AI4PDEs

AI4PDEs is a package that solves partial differential equations (PDEs) using functionality from PyTorch. It currently solves the 2D Navier-Stokes equations, 2D advection-diffusion equations and 3D Navier-Stokes equations.

Gallery

Some flow past a block!

Installation

1. Clone the repo

   git clone https://github.com/ImperialCollegeLondon/AI4PDEs.git

2. Install

   Currently requires python>=3.10.

   python -m pip install . or python -m pip install -e ."[dev]"

3. Run one of the example files

   cd ai4pdes/structured/
   jupyter notebook flow_past_block.ipynb
   jupyter notebook advection_diffusion.ipynb
   jupyter notebook flow_past_buildings.ipynb

Usage

Run your first model of flow past a block!

import ai4pdes
from ai4pdes.models import FlowPastBlock, Block
from ai4pdes.grid import Grid

grid = Grid(nx=254, ny=62)
block = Block(grid)
model = FlowPastBlock(grid, block)
simulation = model.initialize()
simulation.run(ntimesteps=100)

and visualise it

from ai4pdes.plot_state import plot_u, plot_v
plot_u(simulation.prognostic_variables)

Contributing

Contributions are welcome! If you have a suggestion that would make this better, please fork the repo and create a pull request. You can also simply open an issue.

Citing

If you use AI4PDEs in research, teaching, or other activities, please cite the following publications if you use this code.

Chen, B, CE Heaney, CC Pain (2024). Using AI libraries for Incompressible Computational Fluid Dynamics. arXiv:2402.17913, DOI:10.48550/arXiv.2402.17913

The bibtex entry for the paper is:

@misc{chen2024,
      title={Using AI libraries for Incompressible Computational Fluid Dynamics}, 
      author={Boyang Chen and Claire E. Heaney and Christopher C. Pain},
      year={2024},
      eprint={2402.17913},
      archivePrefix={arXiv},
}

Related papers using the AI4PDEs approach are

T. R. F. Phillips, C. E. Heaney, B. Chen, A. G. Buchan and C. C. Pain. Solving the discretised neutron diffusion equations using neural networks. Int J Numer Methods Eng (2023) 124(21):4659--4686 https://doi.org/10.1002/nme.7321

B. Chen, C. E. Heaney, J. L. M. A. Gomes, O. K. Matar and C. C. Pain. Solving the discretised multiphase flow equations with interface capturing on structured grids using machine learning libraries. Computer Methods in Applied Mechanics and Engineering (2024) 426:116974 https://doi.org/10.1016/j.cma.2024.116974