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。

神经流动图上的流体模拟

Fluid Simulation on Neural Flow Maps

Fluid simulation 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 HelmSim toward an accurate and interpretable simulator for fluid.
Inspired by the Helmholtz theorem, we design a HelmDynamic block to learn the
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 HelmDynamic block into a Multiscale
Integration Network, HelmSim can integrate learned Helmholtz dynamics along
temporal dimension in multiple spatial scales to yield future fluid. Comparing
with previous velocity estimating methods, HelmSim is faithfully derived from
Helmholtz theorem and ravels out complex fluid dynamics with physically
interpretable evidence. Experimentally, our proposed HelmSim achieves the
consistent state-of-the-art in both numerical simulated and real-world observed
benchmarks, even for scenarios with complex boundaries.

本文提出了 HelmSim 作为一种准确且可解释的流体模拟器，通过嵌入 HelmDynamic 模块到多尺度积分网络中，来集成学习到的 Helmholtz 动态，并在多个空间尺度上沿时间维度生成未来的流体，实验证明 HelmSim 在数值模拟和真实观测基准测试中保持了一致的最先进水平，甚至在具有复杂边界的场景下也是如此。

HelmSim: 学习亥姆霍兹动力学进行可解释的流体模拟

HelmSim: Learning Helmholtz Dynamics for Interpretable Fluid Simulation

This paper proposes a novel framework to evaluate fluid simulation methods
based on crowd-sourced user studies in order to robustly gather large numbers
of opinions. The key idea for a robust and reliable evaluation is to use a
reference video from a carefully selected real-world setup in the user study.
By conducting a series of controlled user studies and comparing their
evaluation results, we observe various factors that affect the perceptual
evaluation. Our data show that the availability of a reference video makes the
evaluation consistent. We introduce this approach for computing scores of
simulation methods as visual accuracy metric. As an application of the proposed
framework, a variety of popular simulation methods are evaluated.

本文提出了一种全新的评估流体模拟方法的框架，基于众包式用户研究，以此来收集大量意见以获得精确可靠性，其核心思想是通过用户研究中精心挑选实际应用场景中的参考视频来进行评估，通过进行一系列的控制用户研究和比较他们的评估结果，揭示了影响感知评估的各种因素，数据表明参考视频的可用性使得评估结果更加一致，将此方法引入到计算视觉准确度指标的模拟方法评分中，并应用于对各种流行的模拟方法的评估。