Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN

Fang, Yin; Wu, Gang-Zhou; Wang, Yueyue; Dai, Chao-Qing

doi:10.1007/s11071-021-06550-9

Cited by 180 publications

(30 citation statements)

References 30 publications

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“…Also, as identified by Peregrine [34], modulation instability plays a key role in the formation of patterns resembling freak waves or rogue waves [35]. Using physics-informed neural network (PINN) to obtain femtosecond nonparaxial optical solitons of the higher order nonlinear Helmholtz equation and to obtain fractional solitons in nonparaxial regime are other areas worth investigating as have been done for NLSE in [36] and [37] respectively. Some of these issues are currently under investigation and we hope to report on some of them in the near future.…”

Section: Discussionmentioning

confidence: 99%

Chirped Elliptic Waves: Coupled Helmholtz Equations

Saha,

Roy,

Khare

2022

Preprint

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Exact chirped elliptic wave solutions are obtained within the framework of coupled cubic nonlinear Helmholtz equations in the presence of non-Kerr nonlinearity like self steepening and self frequency shift. It is shown that, for a particular combination of the self steepening and the self frequency shift parameters, the associated nontrivial phase gives rise to chirp reversal across the solitary wave profile. But a different combination of non-Kerr terms leads to chirping but no chirp reversal. The effect of nonparaxial parameter on physical quantities such as intensity, speed and pulse-width of the elliptic waves is studied too. It is found that the speed of the solitary wave can be tuned by altering the nonparaxial parameter. Stable propagation of these nonparaxial elliptic waves is achieved by an appropriate choice of parameters.

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Section: Discussionmentioning

confidence: 99%

Chirped Elliptic Waves: Coupled Helmholtz Equations

Saha,

Roy,

Khare

2022

Preprint

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“…The breathers and rogue wave solutions of the nonlinear Schrödinger (NLS) equation were recovered with the aid of the PINN model [14]. What's more, a variety of femtosecond optical soliton solutions of the high-order NLS equation were investigated with the PINN method [15].…”

Section: Introductionmentioning

confidence: 99%

RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations

Qin¹,

Li²,

Xu³

et al. 2022

Preprint

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This work aims to provide an effective deep learning framework to predict the vectorsoliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN) combining with the residual-based adaptive refinement (RAR-PINN) algorithm. Different from the traditional PINN algorithm which takes points randomly, the RAR-PINN algorithm uses an adaptive point-fetching approach to improve the training efficiency for the solutions with steep gradients. A series of experiment comparisons between the RAR-PINN and traditional PINN algorithms are implemented to a coupled generalized nonlinear Schrödinger (CGNLS) equation as an example. The results indicate that the RAR-PINN algorithm has faster convergence rate and better approximation ability, especially in modeling the shape-changing vector-soliton interactions in the coupled systems. Finally, the RAR-PINN method is applied to perform the data-driven discovery of the CGNLS equation, which shows the dispersion and nonlinear coefficients can be well approximated.

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“…Chen and his group solved local wave solution of NPDEs of second-and third-order, and some classical mathematical physics equations such as the Sine-Gordon, nonlinear Schrödinger and derivative nonlinear Schrödinger equations, and obtained important breather, rogue waves and other soliton solutions for these equations in the field of mathematical physics [14][15][16][17][18][19]. Yan and Dai et al studied data-driven solutions of related equations and parameter discovery using PINNs [20][21][22][23]. Bai et al solved Huxley equation using an improved PINN method [24].…”

Section: Introductionmentioning

confidence: 99%

Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation

Zhang

Chen

2021

Nonlinear Dyn

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Recently, the physics-informed neural networks (PINNs) has received more and more attention because of it's ability to solve nonlinear partial differential equations (NPDEs) via only a small amount of data to quickly obtain data-driven solutions with high accuracy. However, despite their remarkable promise in the early stage, their unbalanced backpropagation gradient calculation leads to drastic oscillations in the gradient value during model training, which is prone to unstable prediction accuracy. Based on this, we develop a gradient optimization algorithm, which proposes a new neural network structure and balances the interaction between different terms in the loss function during model training by means of gradient statistics, so that the newly proposed network architecture is more robust to gradient fluctuations. In this paper, we take the complex modified KdV equation as an example and use the gradient optimised PINNs (GOPINNs) deep learning method to obtain data-driven rational wave solution and soliton molecules solution. Numerical results show that the GOPINNs method effectively smooths the gradient fluctuations, and reproduces the dynamic behavior of these data-driven solutions better than the original PINNs method. In summary, our work provides new insights for optimizing the learning performance of neural networks and improves the prediction accuracy by a factor of 10 to 30 when solving the complex modified KdV equation.

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Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN

Cited by 180 publications

References 30 publications

Chirped Elliptic Waves: Coupled Helmholtz Equations

Chirped Elliptic Waves: Coupled Helmholtz Equations

RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations

Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation

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