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.

我们引入了神经流图（Neural Flow Maps）这种新颖的模拟方法，将隐式神经表示的新兴范式与基于流图理论的流体模拟相结合，实现了无粘流体现象的最先进模拟。我们设计了一种新颖的混合神经场表示，即空间稀疏神经场（Spatially Sparse Neural Fields，SSNF），它将小型神经网络与具有重叠、多分辨率和空间稀疏网格的金字塔结合起来，以高准确性紧凑地表示长期时空速度场。在这个神经速度缓冲区的基础上，我们以机械对称的方式计算长期的双向流图及其雅各布矩阵，从而显著提高了现有解决方案的准确性。这些长程双向流图实现了高精度的平流，低耗散，进而促进了具有高保真度的不可压缩流体模拟，从而展现了复杂的旋涡结构。我们展示了神经流体模拟在各种具有挑战性的模拟场景中的有效性，包括跳跃涡旋、碰撞涡旋、涡旋重连接，以及由移动障碍物和密度差异引起的涡旋生成。我们的实例展示了相对现有方法在能量守恒、视觉复杂度、与实验观察的一致性以及对详细旋涡结构的保护方面的性能提升。