Transferable Neural Networks for Partial Differential Equations

Code repository for the paper:
Transferable Neural Networks for Partial Differential Equations
Zezhong Zhang, Feng Bao, Lili Ju, Guannan Zhang
Journal of Scientific Computing, 2024, [paper]

Usage

• PDE accuracy: First run PDE_(problem_name)/problem_setup.ipynb to generate true solution data. Then run PDE_(problem_name)/ls.ipynb for LS-based solutions (TransNet and random feature model), and PDE_(problem_name)/pinn.ipynb for PINN.
• Shape parameter tuning: See basis_train_2d and basis_train_3d.
• Hyperplane density simulation: Simulated hyperplane density can be found in basis_analysis/density_plot.ipynb.
• Portable scripts (for Possion 2D and NS steady state): Single scripts that do not depend on the rest of the repo.

Citation

If you find the idea or code of this paper useful for your research, please consider citing us:

@article{zhang2024transferable,
  title={Transferable Neural Networks for Partial Differential Equations},
  author={Zhang, Zezhong and Bao, Feng and Ju, Lili and Zhang, Guannan},
  journal={Journal of Scientific Computing},
  volume={99},
  number={1},
  pages={2},
  year={2024},
  publisher={Springer}
}