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.

To learn more about our general approach, read our paper Machine learning accelerated computational fluid dynamics (PNAS 2021).

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
  • 2D simulation with a psuedo-spectral solver
  • 2D simulation of channel flow
  • 2D simulation with FVM on a collocated grid (experimental)

• Reproduce results from our PNAS paper:

  • Data analysis and evaluation
  • Running our pre-trained models

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.
• jax_cfd.data: data processing utilities for preparing, evaluating and post-processing data created with JAX-CFD, written in Xarray and Pillow.

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].

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.

• Variational Data Assimilation with a Learned Inverse Observation Operator

Other differentiable CFD codes compatible with deep learning:

• PhiFlow supports TensorFlow, PyTorch and JAX
• Fluid simulation in Autograd

JAX for science:

• JAX-MD
• JAX-DFT
• jax-cosmo
• Veros

Did we miss something? Please let us know!

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}
}

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