Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D

In: Physics of Fluids (AIP) (2021)
 

Abstract

Physically plausible fluid simulations play an important role in modern computer graphics and engineering. 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 have the potential to achieve both, fast fluid simulations and high physical accuracy. However, these approaches rely on massive amounts of training data, require complex pipelines for training and inference or do not generalize to new fluid domains. In this work, we present significant extensions to a recently proposed deep learning framework, which addresses the aforementioned challenges in 2D. We go from 2D to 3D and propose an efficient architecture to cope with the high demands of 3D grids in terms of memory and computational complexity. Furthermore, we condition the neural fluid model on additional information about the fluid's viscosity and density which allows simulating laminar as well as turbulent flows based on the same surrogate model. Our method allows to train fluid models without requiring fluid simulation data beforehand. Inference is fast and simple, as the fluid model directly maps a fluid state and boundary conditions at a moment t to a subsequent fluid state at t+dt. We obtain 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.

Bilder

Zusätzliches Material

  • Paper (PDF-Dokument, 5.3 MB)
  • Video (MPEG-4-Video, 41 MB)

Bibtex

@ARTICLE{wandel-2020-3Dfluid,
    author = {Wandel, Nils and Weinmann, Michael and Klein, Reinhard},
     title = {Teaching the Incompressible Navier-Stokes Equations to Fast Neural Surrogate Models in 3D},
   journal = {Physics of Fluids (AIP)},
      year = {2021},
  abstract = {Physically plausible fluid simulations play an important role in modern computer graphics and
              engineering. 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 have the
              potential to achieve both, fast fluid simulations and high physical accuracy. However, these
              approaches rely on massive amounts of training data, require complex pipelines for training and
              inference or do not generalize to new fluid domains.
              In this work, we present significant extensions to a recently proposed deep learning framework,
              which addresses the aforementioned challenges in 2D. We go from 2D to 3D and propose an efficient
              architecture to cope with the high demands of 3D grids in terms of memory and computational
              complexity. Furthermore, we condition the neural fluid model on additional information about the
              fluid's viscosity and density which allows simulating laminar as well as turbulent flows based on
              the same surrogate model.
              Our method allows to train fluid models without requiring fluid simulation data beforehand.
              Inference is fast and simple, as the fluid model directly maps a fluid state and boundary conditions
              at a moment t to a subsequent fluid state at t+dt. We obtain 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.},
       url = {https://arxiv.org/abs/2012.11893}
}