Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Machine Learning-Based Preconditioner to Solve Poisson Equation. / Chekmeneva, Ekaterina; Khachova, Tatyna; Lisitsa, Vadim.
Lecture Notes in Computer Science. Springer, 2026. стр. 376-387 25 (Lecture Notes in Computer Science; Том 15888 LNCS).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
}
TY - GEN
T1 - Machine Learning-Based Preconditioner to Solve Poisson Equation
AU - Chekmeneva, Ekaterina
AU - Khachova, Tatyna
AU - Lisitsa, Vadim
N1 - The research was supported by the Russian Science Foundation grant no. 22-11-00004-Π.
PY - 2025/5/28
Y1 - 2025/5/28
N2 - 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 U-Net. 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.
AB - 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 U-Net. 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.
KW - Conjugate gradient
KW - Machine Learning
KW - Poisson equation
KW - preconditioner
UR - https://www.scopus.com/pages/publications/105010830791
UR - https://www.mendeley.com/catalogue/dd1d456a-5531-3498-ac1d-0439ab27ecd7/
U2 - 10.1007/978-3-031-97596-7_25
DO - 10.1007/978-3-031-97596-7_25
M3 - Conference contribution
SN - 978-3-031-97595-0
T3 - Lecture Notes in Computer Science
SP - 376
EP - 387
BT - Lecture Notes in Computer Science
PB - Springer
T2 - Computational Science and Its Applications – ICCSA 2025 Workshops
Y2 - 30 June 2025 through 3 July 2025
ER -
ID: 68675366