Machine Learning-Based Preconditioner to Solve Poisson Equation Full article
| Conference |
Computational Science and Its Applications 30 Jun - 3 Jul 2025 , Istanbul |
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| Source | Computational Science and Its Applications (ICCSA 2025 Workshops) : Proceedings Compilation, Springer Cham. Switzerland.2026. 462 c. ISBN 978-3-031-97596-7. |
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| Journal |
Lecture Notes in Computer Science
ISSN: 0302-9743 , E-ISSN: 1611-3349 |
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| Output data | Year: 2025, Volume: 15888, Pages: 376-387 Pages count : 12 DOI: 10.1007/978-3-031-97596-7_25 | ||||||
| Tags | Poisson equation, Conjugate gradient, preconditioner, Machine Learning | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-11-00004-П |
Abstract:
In this paper, we present an attempt to construct a preconditioner based on the machine learning to solve Poisson equation. We use the Conjugate Gradient method. To precondition the algorithm we suggest approximating the inverse Laplace operator with using the UNet. We consider the supervised learning where the vector of unknowns and right-hand sides are known; thus, we use the relative .L2 error as the loss function of the network training. We illustrate that U-Net with five convolutional layers provide insufficient accuracy of inverse Laplace operator approximation, so that the constructed conjugate gradient method stabilizes and possesses irreducible residual.
Cite:
Chekmeneva E.
, Khachova T.
, Lisitsa V.
Machine Learning-Based Preconditioner to Solve Poisson Equation
In compilation Computational Science and Its Applications (ICCSA 2025 Workshops) : Proceedings. – Springer Cham., 2025. – Т.Part III. – C.376-387. – ISBN 978-3-031-97596-7. DOI: 10.1007/978-3-031-97596-7_25 Scopus OpenAlex
Machine Learning-Based Preconditioner to Solve Poisson Equation
In compilation Computational Science and Its Applications (ICCSA 2025 Workshops) : Proceedings. – Springer Cham., 2025. – Т.Part III. – C.376-387. – ISBN 978-3-031-97596-7. DOI: 10.1007/978-3-031-97596-7_25 Scopus OpenAlex
Dates:
| Published print: | May 28, 2025 |
| Published online: | May 28, 2025 |
Identifiers:
| Scopus: | 2-s2.0-105010830791 |
| OpenAlex: | W4412059133 |
Citing:
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