Real-time simulation of fluid and smoke is a long standing problem in computer graphics. Despite significant progress in the literature, state-of-the-art approaches require large compute resources, making real-time applications impractical. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning methods with the precision of standard fluid solvers to obtain both fast and highly realistic simulations. The proposed method solves the incompressible Euler equations following the standard operator splitting method in which the advection, body forces, and incompressibility parts are solved sequentially. Of these three component parts, the latter consumes the largest computational effort as it requires the solution of an often ill-conditioned sparse linear system. We propose replacement of this system by learning a Convolutional Network (ConvNet) from a large training set of simulations produced by running a traditional offline solver. For obtaining realistic simulations, it is more important to produce a low divergence flow (conforming to boundary conditions) than recovering the exact pressure or velocity, and we propose a tailored loss function for expressing these priorities. ConvNets are amenable to efficient GPU implementations and, unlike exact iterative solvers, have fixed computational complexity and latency. The proposed hybrid approach restricts the learning task to a simple projection relieving the need of modeling the well understood advection and influence of external body forces. We present real-time 2D and 3D simulations of fluids and smoke; the obtained results are realistic and show good generalization properties to unseen geometry.

这项工作提出了一种数据驱动的方法，结合深度学习和标准求解器的精度，通过解决大型稀疏线性系统来快速高度逼真地模拟不可压缩的欧拉方程，得到比最近提出的数据驱动方法更好的2D和3D模拟结果，并展示了良好的泛化性能。

使用卷积网络加速欧拉流体模拟