Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver

Code repository for the paper:
Learning Green's Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver
Yuankai Teng, Xiaoping Zhang, Zhu Wang, Lili Ju

Proceedings of Third Mathematical and Scientific Machine Learning Conference (MSML'2022), 2022
[paper]

Training Usage

To train the GF-Nets for a specific problem on given domain

python ./trainer.py 
--pde_case Poisson 
--domain_type square 
--blocks_num 4 4
--z_coarse_num 545  
--x_coarse_num 2105 
--x_middle_num 8265 
--x_refine_num 32753 
--scale 5 10 
--epochs_Adam 20000 
--epochs_LBFGS 10000 
--tol 1e-4 
--cuda_index 0

To finetune your model with smaller sigma (when you have already trained your model with greater value of simga)

python ./trainer.py 
--pde_case Poisson 
--domain_type square 
--blocks_num 4 4
--z_coarse_num 545  
--x_coarse_num 2105 
--x_middle_num 8265 
--x_refine_num 32753 
--scale 5 10 
--sigma 0.015
--scale_resume 5 10
--sigma_resume 0.02
--resume True
--epochs_Adam 20000 
--epochs_LBFGS 10000 
--tol 1e-4 
--cuda_index 0

Testing Usage

To evaluate numerical error and draw your results:

python ./GreenFormula.py
--pde_case Poisson 
--solution_case 6
--domain_type washer 
--blocks_num 4 4
--z_coarse_num 545  
--x_coarse_num 2105 
--x_middle_num 8265 
--x_refine_num 32753 
--scale 5 10

Citation

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

@inproceedings{teng2022learning,
  title={Learning Green’s Functions of Linear Reaction-Diffusion Equations with Application to Fast Numerical Solver},
  author={Teng, Yuankai and Zhang, Xiaoping and Wang, Zhu and Ju, Lili},
  booktitle={Mathematical and Scientific Machine Learning},
  pages={1--16},
  year={2022},
  organization={PMLR}
}