Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation

Abstract We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus...

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Autores principales:	Egor V. Sedov, Pedro J. Freire, Vladimir V. Seredin, Vladyslav A. Kolbasin, Morteza Kamalian-Kopae, Igor S. Chekhovskoy, Sergei K. Turitsyn, Jaroslaw E. Prilepsky
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/90fe5d2116484d4981a9d40767e509f4
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spelling	oai:doaj.org-article:90fe5d2116484d4981a9d40767e509f42021-11-28T12:16:13ZNeural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation10.1038/s41598-021-02252-92045-2322https://doaj.org/article/90fe5d2116484d4981a9d40767e509f42021-11-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-02252-9https://doaj.org/toc/2045-2322Abstract We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net. The Bayesian optimisation is utilised to find the optimal neural network architecture. The benefits of using the NFT-Net as compared to the conventional numerical NFT methods becomes evident when we deal with noise-corrupted signals, where the neural networks-based processing results in effective noise suppression. This advantage becomes more pronounced when the noise level is sufficiently high, and we train the neural network on the noise-corrupted field profiles. The maximum restoration quality corresponds to the case where the signal-to-noise ratio of the training data coincides with that of the validation signals. Finally, we also demonstrate that the NFT b-coefficient important for optical communication applications can be recovered with high accuracy and denoised by the neural network with the same architecture.Egor V. SedovPedro J. FreireVladimir V. SeredinVladyslav A. KolbasinMorteza Kamalian-KopaeIgor S. ChekhovskoySergei K. TuritsynJaroslaw E. PrilepskyNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-15 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Egor V. Sedov Pedro J. Freire Vladimir V. Seredin Vladyslav A. Kolbasin Morteza Kamalian-Kopae Igor S. Chekhovskoy Sergei K. Turitsyn Jaroslaw E. Prilepsky Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation
description	Abstract We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net. The Bayesian optimisation is utilised to find the optimal neural network architecture. The benefits of using the NFT-Net as compared to the conventional numerical NFT methods becomes evident when we deal with noise-corrupted signals, where the neural networks-based processing results in effective noise suppression. This advantage becomes more pronounced when the noise level is sufficiently high, and we train the neural network on the noise-corrupted field profiles. The maximum restoration quality corresponds to the case where the signal-to-noise ratio of the training data coincides with that of the validation signals. Finally, we also demonstrate that the NFT b-coefficient important for optical communication applications can be recovered with high accuracy and denoised by the neural network with the same architecture.
format	article
author	Egor V. Sedov Pedro J. Freire Vladimir V. Seredin Vladyslav A. Kolbasin Morteza Kamalian-Kopae Igor S. Chekhovskoy Sergei K. Turitsyn Jaroslaw E. Prilepsky
author_facet	Egor V. Sedov Pedro J. Freire Vladimir V. Seredin Vladyslav A. Kolbasin Morteza Kamalian-Kopae Igor S. Chekhovskoy Sergei K. Turitsyn Jaroslaw E. Prilepsky
author_sort	Egor V. Sedov
title	Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation
title_short	Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation
title_full	Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation
title_fullStr	Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation
title_full_unstemmed	Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation
title_sort	neural networks for computing and denoising the continuous nonlinear fourier spectrum in focusing nonlinear schrödinger equation
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/90fe5d2116484d4981a9d40767e509f4
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Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation

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