Discovery of PDEs driven by data with sharp gradient or discontinuity

doi:10.1016/j.camwa.2023.03.021

CORC > 力学研究所 > 中国科学院力学研究所 > 非线性力学国家重点实验室

	Discovery of PDEs driven by data with sharp gradient or discontinuity
	Wang, Kang ; Zhang L(张磊); Tang, Shaoqiang
刊名	COMPUTERS & MATHEMATICS WITH APPLICATIONS
	2023-06
卷号	140 页码:33-43
关键词	System identification Partial differential equations Gaussian process Discontinuous data Machine learning
ISSN号	0898-1221
DOI	10.1016/j.camwa.2023.03.021
英文摘要	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.
分类号	一类
WOS研究方向	WOS:000968388000001
语种	英语
资助机构	National Natural Science Foundation of China ; NSFC [12202451]
其他责任者	Zhang, L
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/92243]
专题	力学研究所_非线性力学国家重点实验室
作者单位	1.(Zhang Lei) Univ Chinese Acad Sci Sch Engn Sci Beijing 100049 Peoples R China 2.(Zhang Lei) Chinese Acad Sci Inst Mech State Key Lab Nonlinear Mech Beijing 100190 Peoples R China 3.(Wang Kang, Tang Shaoqiang) Peking Univ Coll Engn HEDPS & LTCS Beijing 100871 Peoples R China
推荐引用方式 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.
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.