Machine Learning-Based Preconditioner to Solve Poisson Equation Научная публикация
| Конференция |
Computational Science and Its Applications 30 июн. - 3 июл. 2025 , Istanbul |
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| Сборник | Computational Science and Its Applications (ICCSA 2025 Workshops) : Proceedings Сборник, Springer Cham. Switzerland.2026. 462 c. ISBN 978-3-031-97596-7. |
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| Журнал |
Lecture Notes in Computer Science
ISSN: 0302-9743 , E-ISSN: 1611-3349 |
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| Вых. Данные | Год: 2025, Том: 15888, Страницы: 376-387 Страниц : 12 DOI: 10.1007/978-3-031-97596-7_25 | ||||||
| Ключевые слова | Poisson equation, Conjugate gradient, preconditioner, Machine Learning | ||||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 | Российский научный фонд | 22-11-00004-П |
Реферат:
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.
Библиографическая ссылка:
Chekmeneva E.
, Khachova T.
, Lisitsa V.
Machine Learning-Based Preconditioner to Solve Poisson Equation
В сборнике 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
В сборнике 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
Даты:
| Опубликована в печати: | 28 мая 2025 г. |
| Опубликована online: | 28 мая 2025 г. |
Идентификаторы БД:
| Scopus: | 2-s2.0-105010830791 |
| OpenAlex: | W4412059133 |
Цитирование в БД:
Пока нет цитирований