Wave-packet behaviors of the defocusing nonlinear Schrödinger equation based on the modified physics-informed neural networks

2021 ◽  
Vol 31 (11) ◽  
pp. 113107
Author(s):  
Sheng Zhang ◽  
Peng Lan ◽  
Jing-Jing Su
Keyword(s):  
Neural Networks ◽  
Schrödinger Equation ◽  
Wave Packet ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

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

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Egor V. Sedov ◽  
Pedro J. Freire ◽  
Vladimir V. Seredin ◽  
Vladyslav A. Kolbasin ◽  
Morteza Kamalian-Kopae ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fourier Spectrum ◽  
Nonlinear Schrodinger Equation ◽  
Training Data ◽  
Nonlinear Schrödinger ◽  
The Neural Network

AbstractWe 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.

Neural networks for computing the continuous nonlinear Fourier spectrum in focusing nonlinear Schrodinger equation: NFT-Net

2021 ◽  
Author(s):  
Egor V. Sedov ◽  
Pedro J. Freire ◽  
Vladimir V. Seredin ◽  
Vladyslav A. Kolbasin ◽  
Morteza Kamalian-Kopae ◽  
...  
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fourier Spectrum ◽  
Nonlinear Schrodinger Equation ◽  
Training Data ◽  
Nonlinear Schrödinger ◽  
The Neural Network

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.

Sign in / Sign up

Export Citation Format

Share Document