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Fluid prediction 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 HelmFluid toward an accurate and interpretable predictor for fluid.Inspired by the Helmholtz theorem, we design a HelmDynamics block to learnHelmholtz dynamics, which decomposes fluid dynamics into more solvablecurl-free and divergence-free parts, physically corresponding to potential andstream functions of fluid. By embedding the HelmDynamics block into aMultiscale Multihead Integral Architecture, HelmFluid can integrate learnedHelmholtz dynamics along temporal dimension in multiple spatial scales to yieldfuture fluid. Compared with previous velocity estimating methods, HelmFluid isfaithfully derived from Helmholtz theorem and ravels out complex fluid dynamicswith physically interpretable evidence. Experimentally, HelmFluid achievesconsistent state-of-the-art in both numerical simulated and real-world observedbenchmarks, even for scenarios with complex boundaries.

HelmFluid: Learning Helmholtz Dynamics for Interpretable Fluid Prediction