  Fluid prediction 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 HelmFluid toward an accurate and interpretable predictor for fluid.
Inspired by the Helmholtz theorem, we design a HelmDynamics block to learn
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 HelmDynamics block into a
Multiscale Multihead Integral Architecture, HelmFluid can integrate learned
Helmholtz dynamics along temporal dimension in multiple spatial scales to yield
future fluid. Compared with previous velocity estimating methods, HelmFluid is
faithfully derived from Helmholtz theorem and ravels out complex fluid dynamics
with physically interpretable evidence. Experimentally, HelmFluid achieves
consistent state-of-the-art in both numerical simulated and real-world observed
benchmarks, even for scenarios with complex boundaries.
