Stable Numerical Solution to Multi-dimensional Nonlinear Inverse Heat Conduction Problems via Artificial Neural Networks | Sciact - Система учета научной деятельности ИМ СО РАН

Stable Numerical Solution to Multi-dimensional Nonlinear Inverse Heat Conduction Problems via Artificial Neural Networks Научная публикация

Журнал

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Вых. Данные

Год: 2026, Том: 47, Номер: 3, Страницы: 1213-1232 Страниц : 20 DOI: 10.1134/s1995080225614705

Ключевые слова

inverse heat conduction, multi-dimensional nonlinear parabolic equation, ill-posed problems, regularization, L-curve method, Beck’s future time approach, artificial neural networks (ANNs)

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 of the Russian Academy of Sciences, Novosibirsk, Russia
4	Department of Mathematics and Statistics, University of North Carolina at Charlotte, 28223, Charlotte, NC, USA

Информация о финансировании (1)

Российский научный фонд

24-41-04004

Multi-dimensional nonlinear inverse heat conduction problems are 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 either the discrepancy principle or the L-curve method. The well-known Beck future time approach is applied to improve the reconstruction of the boundary values near the final time moment. Numerical simulations show that the approach is efficient for these severely ill-posed, multi-dimensional and nonlinear problems.

Hào D.N. , Shishlenin M. , Van C.B.
Stable Numerical Solution to Multi-dimensional Nonlinear Inverse Heat Conduction Problems via Artificial Neural Networks
Lobachevskii Journal of Mathematics. 2026. V.47. N3. P.1213-1232. DOI: 10.1134/s1995080225614705 WOS Scopus OpenAlex

Поступила в редакцию:	12 нояб. 2025 г.
Принята к публикации:	12 янв. 2026 г.
Опубликована в печати:	6 июл. 2026 г.
Опубликована online:	6 июл. 2026 г.

≡ Web of science:	WOS:001812865200003
≡ Scopus:	2-s2.0-105043923079
≡ OpenAlex:	W7167509522