Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

doi:10.1038/s42256-021-00302-5

CSpace

	Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
	Lu, Lu 1; Jin, Pengzhan 2,3; Pang, Guofei 2; Zhang, Zhongqiang 4; Karniadakis, George Em 2
	2021-03-01
发表期刊	NATURE MACHINE INTELLIGENCE
卷号	3 期号:3 页码:218-+
摘要	It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.
DOI	10.1038/s42256-021-00302-5
收录类别	SCI
语种	英语
资助项目	DOE PhILMs project[DE-SC0019453] ; DARPA-CompMods[HR00112090062]
WOS研究方向	Computer Science
WOS类目	Computer Science, Artificial Intelligence ; Computer Science, Interdisciplinary Applications
WOS记录号	WOS:000641834300001
出版者	SPRINGERNATURE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58488
专题	中国科学院数学与系统科学研究院
通讯作者	Karniadakis, George Em
作者单位	1.MIT, Dept Math, Cambridge, MA 02139 USA 2.Brown Univ, Div Appl Math, Providence, RI 02912 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing, Peoples R China 4.Worcester Polytech Inst, Dept Math Sci, Worcester, MA 01609 USA
推荐引用方式 GB/T 7714	Lu, Lu,Jin, Pengzhan,Pang, Guofei,et al. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators[J]. NATURE MACHINE INTELLIGENCE,2021,3(3):218-+.
APA	Lu, Lu,Jin, Pengzhan,Pang, Guofei,Zhang, Zhongqiang,&Karniadakis, George Em.(2021).Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.NATURE MACHINE INTELLIGENCE,3(3),218-+.
MLA	Lu, Lu,et al."Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators".NATURE MACHINE INTELLIGENCE 3.3(2021):218-+.