Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

Fang, Yin; Bo, Wen-Bo; Wang, Ru-Ru; Wang, Yueyue; Dai, Chao-Qing

doi:10.1016/j.chaos.2022.112908

Cited by 15 publications

(2 citation statements)

References 48 publications

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“…Another thing we need to compare is the types of solitons in existing studies. Looking at the study examining the two-soliton, rogue structure [26,28,29] which are the rare types in the literature, it will be seen that the error obtained is similar to the error in this study. It can be seen that the classical PINN method gives poor results compared to advanced numerical methods such as B-Spline and the modified Laplace decomposition method in layered and complex soliton types [30,31].…”

Section: Tablesupporting

confidence: 81%

Soliton Solutions of Some Ocean Waves Supported by Physics Informed Neural Network Method

Onder,

Sahiner,

Secer

et al. 2024

AIA

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In this study, we aim to obtain numerical results of the modified Benjamin-Bona-Mahony equation, Ostrovsky-Benjamin-Bona-Mahony equation and Mikhailov-Novikov-Wang equation via the physics-informed neural networks (PINN) method. The equations are modeled for shallow and long water waves, as well as fundamental and phenomenonal models in ocean engineering. According to the implementation, we obtained the PINN solutions of kink, bright, multisoliton (two-soliton) and mixed dark-bright soliton solutions. According to the inference from the obtained results, we achieved good results in some cases compared to other approximate solution methods in the literature. However, it was also observed that the best possible results could not be obtained in cases where the soliton type was intricate and layered. While the results were obtained, the number of hidden layers and the number of neural networks in the layers also varied. These results are shown in tables. Since it is known that the aforementioned models are not solved by the PINN method, we anticipate that the study will lead to other studies in the field of ocean engineering.

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Section: Tablesupporting

confidence: 81%

Soliton Solutions of Some Ocean Waves Supported by Physics Informed Neural Network Method

Onder,

Sahiner,

Secer

et al. 2024

AIA

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“…Wu et al combined the standard PINN with the conservation laws that enhances the physical model constraint capabilities of the PINN [25]. Fang et al proposed a strongly-constrained physically informed neural network (SCPINN) by adding the information of the complex derivatives to the PINN, which efectively predicts a series of nonlinear dynamical equations [26]. Ramabathiran and Ramachandran proposed a method that mixes a PINN with traditional meshless numerical algorithms to improve the interpretability of the PINN, and this method can also solve the discontinuity problem [27].…”

Section: Introductionmentioning

confidence: 99%

An Improved Physics-Informed Neural Network Algorithm for Predicting the Phreatic Line of Seepage

Gao

Yao

et al. 2023

Advances in Civil Engineering

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As new ways to solve partial differential equations (PDEs), physics-informed neural network (PINN) algorithms have received widespread attention and have been applied in many fields of study. However, the standard PINN framework lacks sufficient seepage head data, and the method is difficult to apply effectively in seepage analysis with complex boundary conditions. In addition, the differential type Neumann boundary makes the solution more difficult. This study proposed an improved prediction method based on a PINN with the aim of calculating PDEs with complex boundary conditions such as Neumann boundary conditions, in which the spatial distribution characteristic information is increased by a small amount of measured data and the loss equation is dynamically adjusted by loss weighting coefficients. The measured data are converted into a quadratic regular term and added to the loss function as feature data to guide the update process for the weight and bias coefficient of each neuron in the neural network. A typical geotechnical problem concerning seepage phreatic line determination in a rectangular dam is analyzed to demonstrate the efficiency of the improved method. Compared with the standard PINN algorithm, due to the addition of measurement data and dynamic loss weighting coefficients, the improved PINN algorithm has better convergence and can handle more complex boundary conditions. The results show that the improved method makes it convenient to predict the phreatic line in seepage analysis for geotechnical engineering projects with measured data.

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Data-driven forward-inverse problems of the 2-coupled mixed derivative nonlinear Schrödinger equation using deep learning

Qiu,

Geng,

Zhu

et al. 2024

Nonlinear Dyn

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Predicting nonlinear dynamics of optical solitons in optical fiber via the SCPINN

Cited by 15 publications

References 48 publications

Soliton Solutions of Some Ocean Waves Supported by Physics Informed Neural Network Method

Soliton Solutions of Some Ocean Waves Supported by Physics Informed Neural Network Method

An Improved Physics-Informed Neural Network Algorithm for Predicting the Phreatic Line of Seepage

Data-driven forward-inverse problems of the 2-coupled mixed derivative nonlinear Schrödinger equation using deep learning

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