Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm

Mo, Yi-Fan; Ling, Liming; Zeng, Delu

doi:10.1016/j.physleta.2021.127739

Cited by 67 publications

(16 citation statements)

References 50 publications

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“…Vector solitons, which are solitary waves with multiple components in the the coupled nonlinear Schrödinger equation (CNLSE) is addressed by Mo et al [115], who extended PINNs with a pre-fixed multi-stage training algorithm. These findings can be extendable to similar type of equations, such as equations with a rogue wave [176] solution or the Sasa-Satsuma equation and Camassa-Holm equation.…”

Section: Quantum Problems a 1d Nonlinear Schrödinger Equation Is Addr...mentioning

confidence: 99%

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

et al. 2022

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Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

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Section: Quantum Problems a 1d Nonlinear Schrödinger Equation Is Addr...mentioning

confidence: 99%

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

et al. 2022

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show abstract

“…Vector solitons, which are solitary waves with multiple components in the the coupled nonlinear Schrödinger equation (CNLSE) is addressed by Mo et al (2022), who extended PINNs with a pre-fixed multi-stage training algorithm. These findings can be extendable to similar type of equations, such as equations with a rogue wave (Wang and Yan, 2021) solution or the Sasa-Satsuma equation and Camassa-Holm equation.…”

Section: Quantum Physicsmentioning

confidence: 99%

“…Lets start by discussing convergence, whether or not the convergence of PINN is achieved is a matter of research. For example, the relative error for several neural architectures was calculated by altering the number of hidden layers and the number of neurons per layer in Mo et al (2022). In another example, Blechschmidt and Ernst (2021) show the number of successes (i.e.…”

Section: Pinn Challengesmentioning

confidence: 99%

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Cuomo¹,

Cola²,

Giampaolo³

et al. 2022

Preprint

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“…The non-degenerate vectorsoliton solutions can be applied in the fields of Bose-Einstein condensates [25,26] and optics communication [12]. Up until now, the Manakov system has been solved by a pre-fixed multi-stage training algorithm [27]. In this paper, we will apply the RAR-PINN method to model various types of vector solitons and their interactions of Eq.…”

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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Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm

Cited by 67 publications

References 50 publications

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

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

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