Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer aided aerodynamic design of automobiles or airplanes to simulations of physical effects in CGI to research in meteorology. Recent differentiable fluid simulations allow gradient based methods to optimize e.g. fluid control systems in an informed manner. Solving the partial differential equations governed by the dynamics of the underlying physical systems, however, is a challenging task and current numerical approximation schemes still come at high computational costs. In this work, we propose an unsupervised framework that allows powerful deep neural networks to learn the dynamics of incompressible fluids end to end on a grid-based representation. For this purpose, we introduce a loss function that penalizes residuals of the incompressible Navier Stokes equations. After training, the framework yields models that are capable of fast and differentiable fluid simulations and can handle various fluid phenomena such as the Magnus effect and K\'arm\'an vortex streets. Besides demonstrating its real-time capability on a GPU, we exploit our approach in a control optimization scenario.

本篇论文提出了一种基于物理约束的训练方法，利用卷积神经网络在单次前向传播中将流体状态从时间点 t 映射到时间点 t + dt 的新框架来加速流体模拟，并在控制实验中证明了模型的可靠性与高效性。

从头学习不可压缩流体动力学 -- 朝向快速、可微分的流体模型的推广