JAX-CFD: Computational Fluid Dynamics in JAX

Authors: Dmitrii Kochkov, Jamie A. Smith, 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).

Getting started

Take a look at "demo" notebook in the "notebooks" directory for an example of how to use JAX-CFD for simulate a 2D turbulent flow.

We are currently preparing more example notebooks, inculding:

Reusing our training data and/or evaluation setup (without running JAX-CFD)
Simulations using our pre-trained turbulence models.
Training a simple hybrid ML + CFD model from scratch

Organization

JAX-CFD is organized around sub-modules:

jax_cfd.base: core numerical 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].

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.
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.,

Spectral methods
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.

Other awesome projects

Other differentiable CFD codes compatible with deep learning:

PhiFlow supports TensorFlow, PyTorch and JAX
Fluid simulation in Autograd

JAX for science:

Did we miss something? Please let us know!

Citation

@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}
}

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

jatropj / jax-cfd