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.
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Funding: JEP and SKT acknowledge the support of Leverhulme Trust project RPG-2018-063. SKT is supported by the EPSRC programme Grant TRANSNET, EP/R035342/1. PJF acknowledges the support from the EU Horizon 2020 program under the Marie Sklodowska-Curie Grant Agreement 813144 (REAL-NET). EVS acknowledges the support from the Russian Science Foundation under Grant 17-72-30006, ISC research was supported by the grant of the President of the Russian Federation (MK-677.2020.9). VAK and JEP acknowledge the Erasmus+ mobility scheme between National Technical University “Kharkiv Polytechnic Institute” and Aston University.