A fully-differentiable compressible high-order computational fluid dynamics solver
This addresses computational bottlenecks in fluid dynamics for engineering applications, representing an incremental advance by extending differentiable methods to 3D compressible flows.
The paper tackles the high computational cost of simulating compressible fluid flows by developing a fully-differentiable 3D framework using high-order numerical methods, enabling end-to-end optimization to improve numerical schemes, such as substituting conventional flux functions with neural networks.
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes equations govern compressible flows and allow for complex phenomena like turbulence and shocks. Despite tremendous progress in hardware and software, capturing the smallest length-scales in fluid flows still introduces prohibitive computational cost for real-life applications. We are currently witnessing a paradigm shift towards machine learning supported design of numerical schemes as a means to tackle aforementioned problem. While prior work has explored differentiable algorithms for one- or two-dimensional incompressible fluid flows, we present a fully-differentiable three-dimensional framework for the computation of compressible fluid flows using high-order state-of-the-art numerical methods. Firstly, we demonstrate the efficiency of our solver by computing classical two- and three-dimensional test cases, including strong shocks and transition to turbulence. Secondly, and more importantly, our framework allows for end-to-end optimization to improve existing numerical schemes inside computational fluid dynamics algorithms. In particular, we are using neural networks to substitute a conventional numerical flux function.