Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
文献类型：期刊论文
| 作者 | Lu, Lu1; Jin, Pengzhan2,3; Pang, Guofei2; Zhang, Zhongqiang4; Karniadakis, George Em2 |
| 刊名 | NATURE MACHINE INTELLIGENCE
 |
| 出版日期 | 2021-03-01 |
| 卷号 | 3期号:3页码:218-+ |
| DOI | 10.1038/s42256-021-00302-5 |
| 英文摘要 | 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. |
| 资助项目 | DOE PhILMs project[DE-SC0019453] ; DARPA-CompMods[HR00112090062] |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000641834300001 |
| 出版者 | SPRINGERNATURE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58487]  |
| 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-+. |
入库方式： OAI收割
来源：数学与系统科学研究院
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