Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving

Here are some examples of notebooks demonstrating the application of the proposed approach for solving Poisson and Diffusion equations:

1. Fixed Grid:

• FCG with SNO for Poisson 2D
  • Update FCG with SNO for Poisson 2D
• FCG with SNO for Diffusion 2D
  • Update FCG with SNO for Diffusion 2D
• FCG with FNO for Poisson 2D
• FCG with FNO for Diffusion 2D
• FCG with DilResNet for Poisson 2D
• FCG with DilResNet for Diffusion 2D
• FCG with UNet for Poisson 2D
• FCG with UNet for Diffusion 2D

2. Different Grids:

• FCG with SNO for different grids for Poisson 2D
• FCG with SNO for different grids for Diffusion 2D

Here are some examples of pipelines for solving Poisson and Diffusion equation, including cases where the grid is fixed and where the grid is switched from coarse to fine:

1. Fixed Grid:

• FCG with SNO for Poisson 2D
• FCG with SNO for Diffusion 2D

2. Different Grids:

• FCG with SNO for different grids for Poisson 2D
• FCG with SNO for different grids for Diffusion 2D

Citing

If you use this code in your work, we kindly ask you to cite cite the paper

@article{rudikov2024neural,
  title={Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving},
  author={Rudikov, Alexander and Fanaskov, Vladimir and Muravleva, Ekaterina and Laevsky, Yuri M and Oseledets, Ivan},
  journal={arXiv preprint arXiv:2402.05598},
  year={2024}
}