# A fully-differentiable compressible high-order computational fluid dynamics solver

arXiv: https://arxiv.org/abs/2112.04979 · HTML: https://mlsanity.com/paper/2112.04979/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 9 Dec 2021.

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Enhancement of shock-capturing methods via machine learning](https://mlsanity.com/paper/2002.02521/) (2020)
- [Consistent and symmetry preserving data-driven interface reconstruction for the level-set method](https://mlsanity.com/paper/2104.11578/) (2021)

## Built on by (most cited first, 2 of 2)

- [A probabilistic, data-driven closure model for RANS simulations with aleatoric, model uncertainty](https://mlsanity.com/paper/2307.02432/) (2023)
- [Deep Neural Networks to Correct Sub-Precision Errors in CFD](https://mlsanity.com/paper/2202.04233/) (2022)

## Abstract (arXiv)

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.