Accelerating Eulerian Fluid Simulation With Convolutional Networks
This addresses the need for faster fluid simulations in applied mathematics, though it is incremental as it builds on existing operator splitting methods.
The paper tackles the problem of efficiently simulating the Navier-Stokes equations for fluid flow by proposing a data-driven approach that uses a convolutional network to solve linear systems in standard solvers, achieving real-time 2D and 3D simulations that outperform recent data-driven methods with realistic results and good generalization.
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.