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Stable Numerical Solution to the Cauchy Problem for Multi-Dimensional Nonlinear Elliptic Equations via Artificial Neural Networks Научная публикация

Журнал

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662

Вых. Данные

Год: 2026, Том: 66, Номер: 7, Страницы: 1397–1421 Страниц : 25 DOI: 10.1134/S0965542526700727

Ключевые слова

Cauchy problem, multi-dimensional nonlinear elliptic equation, ill-posed problems, regularization, L-curve method, artificial neural networks

Авторы

Hào Dinh Nho ¹ , Shishlenin Maxim ^2,3 , Van Cong B. ⁴

Организации

1	Hanoi Institute of Mathematics, VAST, Hanoi, Vietnam
2	Sobolev Institute of Mathematics
3	Institute of Computational Mathematics and Mathematical Geophysics
4	Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC, 28223 USA

Информация о финансировании (1)

Российский научный фонд

24-41-04004

The Cauchy problem for multi-dimensional nonlinear elliptic equations is reformulated as a least squares problem and then stabilized by Tikhonov regularization method. The last is solved in the framework of artificial neural networks, while the regularization parameter is chosen by the discrepancy principle or the L-curve method. Numerical simulations show that the approach is efficient for this severely ill-posed, multi-dimensional and nonlinear problem.

Hào D.N. , Shishlenin M. , Van C.B.
Stable Numerical Solution to the Cauchy Problem for Multi-Dimensional Nonlinear Elliptic Equations via Artificial Neural Networks
Computational Mathematics and Mathematical Physics. 2026. V.66. N7. P.1397–1421. DOI: 10.1134/S0965542526700727 WOS Scopus OpenAlex

Поступила в редакцию:	10 сент. 2025 г.
Принята к публикации:	10 апр. 2026 г.
Опубликована в печати:	27 авг. 2026 г.
Опубликована online:	27 авг. 2026 г.

≡ Web of science:	WOS:001862007100009
≡ Scopus:	2-s2.0-105048646548
≡ OpenAlex:	W7204435815