Neural design of preconditioner

Table of Links

Abstract and 1 Introduction

2 Neural design of preconditioner

3 Learn correction for ILU and 3.1 Graph neural network with preserving sparsity pattern

3.2 PreCorrector

4 Dataset

5 Experiments

5.1 Experiment environment and 5.2 Comparison with classical preconditioners

5.3 Loss function

5.4 Generalization to different grids and datasets

6 Related work

7 Conclusion and further work, and References

Appendix

2 Neural design of preconditioner

This loss function previously appeared in related research Li et al. [2023] but with understanding of inductive bias from PDE data distribution. In experiment section we evidence our hypothesis, that loss (5) indeed mitigate low-frequency components.