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

doi:10.1016/j.chaos.2022.112787

	Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator
	Zhong, Ming 1; Yan, Zhenya 2
刊名	CHAOS SOLITONS & FRACTALS
	2022-12-01
卷号	165 页码:14
关键词	Integrable fractional nonlinear wave equations Fourier neural operator Deep learning Data-driven soliton mapping Activation function Channel of fully-connected layer
ISSN号	0960-0779
DOI	10.1016/j.chaos.2022.112787
英文摘要	In this paper, we firstly extend the Fourier neural operator (FNO) to discovery the mapping between two infinite-dimensional function spaces, where one is the fractional-order index space {e\|e is an element of (0 ,1)} in the fractional integrable nonlinear wave equations while another denotes the soliton solution in the spatio-temporal function space. In other words, once the FNO network is trained, for any given e is an element of (0 ,1) , the corresponding soliton solution can be quickly obtained. To be specific, the soliton solutions are learned for the fractional nonlinear Schrodinger (fNLS), fractional Korteweg-de Vries (fKdV), fractional modified Korteweg-de Vries (fmKdV) and fractional sine-Gordon (fsineG) equations. The FNO architecture is utilized to learn the soliton mappings of the above four equations. The data-driven solitons are also compared with exact solutions to illustrate the powerful approximation capability of the FNO. Moreover, we study the influences of several critical factors (e.g., activation functions containing Relu(x) , Sigmoid(x) , Swish(x) and the new one xtanh(x) , channels of fully connected layer) on the performance of the FNO algorithm. As a result, we find that the x tanh(x) and Swish(x) functions perform better than the Relu(x) and Sigmoid(x) functions in the FNO, and the FNO network with a more-channel fully-connected layer performs better as we expect. These results obtained in this paper will be useful to further understand the neural networks for fractional integrable nonlinear wave equations and the mappings between two infinite-dimensional function spaces.
资助项目	National Natural Science Foundation of China ; [11925108]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000878870900004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60695]
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Zhenya
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhong, Ming,Yan, Zhenya. Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator[J]. CHAOS SOLITONS & FRACTALS,2022,165:14.
APA	Zhong, Ming,&Yan, Zhenya.(2022).Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator.CHAOS SOLITONS & FRACTALS,165,14.
MLA	Zhong, Ming,et al."Data-driven soliton mappings for integrable fractional nonlinear wave equations via deep learning with Fourier neural operator".CHAOS SOLITONS & FRACTALS 165(2022):14.