KMS Of Academy of mathematics and systems sciences, CAS
| Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators | |
| Lu, Lu1; Jin, Pengzhan2,3; Pang, Guofei2; Zhang, Zhongqiang4; Karniadakis, George Em2 | |
| 2021-03-01 | |
| Source Publication | NATURE MACHINE INTELLIGENCE
 |
| Volume | 3Issue:3Pages:218-+ |
| Abstract | 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 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | DOE PhILMs project[DE-SC0019453] ; DARPA-CompMods[HR00112090062] |
| WOS Research Area | Computer Science |
| WOS Subject | Computer Science, Artificial Intelligence ; Computer Science, Interdisciplinary Applications |
| WOS ID | WOS:000641834300001 |
| Publisher | SPRINGERNATURE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58488 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Karniadakis, George Em |
| Affiliation | 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 |
| Recommended Citation 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-+. |
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