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

Yin Fang, Gang-Zhou Wu, Nikolay A. Kudryashov, Yue-Yue Wang and Chao-Qing Dai

Chaos, Solitons & Fractals, 2022, vol. 158, issue C

Abstract: In 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.

Keywords: Conservation-law constraint; Neural network; Flexible learning rate; Nonlinear Schrödinger equation; Korteweg-de Vries and modified Korteweg-de Vries equations (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (12)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922003289

DOI: 10.1016/j.chaos.2022.112118

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