# Machine learning–accelerated computational fluid dynamics

“Machine learning–accelerated computational fluid dynamics” (2021), by Dmitrii Kochkov et al. Physics and Astronomy research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Dmitrii Kochkov, Jamie Smith, Ayya Alieva, Mengqing Wang, Michael P. Brenner, Stephan Hoyer
- Published: May 18, 2021
- Field: Physics and Astronomy
- DOI: https://doi.org/10.1073/pnas.2101784118
- Free PDF: https://arxiv.org/pdf/2102.01010

## Abstract

Numerical simulation of fluids plays an essential role in modeling many physical phenomena, such as weather, climate, aerodynamics, and plasma physics. Fluids are well described by the Navier-Stokes equations, but solving these equations at scale remains daunting, limited by the computational cost of resolving the smallest spatiotemporal features. This leads to unfavorable trade-offs between accuracy and tractability. Here we use end-to-end deep learning to improve approximations inside computational fluid dynamics for modeling two-dimensional turbulent flows. For both direct numerical simulation of turbulence and large-eddy simulation, our results are as accurate as baseline solvers with 8 to 10× finer resolution in each spatial dimension, resulting in 40- to 80-fold computational speedups. Our method remains stable during long simulations and generalizes to forcing functions and Reynolds numbers outside of the flows where it is trained, in contrast to black-box machine-learning approaches. Our approach exemplifies how scientific computing can leverage machine learning and hardware accelerators to improve simulations without sacrificing accuracy or generalization.

Canonical page: https://nerdi.pages.dev/paper/W3128704025
Read three real papers a day in Nerdi (iPhone): https://apps.apple.com/app/apple-store/id6813826387?pt=128757794&ct=web-paper&mt=8