Publication:
Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method

Дата
2022
Авторы
Fang, Y.
Wu, G. Z.
Wang, Y. Y.
Dai, C. Q.
Kudryashov, N. A.
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Научные группы
Организационные подразделения
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Организационная единица
Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
Выпуск журнала
Аннотация
© 2022 Elsevier LtdIn the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law constrained neural network method with the flexible learning rate to predict solutions and parameters of nonlinear wave models. As some examples, we study real and complex typical nonlinear wave models, including nonlinear Schrödinger equation, Korteweg-de Vries and modified Korteweg-de Vries equations. Compared with the traditional physics-informed neural network method, this new method can more accurately predict solutions and parameters of some specific nonlinear wave models even when less information is needed, for example, in the absence of the boundary conditions. This provides a reference to further study solutions of nonlinear wave models by combining the deep learning and the integrable theory.
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Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method / Fang, Y. [et al.] // Chaos, Solitons and Fractals. - 2022. - 158. - 10.1016/j.chaos.2022.112118
URI
https://www.doi.org/10.1016/j.chaos.2022.112118
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85129196777&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000830316700022
 https://openrepository.mephi.ru/handle/123456789/27893
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