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Appendix

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Authors:

(1) Vladislav Trifonov, Skoltech ([email protected]);

(2) Alexander Rudikov, AIRI, Skoltech;

(3) Oleg Iliev, Fraunhofer ITWM;

(4) Ivan Oseledets, AIRI, Skoltech;

(5) Ekaterina Muravleva, Skoltech.

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

A Appendix

A.1 Details on training data

Table 4: Dataset specification.


Table 5: Size of linear systems and number of nonzero elements (nnz) for different grids and matrices.

A.2 Additional experiments with ICt(5) preconditioner

A.3 Details about correction coefficient α

Table 7: Values of the learned coefficient alpha from 6.


This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license.


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