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A framework for fluid flow (Reynolds-averaged Navier Stokes) predictions with deep learning

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Deep Flow Prediction is a framework for fluid flow (Reynolds-averaged Navier Stokes) predictions with deep learning. It contains code for data generation, network training, and evaluation. Linux is highly recommended, and assumed as OS the following.

Full details can be found in the arXiv paper from 2018 below, which was later on published in the AIAA Journal as "Deep learning methods for Reynolds-averaged Navier-Stokes simulations of airfoil flows":

Authors: N. Thuerey, K. Weissenow, L. Prantl, Xiangyu Hu With additional code contributions from: H. Mehrotra, N. Mainali

For additional physics-based deep learning works please check out, and

If you find this codebase useful, please cite our paper via:

  title={Deep learning methods for Reynolds-averaged Navier--Stokes simulations of airfoil flows},
  author={Thuerey, Nils and Wei{\ss}enow, Konstantin and Prantl, Lukas and Hu, Xiangyu},
  journal={AIAA Journal}, year={2020},
  volume={58}, number={1}, pages={25--36},
  publisher={American Institute of Aeronautics and Astronautics}

An example inference result

A quick how-to

All scripts below assume they're executed from their respective directories.

Required software

This codebase requires PyTorch and numpy for the deep learning part, and openfoam and gmsh for data generation and meshing (you don't need the latter two if you download the pre-computed training data below). To install these under linux run, use e.g.:

sudo pip install torch numpy
sudo apt-get install openfoam5 gmsh
(Details can be found on the installation pages of PyTorch and OpenFOAM.)

Data generation

Note that you can skip the next two steps if you download the training data packages below. Simply make sure you have

in the source directory, then you can continue with the training step.

Download airfoils

First, enter the

directory. Download the airfoil profiles by running
, this will create
directories. (The latter contains a subset that shouldn't be used for training.) The airfoild database should contain 1498 files afterwards.

Generate data

Now run

python ./
to generate a first set of 100 airfoils. This script executes openfoam and runs gmsh for meshing the airfoil profiles.

has finished, you should find 100 .npz files in a new directory called
. You can call this script repeatedly to generate more data, or adjust the
variables to generate more samples with a single call. For a first test, 100 samples are sufficient, for higher quality models, more than 10k are recommended..

Output files are saved as compressed numpy arrays. The tensor size in each sample file is 6x128x128 with dimensions: channels, x, y. The first three channels represent the input, consisting (in this order) of two fields corresponding to the freestream velocities in x and y direction and one field containing a mask of the airfoil geometry as a mask. The last three channels represent the target, containing one pressure and two velocity fields.

Convolutional neural network training

Training and neural network architecture overview

Switch to the directory containing the training scripts, i.e.,

, and execute
python ./
. By default, this will execute a short training run with 10k iterations on the GPU, loading all data that is available in
. The L1 validation loss is printed during training, and should decrease significantly. Once the script has finished, it will save the trained model as

If you don't have a working GPU, you can use '' to train a smaller model on the CPU.

A sample image will be generated for each epoch in the

directory. Optionally, you can also save txt files with the loss progression (see
in the script). explain created files:

Test evaluation

To compute relative inference errors for a test data set, you can use the

script. By default, it assumes that the test data samples (with the same file format as the training samples) are located in
. Hence, you either have to generate data in a new directory with the
script from above, or download the test data set via the link below.

The model exponent

is set in the
script, so e.g. make sure to reduce it to 3 when evaluating a model trained by ''.

Once the test data is in place, execute

python ./
. This script can compute accuracy evaluations for a range of models, it will automatically evaluate the test samples for all existing model files named
, etc.

The text output will also be written to a file

. In addition, visualized reference data and corresponding inferred outputs are written to
as PNGs.

Changes after publication

After the initial version of this paper appeared in 2018 and the AIAA version was finally accepted in 2020, a few smaller updates and improvements were made:

  • for symmetry reasons, we switched one convolutional layer of the encoder part to have a kernel size of 4 instead of 2. This doesn't really influence model performance, but matches the decoder.

  • the upsampling in the decoder originally used nearest-neighbor sampling by default. The code was updated to use bilinear upsampling now, which visually gives smoother results. However, it does not have a significant influence on the accuracy measurements.

Further steps

For further experiments, you can increase the

parameter in
(note, non-integers are allowed). For large models you'll need much more data, though, to avoid overfitting.

In addition, the
file is worth a look: it contains most of the non-standard code for the RANS flow prediction. E.g., here you can find the U-net setup and data normalization. Hence, this class is a good starting point for experimenting with different architectures.

Note that both the
scripts also accept a prefix as command line argument. This can come in handy for automated runs with varying parameters.

Data sets and Models

Below you can download a large-scale training data set, and the test data set used in the accompanying paper, as well as pre-trained models:

The following pre-trained models are available:

Note: these are from the original paper and code release. Hence, the models only work with commit


Additional inference results, download full resolution as PNG via the link below


Based on this framework, you should be able to train deep learning models that yield relative errors of 2-3% for the RANS data sets. In addition, the network architecture should be applicable to other types of dense PDE solutions.

Let us know if things don't work, or if you find ways to make it work even better :) ! The authors

Thuerey Group , Hu Group , TUM


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