| Discovery of PDEs driven by data with sharp gradient or discontinuity | |
| Wang, Kang; Zhang L(张磊); Tang, Shaoqiang | |
| Source Publication | COMPUTERS & MATHEMATICS WITH APPLICATIONS
 |
| 2023-06 | |
| Volume | 140Pages:33-43 |
| ISSN | 0898-1221 |
| Abstract | In the data-driven discovery of partial differential equations, previous researchers have successfully employed various methods to derive estimation of parameters from smooth data, but not from data with sharp gradient or discontinuity. To capture the sharp gradient/discontinuous part in data, we introduce a non-zero mean function in terms of the Sigmoid function in the Gaussian process prior. We test the method using noise-free and noisy data on the regression problem and the inverse problem of Burgers' equation, inviscid Burgers' equation, and the nonlinear wave system (NLWS), and verify its effectiveness and robustness. |
| Keyword | System identification Partial differential equations Gaussian process Discontinuous data Machine learning |
| DOI | 10.1016/j.camwa.2023.03.021 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:000968388000001 |
| Funding Organization | National Natural Science Foundation of China ; NSFC [12202451] |
| Classification | 一类 |
| Ranking | 1 |
| Contributor | Zhang, L |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/92243 |
| Collection | 非线性力学国家重点实验室 |
| Affiliation | 1.(Wang Kang, Tang Shaoqiang) Peking Univ Coll Engn HEDPS & LTCS Beijing 100871 Peoples R China 2.(Zhang Lei) Chinese Acad Sci Inst Mech State Key Lab Nonlinear Mech Beijing 100190 Peoples R China 3.(Zhang Lei) Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China |
| Recommended Citation GB/T 7714 | Wang, Kang,Zhang L,Tang, Shaoqiang. Discovery of PDEs driven by data with sharp gradient or discontinuity[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS,2023,140:33-43.Rp_Au:Zhang, L |
| APA | Wang, Kang,张磊,&Tang, Shaoqiang.(2023).Discovery of PDEs driven by data with sharp gradient or discontinuity.COMPUTERS & MATHEMATICS WITH APPLICATIONS,140,33-43. |
| MLA | Wang, Kang,et al."Discovery of PDEs driven by data with sharp gradient or discontinuity".COMPUTERS & MATHEMATICS WITH APPLICATIONS 140(2023):33-43. |
| Files in This Item: | Download All | |||||
| File Name/Size | DocType | Version | Access | License | ||
| Jp2023Fa046.pdf（1166KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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