Deep reinforcement learning of viscous incompressible flow

We develop a new computational method to solve viscous incompressible fluid flow. This method is an extension of the Derivative-Free Loss Method, which solves elliptic and parabolic partial differential equations using Brownian motion, the Feynman-Kac formula, and reinforcement learning. Herein we derive a martingale condition and directly incorporate a projection of the velocity to solve the incompressible Navier-Stokes equations. Our method is mesh-free, scalable, and flexible, as demonstrated with several test cases.