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Fluid simulation is a long-standing challenge due to the intrinsichigh-dimensional non-linear dynamics. Previous methods usually utilize thenon-linear modeling capability of deep models to directly estimate velocityfields for future prediction. However, skipping over inherent physicalproperties but directly learning superficial velocity fields will overwhelm themodel from generating precise or physics-reliable results. In this paper, wepropose the HelmSim toward an accurate and interpretable simulator for fluid.Inspired by the Helmholtz theorem, we design a HelmDynamic block to learn theHelmholtz dynamics, which decomposes fluid dynamics into more solvablecurl-free and divergence-free parts, physically corresponding to potential andstream functions of fluid. By embedding the HelmDynamic block into a MultiscaleIntegration Network, HelmSim can integrate learned Helmholtz dynamics alongtemporal dimension in multiple spatial scales to yield future fluid. Comparingwith previous velocity estimating methods, HelmSim is faithfully derived fromHelmholtz theorem and ravels out complex fluid dynamics with physicallyinterpretable evidence. Experimentally, our proposed HelmSim achieves theconsistent state-of-the-art in both numerical simulated and real-world observedbenchmarks, even for scenarios with complex boundaries.

HelmSim: Learning Helmholtz Dynamics for Interpretable Fluid Simulation