Computing continuous nonlinear Fourier spectrum of optical signal with artificial neural networks

Egor Sedov, Yaroslav Prylepskiy, Igor Chekhovskoy, Sergei Turitsyn, Michael E. Zelinski (Editor), Tarek M. Taha (Editor), Jonathan Howe (Editor)

Research output: Contribution to journalConference articlepeer-review


In this work, we demonstrate that the high-accuracy computation of the continuous nonlinear spectrum can be performed by using artificial neural networks. We propose the artificial neural network (NN) architecture that can efficiently perform the nonlinear Fourier (NF) optical signal processing. The NN consists of sequential convolution layers and fully connected output layers. This NN predicts only one component of the continuous NF spectrum, such that two identical NNs have to be used to predict the real and imaginary parts of the reflection coefficient. To train the NN, we precomputed 94035 optical signals. 9403 signals were used for validation and excluded from training. The final value of the relative error for the entire validation dataset was less than 0.3%. Our findings highlight the fundamental possibility of using the NNs to analyze and process complex optical signals when the conventional algorithms can fail to deliver an acceptable result.
Original languageEnglish
Article number118430J
Number of pages22
JournalProceedings of SPIE - International Society for Optical Engineering
Publication statusPublished - 1 Aug 2021
EventApplications of Machine Learning 2021 - San Diego, United States
Duration: 1 Aug 20215 Aug 2021

Bibliographical note

Copyright 2021 SPIE. One print or electronic copy may be made for personal use only. Systematic reproduction, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.

Funding: E.S. and I.C. acknowledges the support from Russian Science Foundation under Grant 17-72-30006 and the support by the grant of the President of the Russian Federation (MK-677.2020.9). E.S. and S.T. are supported by the EPSRC programme grant TRANSNET, EP/R035342/1. S.T. and J.P. acknowledge the support of Leverhulme Trust project RPG-2018-063.


  • Nonlinear Fourier transform
  • Neural network
  • Optical communication
  • Signal processing


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