Neural Monte Carlo Fluid Simulation

The idea of using a neural network to represent continuous vector fields (i.e., neural fields) has become popular for solving PDEs arising from physics simulations. Here, the classical spatial discretization (e.g., finite difference) of PDE solvers is replaced with a neural network that models a differentiable function, so the spatial gradients of the PDEs can be readily computed via autodifferentiation. When used in fluid simulation, however, neural fields fail to capture many important phenomena, such as the vortex shedding experienced in the von Kármán vortex street experiment. We present a novel neural network representation for fluid simulation that augments neural fields with explicitly enforced boundary conditions as well as a Monte Carlo pressure solver to get rid of all weakly enforced boundary conditions. Our method, the Neural Monte Carlo method (NMC), is completely mesh-free, i.e., it doesn't depend on any grid-based discretization. While NMC does not achieve the state-of-the-art accuracy of the well-established grid-based methods, it significantly outperforms previous mesh-free neural fluid methods on fluid flows involving intricate boundaries and turbulence regimes.