Unsupervised Deep Learning of Incompressible Fluid Dynamics

In: arXiv:2006.08762 (2020)
 

Abstract

Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer aided aerodynamic design of automobiles or airplanes to simulations of physical effects in CGI to research in meteorology. Recent differentiable fluid simulations allow gradient based methods to optimize e.g. fluid control systems in an informed manner. Solving the partial differential equations governed by the dynamics of the underlying physical systems, however, is a challenging task and current numerical approximation schemes still come at high computational costs. In this work, we propose an unsupervised framework that allows powerful deep neural networks to learn the dynamics of incompressible fluids end to end on a grid-based representation. For this purpose, we introduce a loss function that penalizes residuals of the incompressible Navier Stokes equations. After training, the framework yields models that are capable of fast and differentiable fluid simulations and can handle various fluid phenomena such as the Magnus effect and Kármán vortex streets. Besides demonstrating its real-time capability on a GPU, we exploit our approach in a control optimization scenario.

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Zusätzliches Material

Bibtex

@ARTICLE{wandel-2020-fluid,
    author = {Wandel, Nils and Weinmann, Michael and Klein, Reinhard},
     title = {Unsupervised Deep Learning of Incompressible Fluid Dynamics},
   journal = {arXiv:2006.08762},
      year = {2020},
  abstract = {Fast and stable fluid simulations are an essential prerequisite for applications ranging from
              computer aided aerodynamic design of automobiles or airplanes to simulations of physical effects in
              CGI to research in meteorology. Recent differentiable fluid simulations allow gradient based methods
              to optimize e.g. fluid control systems in an informed manner. Solving the partial differential
              equations governed by the dynamics of the underlying physical systems, however, is a challenging
              task and current numerical approximation schemes still come at high computational costs.
              In this work, we propose an unsupervised framework that allows powerful deep neural networks to
              learn the dynamics of incompressible fluids end to end on a grid-based representation. For this
              purpose, we introduce a loss function that penalizes residuals of the incompressible Navier Stokes
              equations. After training, the framework yields models that are capable of fast and differentiable
              fluid simulations and can handle various fluid phenomena such as the Magnus effect and K{\'a}rm{\'a}n
              vortex streets. Besides demonstrating its real-time capability on a GPU, we exploit our approach in
              a control optimization scenario.},
       url = {https://arxiv.org/abs/2006.08762}
}