MM-PDE: Better Neural PDE Solvers Through Data-Free Mesh Movers

Link to the paper (ICLR 2024)

This paper introduces a neural-network-based mesh adapter called Data-free Mesh Mover (DMM), which is trained in a physics-informed data-free way. The DMM can be embedded into the neural PDE solver through proper architectural design, called MM-PDE.

Environment

Install the environment using conda with attached environment file as follows.

conda env create -f env.yml

Dataset

Download the datasets into the "mesh/data/" folder in the local repo via this link.

Training of Data-free Mesh Mover (DMM)

• Burgers' equation:

  cd mesh  
  python dmm.py

• Flow around a cylinder:

  cd mesh  
  python dmm.py --experiment cy --train_sample_grid 1500 --branch_layers 4,3 --trunk_layers 16,512

Training of MM-PDE

• Burgers' equation:

  python mmpde.py --lr 6e-4

• Flow around a cylinder:

  python mmpde.py --experiment cy --base_resolution 30,2521

Training of GNN

• Burgers' equation:

  python mmpde.py --lr 6e-4 --moving_mesh False

• Flow around a cylinder:

  python mmpde.py --experiment cy --base_resolution 30,2521 --moving_mesh False

Citation

If you find our work and/or our code useful, please cite us via:

@inproceedings{
hu2024better,
title={Better Neural {PDE} Solvers Through Data-Free Mesh Movers},
author={Peiyan Hu and Yue Wang and Zhi-Ming Ma},
booktitle={The Twelfth International Conference on Learning Representations},
year={2024}
}