Jianmin Wang, Mingsheng Long

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Keywords: Interpretable fluid simulation, Helmholtz decomposition

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TL;DR: We present the HelmSim for fluid simulation by learning Helmholtz Dynamics, which ravels out intricate dynamics and brings physical interpretability.

Abstract: Fluid simulation is a long-standing challenge due to the intrinsic high-dimensional non-linear dynamics. Previous methods usually utilize the non-linear modeling capability of deep models to directly estimate velocity fields for future prediction. However, skipping over inherent physical properties but directly learning superficial velocity fields will overwhelm the model from generating precise or physics reliable results. In this paper, we propose the HelmSim toward an accurate and interpretable simulator for fluid. Inspired by Helmholtz theorem, we design a HelmDynamic block to learn the Helmholtz dynamics, which decomposes fluid dynamics into more solvable curl-free and divergence-free parts, physically corresponding to potential and stream functions of fluid. By embedding the HelmDynamic block into a Multiscale Intergation Network, HelmSim can integrate learned Helmholtz dynamics along temporal dimension in multiple spatial scales to yield future fluid. Comparing with previous velocity estimating methods, HelmSim is faithfully derived from Helmholtz theorem and ravels out complex fluid dynamics with physically interpretable evidence. Experimentally, our proposed HelmSim achieves the consistent state-of-the-art in both numerical simulated and real-world observed benchmarks, even for scenarios with complex boundaries.

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Submission Number: 622