Neural Monte Carlo Fluid Simulation

SIGGRAPH 2024

Pranav Jain, University of Southern California

Ziyin Qu, University of Pennsylvania

Peter Yichen Chen, MIT CSAIL

Oded Stein, University of Southern California

Figure 1. Our method simulates fluids in the presence of obstacles with a combined neural network and Monte Carlo approach to operator splitting for the Navier Stokes equations. With our method, we can simulate important qualitative vorticity-based phenomena, such as vortex shedding in the von Kármán vortex street experiment, previous neural spatial representation papers [Chen et al. 2023] cannot (left).

Abstract

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 gridbased methods, it significantly outperforms previous mesh-free neural fluid methods on fluid flows involving intricate boundaries and turbulence regimes.

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Acknowledgements

We thank Bailey Miller and Rohan Sawhney for technical help with WoSt [Sawhney et al. 2023].We thank Rundi Wu and Honglin Chen for technical help with previous work. We thank Sifan Wang and Shyam Sankaran for technical help with Wang et al. [2023].