Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations. Our method solves the incompressible Euler equations using the standard operator splitting method, in which a large sparse linear system with many free parameters must be solved. We use a Convolutional Network with a highly tailored architecture, trained using a novel unsupervised learning framework to solve the linear system. We present real-time 2D and 3D simulations that outperform recently proposed data-driven methods; the obtained results are realistic and show good generalization properties.
翻译:在应用数学中,对流体流的纳维埃-斯托克斯等方程式的有效模拟是一个长期存在的问题,对此,最先进的计算方法需要大量资源。在这项工作中,我们提出一种数据驱动方法,利用深度学习的近似力量和标准解答器的精确度来获得快速和高度现实的模拟。我们的方法用标准的操作员分解方法解决了无法压缩的 Euler 等方程式,在这个方法中,必须解决一个拥有许多自由参数的庞大稀疏线性线性系统。我们使用一个具有高度定制的建筑的革命网络,我们用一个新型的、不受监督的学习框架来培训,解决线性系统。我们提出实时的2D和3D模拟,这些模拟超过了最近提出的数据驱动方法;获得的结果是现实的,并显示出良好的概括性。