KFU. Card publication. Analysis of the Physics-Informed Neural Network Approach to Solving Diffusion Equation

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ANALYSIS OF THE PHYSICS-INFORMED NEURAL NETWORK APPROACH TO SOLVING DIFFUSION EQUATION

Form of presentation

Articles in international journals and collections

Year of publication

2025

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Authors, employees of KFU

Konyukhov Vladimir Mikhaylovich, author

Bibliographic description in the original language

Konyukhov I.V., Konyukhov V.M., Kurdyukov A.V., Analysis of the Physics-Informed Neural Network Approach to Solving Diffusion Equation//Lobachevskii Journal of Mathematics. - 2025. - Vol.46, Is.4. - P.1860-1870.

Annotation

The application of physics-informed neural networks for solving the differential equation of parabolic type is considered. The influence of the neural network structure, optimization algorithms, software and processors' types on the learning process and accuracy of the solution of the two-dimensional diffusion problem is investigated using computational experiments. The accuracy of the neural network solution is evaluated on the basis of comparison with the numerical solution. Based on the analysis of the results of multivariate calculations, it is shown that if the initial condition is included into the loss function expression, the accuracy of the solution increases significantly.

Keywords

machine learning, physics-informed neural networks, partial differential equations, diffusion equation, numerical methods

The name of the journal

Lobachevskii Journal of Mathematics

URL

https://www.scopus.com/inward/record.uri?eid=2-s2.0-105013865670&doi=10.1134%2FS1995080225605788&partnerID=40&md5=bd11f141acdaa0a75be7173d37e1d5fb

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=317483&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Konyukhov Vladimir Mikhaylovich	ru_RU
dc.date.accessioned	2025-01-01T00:00:00Z	ru_RU
dc.date.available	2025-01-01T00:00:00Z	ru_RU
dc.date.issued	2025	ru_RU
dc.identifier.citation	Konyukhov I.V., Konyukhov V.M., Kurdyukov A.V., Analysis of the Physics-Informed Neural Network Approach to Solving Diffusion Equation//Lobachevskii Journal of Mathematics. - 2025. - Vol.46, Is.4. - P.1860-1870.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=317483&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	The application of physics-informed neural networks for solving the differential equation of parabolic type is considered. The influence of the neural network structure, optimization algorithms, software and processors' types on the learning process and accuracy of the solution of the two-dimensional diffusion problem is investigated using computational experiments. The accuracy of the neural network solution is evaluated on the basis of comparison with the numerical solution. Based on the analysis of the results of multivariate calculations, it is shown that if the initial condition is included into the loss function expression, the accuracy of the solution increases significantly.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	machine learning	ru_RU
dc.subject	physics-informed neural networks	ru_RU
dc.subject	partial differential equations	ru_RU
dc.subject	diffusion equation	ru_RU
dc.subject	numerical methods	ru_RU
dc.title	Analysis of the Physics-Informed Neural Network Approach to Solving Diffusion Equation	ru_RU
dc.type	Articles in international journals and collections	ru_RU