Fast Fluid Simulations in 3D with Physics-Informed Deep Learning

Physically plausible fluid simulations play an important role in modern computer graphics. However, in order to achieve real-time performance, computational speed needs to be traded-off with physical accuracy. Surrogate fluid models based on neural networks are a promising candidate to achieve both: fast fluid simulations and high physical accuracy. However, these approaches do not generalize to new fluid domains, rely on massive amounts of training data or require complex pipelines for training and inference. In this work, we present a 3D extension to our recently proposed fluid training framework, which addresses the aforementioned issues in 2D. Our method allows to train fluid models that generalize to new fluid domains without requiring fluid simulation data and simplifies the training and inference pipeline as the fluid models directly map a fluid state and boundary conditions at a moment t to a subsequent state at t+dt. To this end, we introduce a physics-informed loss function based on the residuals of the Navier-Stokes equations on a 3D staggered Marker-and-Cell grid. Furthermore, we propose an efficient 3D U-Net based architecture in order to cope with the high demands of 3D grids in terms of memory and computational complexity. Our method allows for real-time fluid simulations on a 128x64x64 grid that include various fluid phenomena such as the Magnus effect or Karman vortex streets, and generalize to domain geometries not considered during training. Our method indicates strong improvements in terms of accuracy, speed and generalization capabilities over current 3D NN-based fluid models.