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Enhancing the stability of physics-informed neural networks applied to convection problems. / Tsgoev, Ch A.; Bratenkov, M. A.; Sakharov, D. I. et al.

In: Thermophysics and Aeromechanics, Vol. 32, No. 2, 03.2025, p. 449-463.

Research output: Contribution to journal › Article › peer-review

Harvard

Tsgoev, CA, Bratenkov, MA, Sakharov, DI, Travnikov, VA, Seredkin, AV, Kalinin, VA, Fomichev, DV & Mullyadzhanov, RI 2025, 'Enhancing the stability of physics-informed neural networks applied to convection problems', Thermophysics and Aeromechanics, vol. 32, no. 2, pp. 449-463. https://doi.org/10.1134/S0869864325020180

APA

Tsgoev, C. A., Bratenkov, M. A., Sakharov, D. I., Travnikov, V. A., Seredkin, A. V., Kalinin, V. A., Fomichev, D. V., & Mullyadzhanov, R. I. (2025). Enhancing the stability of physics-informed neural networks applied to convection problems. Thermophysics and Aeromechanics, 32(2), 449-463. https://doi.org/10.1134/S0869864325020180

Vancouver

Tsgoev CA, Bratenkov MA, Sakharov DI, Travnikov VA, Seredkin AV, Kalinin VA et al. Enhancing the stability of physics-informed neural networks applied to convection problems. Thermophysics and Aeromechanics. 2025 Mar;32(2):449-463. doi: 10.1134/S0869864325020180

Author

Tsgoev, Ch A. ; Bratenkov, M. A. ; Sakharov, D. I. et al. / Enhancing the stability of physics-informed neural networks applied to convection problems. In: Thermophysics and Aeromechanics. 2025 ; Vol. 32, No. 2. pp. 449-463.

BibTeX

@article{18610cda341544e78e6574588c4b906a,
title = "Enhancing the stability of physics-informed neural networks applied to convection problems",
abstract = "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.",
keywords = "convection problem, neural networks, physics-informed machine learning, ФИЗИЧЕСКИ-ИНФОРМИРОВАННОЕ МАШИННОЕ ОБУЧЕНИЕ, НЕЙРОННЫЕ СЕТИ, ЗАДАЧА КОНВЕКЦИИ",
author = "Tsgoev, {Ch A.} and Bratenkov, {M. A.} and Sakharov, {D. I.} and Travnikov, {V. A.} and Seredkin, {A. V.} and Kalinin, {V. A.} and Fomichev, {D. V.} and Mullyadzhanov, {R. I.}",
note = "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).",
year = "2025",
month = mar,
doi = "10.1134/S0869864325020180",
language = "English",
volume = "32",
pages = "449--463",
journal = "Thermophysics and Aeromechanics",
issn = "0869-8643",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

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