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Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows

arXiv 1810.08217 ↗First posted 18 Oct 2018cs.LG physics.flu-dyn stat.MLcited by 147

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Abstract (arXiv)

With this study we investigate the accuracy of deep learning models for the inference of Reynolds-Averaged Navier-Stokes solutions. We focus on a modernized U-net architecture, and evaluate a large number of trained neural networks with respect to their accuracy for the calculation of pressure and velocity distributions. In particular, we illustrate how training data size and the number of weights influence the accuracy of the solutions. With our best models we arrive at a mean relative pressure and velocity error of less than 3% across a range of previously unseen airfoil shapes. In addition all source code is publicly available in order to ensure reproducibility and to provide a starting point for researchers interested in deep learning methods for physics problems. While this work focuses on RANS solutions, the neural network architecture and learning setup are very generic, and applicable to a wide range of PDE boundary value problems on Cartesian grids.

Key facts. Cited by 147 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Oct 2018.

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Citing papers per year: 2021: 21; 2022: 31; 2023: 30; 2024: 24; 2025: 23; 2026: 18.

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38 more
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  13. 2023Uncertainty-aware Surrogate Models for Airfoil Flow Simulations with Denoising Diffusion Probabilistic Modelscited by 22
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  23. 2021Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networkscited by 14
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  28. 2021Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order modelscited by 12
  29. 2022Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networkscited by 11
  30. 2025Guiding diffusion models to reconstruct flow fields from sparse datacited by 11
  31. 2021Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulationscited by 10
  32. 2023Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operatorcited by 10
  33. 2021Surrogate Modeling of Fluid Dynamics with a Multigrid Inspired Neural Network Architecturecited by 9
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  35. 2024Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanicscited by 9
  36. 2021SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasetscited by 8
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  38. 2024Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogatescited by 8

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