Ukrainian Journal of Physical Optics

2024 Volume 25, Issue 5

ISSN 1609-1833 (Print)


Su-Yong Xu, Ao-Cheng Yang and Qin Zhou

1Research Group of Nonlinear Optical Science and Technology, Research Center of Nonlinear Science, School of Mathematical and Physical Sciences, Wuhan Textile University, Wuhan 430200, China,
2College of Optical, Mechanical and Electrical Engineering, Zhejiang A&F University, Lin'an 311300, China
3State Key Laboratory of New Textile Materials and Advanced Processing Technologies, Wuhan Textile University, Wuhan 430200, China


This paper uses parallel hard-constraint physics-informed neural networks to investigate the prediction of nondegenerate soliton and estimate parameters for the coupled nonlinear Schrödinger’s equation. Based on our previous analytical results, three types of nondegenerate solitons have been predicted in the forward problem under the corresponding initial and boundary conditions. In the inverse problem, when employing pure data as the training set, the relative errors in predicting the system’s parameters of group velocity dispersion β2 and Kerr nonlinearity γ are both less than 1%. Moreover, upon introducing a 5% noise level to the training set, the relative errors for β2 and γ remain below 3%. Additionally, we introduce for the first time the application of Deep Operator Networks (DeepONet) to predict nondegenerate soliton, reducing relative L2 error to 10-3 and achieving a speedup of approximately 103 times higher compared to the phPINN method. This demonstrates the efficacy of operator learning methods in addressing nonlinear optical problems.

Keywords: nondegenerate solitons, coupled nonlinear Schrodinger's equation, phPINN, DeepONet

UDC: 535.32

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    У цій статті використовуються паралельні нейронні мережі з жорсткими обмеженнями, засновані на фізичних даних, для дослідження передбачення невиродженого солітону та оцінки параметрів для зв’язаного нелінійного рівняння Шредінгера. На основі наших попередніх аналітичних результатів у прямій задачі було передбачено три типи невироджених солітонів за відповідних початкових і граничних умов. У зворотній задачі, коли в якості навчального набору використовуються чисті дані, відносні похибки у передбаченні параметрів системи дисперсії групової швидкості β2 та нелінійності Керра γ становлять менше ніж 1%. Крім того, при введенні 5% рівня шуму в навчальну множину відносні похибки для β2 і γ залишаються нижчими ніж 3%. Крім того, ми вперше представляємо застосування Deep Operator Networks для прогнозування невироджених солітонів, зменшуючи відносну помилку L2 до 10-3 і досягаючи прискорення приблизно в 103 рази більшого порівняно з методом phPINN. Це демонструє ефективність методів навчання операторів у вирішенні нелінійних оптичних проблем.

    Ключові слова: невироджені солітони, зв’язане нелінійне рівняння Шредінгера, phPINN, DeepONet

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