Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Enhancing the stability of physics-informed neural networks applied to convection problems. / Tsgoev, Ch A.; Bratenkov, M. A.; Sakharov, D. I. и др.
в: Thermophysics and Aeromechanics, Том 32, № 2, 03.2025, стр. 449-463.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
}
TY - JOUR
T1 - Enhancing the stability of physics-informed neural networks applied to convection problems
AU - Tsgoev, Ch A.
AU - Bratenkov, M. A.
AU - Sakharov, D. I.
AU - Travnikov, V. A.
AU - Seredkin, A. V.
AU - Kalinin, V. A.
AU - Fomichev, D. V.
AU - Mullyadzhanov, R. I.
N1 - Tsgoev, C.A., Bratenkov, M.A., Sakharov, D.I. et al. Enhancing the stability of physics-informed neural networks applied to convection problems. Thermophys. Aeromech. 32, 449–463 (2025). https://doi.org/10.1134/S0869864325020180 This work was supported by the grant of the state program of the «Sirius» Federal Territory «Scientific and technological development of the «Sirius» Federal Territory» (Agreement № 18-03 date 10.09.2024).
PY - 2025/3
Y1 - 2025/3
N2 - Physics-Informed Neural Networks (PINNs) represent an innovative method for solving a wide range of problems in mathematics, physics, and engineering. PINNs combine the neural networks concepts and physical equations aimed at modeling and analyzing various physical processes. In particular, PINNs can be applied to solve differential equations, including the one-dimensional convection equation. The research shows that the standard implementation of PINNs efficiently solves a one-dimensional convection equation at relatively small convection velocity values, but diverges for higher values of this parameter. This paper provides an overview of existing approaches for solving the one-dimensional convection equation using PINNs and demonstrates improvement for model performance through different methods. The results of comparison indicate the superiority of the approach based on dynamically adjusting collocation points according to the residual at the current training step.
AB - Physics-Informed Neural Networks (PINNs) represent an innovative method for solving a wide range of problems in mathematics, physics, and engineering. PINNs combine the neural networks concepts and physical equations aimed at modeling and analyzing various physical processes. In particular, PINNs can be applied to solve differential equations, including the one-dimensional convection equation. The research shows that the standard implementation of PINNs efficiently solves a one-dimensional convection equation at relatively small convection velocity values, but diverges for higher values of this parameter. This paper provides an overview of existing approaches for solving the one-dimensional convection equation using PINNs and demonstrates improvement for model performance through different methods. The results of comparison indicate the superiority of the approach based on dynamically adjusting collocation points according to the residual at the current training step.
KW - convection problem
KW - neural networks
KW - physics-informed machine learning
KW - ФИЗИЧЕСКИ-ИНФОРМИРОВАННОЕ МАШИННОЕ ОБУЧЕНИЕ
KW - НЕЙРОННЫЕ СЕТИ
KW - ЗАДАЧА КОНВЕКЦИИ
UR - https://www.scopus.com/pages/publications/105030179694
UR - https://elibrary.ru/item.asp?id=82745276
UR - https://www.mendeley.com/catalogue/27fc56e3-a098-3ed6-99e6-c56cefa07885/
U2 - 10.1134/S0869864325020180
DO - 10.1134/S0869864325020180
M3 - Article
VL - 32
SP - 449
EP - 463
JO - Thermophysics and Aeromechanics
JF - Thermophysics and Aeromechanics
SN - 0869-8643
IS - 2
ER -
ID: 75452619