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https://github.com/google/jax-cfd

Computational Fluid Dynamics in JAX
https://github.com/google/jax-cfd

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Computational Fluid Dynamics in JAX

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# JAX-CFD: Computational Fluid Dynamics in JAX



Authors: Dmitrii Kochkov, Jamie A. Smith, Peter Norgaard, Gideon Dresdner, Ayya Alieva, Stephan Hoyer



JAX-CFD is an experimental research project for exploring the potential of

machine learning, automatic differentiation and hardware accelerators (GPU/TPU)

for computational fluid dynamics. It is implemented in

[JAX](https://github.com/google/jax).



To learn more about our general approach, read our paper [Machine learning accelerated computational fluid dynamics](https://www.pnas.org/content/118/21/e2101784118)

(PNAS 2021).



## Getting started



The "notebooks" directory contains several demonstrations of using the JAX-CFD

code.



- Demos of different simulation setups:

  - [2D simulation with FVM on a staggered grid](https://colab.research.google.com/github/google/jax-cfd/blob/main/notebooks/demo.ipynb)

  - [2D simulation with a psuedo-spectral solver](https://colab.research.google.com/github/google/jax-cfd/blob/main/notebooks/spectral_forced_turbulence.ipynb)

  - [2D simulation of channel flow](https://colab.research.google.com/github/google/jax-cfd/blob/main/notebooks/channel_flow_demo.ipynb)

  - [2D simulation with FVM on a collocated grid](https://colab.research.google.com/github/google/jax-cfd/blob/main/notebooks/collocated_demo.ipynb) (experimental)



- Reproduce results from our PNAS paper:

  - [Data analysis and evaluation](https://colab.research.google.com/github/google/jax-cfd/blob/main/notebooks/ml_accelerated_cfd_data_analysis.ipynb)

  - [Running our pre-trained models](https://colab.research.google.com/github/google/jax-cfd/blob/main/notebooks/ml_model_inference_demo.ipynb)



## Organization



JAX-CFD is organized around sub-modules:



- `jax_cfd.base`: core finite volume/difference methods for CFD, written in JAX.

- `jax_cfd.spectral`: core pseudospectral methods for CFD, written in JAX.

- `jax_cfd.ml`: machine learning augmented models for CFD,

  written in JAX and [Haiku](https://dm-haiku.readthedocs.io/en/latest/).

- `jax_cfd.data`: data processing utilities for preparing, evaluating and

  post-processing data created with JAX-CFD, written in

  [Xarray](http://xarray.pydata.org/) and

  [Pillow](https://pillow.readthedocs.io/).



A base install with `pip install jax-cfd` only requires NumPy, SciPy and JAX.

To install dependencies for the other submodules, use `pip install jax-cfd[ml]`,

`pip install jax-cfd[data]` or `pip install jax-cfd[complete]`.



## Numerics



JAX-CFD is currently focused on unsteady turbulent flows:



- *Spatial discretization*:

  - *Finite volume/difference* methods on a staggered grid (the "Arakawa C" or

  "MAC" grid) with pressure at the center of each cell and velocity components

  defined on corresponding faces.

  - *Pseudospectral* methods for vorticity which use anti-aliasing filtering

  techniques for non-linear terms to maintain stability.

- *Temporal discretization*: Currently only first-order temporal

  discretization, using explicit time-stepping for advection and either implicit

  or explicit time-stepping for diffusion.

- *Pressure solves*: Either CG or fast diagonalization with real-valued FFTs

  (suitable for periodic boundary conditions).

- *Boundary conditions*: Currently only periodic boundary conditions are

  supported.

- *Advection*: We implement 2nd order accurate "Van Leer" schemes.

- *Closures*: We currently implement Smagorinsky eddy-viscosity models.



TODO: add a notebook explaining our numerical models in more depth.



In the long term, we're interested in expanding JAX-CFD to implement methods

relevant for related research, e.g.,



- Colocated grids

- Alternative boundary conditions (e.g., non-periodic boundaries and immersed

  boundary methods)

- Higher order time-stepping

- Geometric multigrid

- Steady state simulation (e.g., RANS)

- Distributed simulations across multiple TPUs/GPUs



We would welcome collaboration on any of these! Please reach out (either on

GitHub or by email) to coordinate before starting significant work.



## Projects using JAX-CFD



- [Variational Data Assimilation with a Learned Inverse Observation Operator](https://github.com/googleinterns/invobs-data-assimilation)



## Other awesome projects



Other differentiable CFD codes compatible with deep learning:



- [PhiFlow](https://github.com/tum-pbs/PhiFlow/) supports TensorFlow, PyTorch and JAX

- [Fluid simulation in Autograd](https://github.com/HIPS/autograd#end-to-end-examples)



JAX for science:



- [JAX-MD](https://github.com/google/jax-md)

- [JAX-DFT](https://github.com/google-research/google-research/tree/master/jax_dft)

- [jax-cosmo](https://github.com/DifferentiableUniverseInitiative/jax_cosmo)

- [Veros](https://github.com/team-ocean/veros)



Did we miss something? Please let us know!



## Citation



If you use our finite volume method (FVM) or ML models, please cite:



```

@article{Kochkov2021-ML-CFD,

  author = {Kochkov, Dmitrii and Smith, Jamie A. and Alieva, Ayya and Wang, Qing and Brenner, Michael P. and Hoyer, Stephan},

  title = {Machine learning{\textendash}accelerated computational fluid dynamics},

  volume = {118},

  number = {21},

  elocation-id = {e2101784118},

  year = {2021},

  doi = {10.1073/pnas.2101784118},

  publisher = {National Academy of Sciences},

  issn = {0027-8424},

  URL = {https://www.pnas.org/content/118/21/e2101784118},

  eprint = {https://www.pnas.org/content/118/21/e2101784118.full.pdf},

  journal = {Proceedings of the National Academy of Sciences}

}

```



If you use our spectral code, please cite:



```

@article{Dresdner2022-Spectral-ML,

  doi = {10.48550/ARXIV.2207.00556},

  url = {https://arxiv.org/abs/2207.00556},

  author = {Dresdner, Gideon and Kochkov, Dmitrii and Norgaard, Peter and Zepeda-Núñez, Leonardo and Smith, Jamie A. and Brenner, Michael P. and Hoyer, Stephan},

  title = {Learning to correct spectral methods for simulating turbulent flows},

  publisher = {arXiv},

  year = {2022},

  copyright = {arXiv.org perpetual, non-exclusive license}

}

```



## Local development



To locally install for development:

```

git clone https://github.com/google/jax-cfd.git

cd jax-cfd

pip install jaxlib

pip install -e ".[complete]"

```



Then to manually run the test suite:

```

pytest -n auto jax_cfd --dist=loadfile --ignore=jax_cfd/base/validation_test.py

```