Fluid Simulation on Neural Flow Maps
Yitong Deng Hong-Xing Yu Diyang Zhang Jiajun Wu Bo Zhu
We introduce Neural Flow Maps, a novel simulation method bridging the
emerging paradigm of implicit neural representations with fluid simulation
based on the theory of flow maps, to achieve state-of-the-art simulation of
inviscid fluid phenomena. We devise a novel hybrid neural field representation,
Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a
pyramid of overlapping, multi-resolution, and spatially sparse grids, to
compactly represent long-term spatiotemporal velocity fields at high accuracy.
With this neural velocity buffer in hand, we compute long-term, bidirectional
flow maps and their Jacobians in a mechanistically symmetric manner, to
facilitate drastic accuracy improvement over existing solutions. These
long-range, bidirectional flow maps enable high advection accuracy with low
dissipation, which in turn facilitates high-fidelity incompressible flow
simulations that manifest intricate vortical structures. We demonstrate the
efficacy of our neural fluid simulation in a variety of challenging simulation
scenarios, including leapfrogging vortices, colliding vortices, vortex
reconnections, as well as vortex generation from moving obstacles and density
differences. Our examples show increased performance over existing methods in
terms of energy conservation, visual complexity, adherence to experimental
observations, and preservation of detailed vortical structures.