Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2023, Volume 514, Number 2, Pages 28–38
DOI: https://doi.org/10.31857/S2686954323601586 (Mi danma448) 		 
SPECIAL ISSUE: ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING TECHNOLOGIES

Optimization of physics-informed neural networks for nonlinear Schrödinger equation

I. A. Chuprov, J. Gao, D. S. Efremenko, E. A. Kazakov, F. A. Buzaev, V. Zemlyakov

Huawei Russian Research Institute, Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954323601586
Abstract: In this paper, PINN is applied to the NLSE equation in order to determine the performance range and limiting factors. Some tools, such as manual weights of the loss function components, and selective application of the sinusoidal activation function, are applied to improve the results. Accepting the fact that PINN loses to SSFM in terms of performance, the application of Meta-PINN to NLSE is investigated to cover the range of parameters, demonstrating the successful generalisation ability of Meta- PINN. The paper concludes with a recommendation on how to tune PINN to successfully solve NLSE.
Keywords: physics-informed neural networks, nonlinear Schrödinger equation, nonlinear fiber optics, fine-tuning neural networks.
Presented: A. L. Semenov
Received: 01.09.2023
Revised: 15.09.2023
Accepted: 15.09.2023
English version:
Doklady Mathematics, 2023, Volume 108, Issue suppl. 2, Pages S186–S195
DOI: https://doi.org/10.1134/S1064562423701120
Bibliographic databases:
Document Type: Article
UDC: 519.6
Language: Russian
Citation: I. A. Chuprov, J. Gao, D. S. Efremenko, E. A. Kazakov, F. A. Buzaev, V. Zemlyakov, “Optimization of physics-informed neural networks for nonlinear Schrödinger equation”, Dokl. RAN. Math. Inf. Proc. Upr., 514:2 (2023), 28–38; Dokl. Math., 108:suppl. 2 (2023), S186–S195
Citation in format AMSBIB
\Bibitem{ChuGaoEfr23}
\by I.~A.~Chuprov, J.~Gao, D.~S.~Efremenko, E.~A.~Kazakov, F.~A.~Buzaev, V.~Zemlyakov
\paper Optimization of physics-informed neural networks for nonlinear Schr\"odinger equation
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2023
\vol 514
\issue 2
\pages 28--38
\mathnet{http://mi.mathnet.ru/danma448}
\crossref{https://doi.org/10.31857/S2686954323601586}
\elib{https://elibrary.ru/item.asp?id=56717711}
\transl
\jour Dokl. Math.
\yr 2023
\vol 108
\issue suppl. 2
\pages S186--S195
\crossref{https://doi.org/10.1134/S1064562423701120}
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