Physics-informed neural network model using natural gradient descent with Dirichlet distribution

In this article we propose the physics-informed neural network model which contains the natural gradient descent with Dirichlet distribution. Such an optimizer can more accurately converge in the global minimum of the loss function in a short number of iterations. Due to natural gradient, one consid...

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Главные авторы:	Abdulkadirov, R. I., Абдулкадиров, Р. И., Lyakhov, P. A., Ляхов, П. А., Baboshina, V. A., Бабошина, В. А.
Формат:	Статья
Язык:	English
Опубликовано:	Elsevier Ltd 2025
Темы:	Machine learning Physics-informed neural networks Natural gradient descent Partial differential equations Optimization
Online-ссылка:	https://dspace.ncfu.ru/handle/123456789/30520
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id	ir-123456789-30520
record_format	dspace
spelling	ir-123456789-305202025-06-18T12:30:42Z Physics-informed neural network model using natural gradient descent with Dirichlet distribution Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Baboshina, V. A. Бабошина, В. А. Machine learning Physics-informed neural networks Natural gradient descent Partial differential equations Optimization In this article we propose the physics-informed neural network model which contains the natural gradient descent with Dirichlet distribution. Such an optimizer can more accurately converge in the global minimum of the loss function in a short number of iterations. Due to natural gradient, one considers not only the gradient directions but also convexity of the loss function. Using the Dirichlet distribution, natural gradient allows for a reduction in time consumption comparing with the second order approaches. The proposed physics-informed neural model increases the accuracy of solving initial and boundary value problems for partial differential equations, such as the heat and Burgers equation, on 0%−10% Gaussian noised data. Compared with the state-of-the-art optimization methods, the proposed natural gradient descent with Dirichlet distribution achieves the more accurate solution by 9%−62%, estimated by mean squared error and L2 error. 2025-06-18T12:29:17Z 2025-06-18T12:29:17Z 2025 Статья Abdulkadirov R., Lyakhov P., Baboshina V. Physics-informed neural network model using natural gradient descent with Dirichlet distribution // Engineering Analysis with Boundary Elements. - 2025. - 178. - art. no. 106282. - DOI: 10.1016/j.enganabound.2025.106282 https://dspace.ncfu.ru/handle/123456789/30520 en Engineering Analysis with Boundary Elements application/pdf application/pdf Elsevier Ltd
institution	СКФУ
collection	Репозиторий
language	English
topic	Machine learning Physics-informed neural networks Natural gradient descent Partial differential equations Optimization
spellingShingle	Machine learning Physics-informed neural networks Natural gradient descent Partial differential equations Optimization Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Baboshina, V. A. Бабошина, В. А. Physics-informed neural network model using natural gradient descent with Dirichlet distribution
description	In this article we propose the physics-informed neural network model which contains the natural gradient descent with Dirichlet distribution. Such an optimizer can more accurately converge in the global minimum of the loss function in a short number of iterations. Due to natural gradient, one considers not only the gradient directions but also convexity of the loss function. Using the Dirichlet distribution, natural gradient allows for a reduction in time consumption comparing with the second order approaches. The proposed physics-informed neural model increases the accuracy of solving initial and boundary value problems for partial differential equations, such as the heat and Burgers equation, on 0%−10% Gaussian noised data. Compared with the state-of-the-art optimization methods, the proposed natural gradient descent with Dirichlet distribution achieves the more accurate solution by 9%−62%, estimated by mean squared error and L2 error.
format	Статья
author	Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Baboshina, V. A. Бабошина, В. А.
author_facet	Abdulkadirov, R. I. Абдулкадиров, Р. И. Lyakhov, P. A. Ляхов, П. А. Baboshina, V. A. Бабошина, В. А.
author_sort	Abdulkadirov, R. I.
title	Physics-informed neural network model using natural gradient descent with Dirichlet distribution
title_short	Physics-informed neural network model using natural gradient descent with Dirichlet distribution
title_full	Physics-informed neural network model using natural gradient descent with Dirichlet distribution
title_fullStr	Physics-informed neural network model using natural gradient descent with Dirichlet distribution
title_full_unstemmed	Physics-informed neural network model using natural gradient descent with Dirichlet distribution
title_sort	physics-informed neural network model using natural gradient descent with dirichlet distribution
publisher	Elsevier Ltd
publishDate	2025
url	https://dspace.ncfu.ru/handle/123456789/30520
work_keys_str_mv	AT abdulkadirovri physicsinformedneuralnetworkmodelusingnaturalgradientdescentwithdirichletdistribution AT abdulkadirovri physicsinformedneuralnetworkmodelusingnaturalgradientdescentwithdirichletdistribution AT lyakhovpa physicsinformedneuralnetworkmodelusingnaturalgradientdescentwithdirichletdistribution AT lâhovpa physicsinformedneuralnetworkmodelusingnaturalgradientdescentwithdirichletdistribution AT baboshinava physicsinformedneuralnetworkmodelusingnaturalgradientdescentwithdirichletdistribution AT babošinava physicsinformedneuralnetworkmodelusingnaturalgradientdescentwithdirichletdistribution
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Physics-informed neural network model using natural gradient descent with Dirichlet distribution

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