Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator

DOI10.1016/j.chaos.2022.112787OpenAlexW4306749483WikidataQ114952558 ScholiaQ114952558MaRDI QIDQ2679950

Ming Zhong, Zhenya Yan

Publication date: 26 January 2023

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.14291

zbMATH Keywords

activation functiondeep learningchannel of fully-connected layerdata-driven soliton mappingFourier neural operatorintegrable fractional nonlinear wave equations

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Approximation methods and numerical treatment of dynamical systems (37M99) Soliton solutions (35C08)

Related Items (3)

Inverse scattering transform for the integrable fractional derivative nonlinear Schrödinger equation ⋮ Pre-training physics-informed neural network with mixed sampling and its application in high-dimensional systems ⋮ Data-driven forward and inverse problems for chaotic and hyperchaotic dynamic systems based on two machine learning architectures

Uses Software

• Julia
• TensorFlow
• PyTorch
• ImageNet
• Tensor2Tensor
• BERT
• DeepXDE
• AlexNet
• Wasserstein GAN
• DeepONet

Cites Work

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