Graph-based prior and forward models for inverse problems on manifolds with boundaries

doi:10.1088/1361-6420/ac3994

	Graph-based prior and forward models for inverse problems on manifolds with boundaries
	Harlim, John 1; Jiang, Shixiao W.2 ; Kim, Hwanwoo 3; Sanz-Alonso, Daniel 3
	2022-03
发表期刊	INVERSE PROBLEMS (IF:2.0[JCR-2023],2.4[5-Year])
ISSN	0266-5611
EISSN	1361-6420
卷号	38 期号:3
发表状态	已发表
DOI	10.1088/1361-6420/ac3994
摘要	This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matern-type Gaussian field priors that enable flexible modeling near the boundaries, representing boundary values by superposition of harmonic functions with appropriate Dirichlet boundary conditions. We also investigate the graph-based approximation of forward models from PDE parameters to observed quantities. In the construction of graph-based prior and forward models, we leverage the ghost point diffusion map algorithm to approximate second-order elliptic operators with classical boundary conditions. Numerical results validate our graph-based approach and demonstrate the need to design prior covariance models that account for boundary conditions.
关键词	Bayesian inverse problem manifold with boundary ghost point diffusion map graph-based prior
URL	查看原文
收录类别	SCI ; EI ; SCIE
语种	英语
资助项目	NSF["DMS-1854299","DMS-1912818/1912802"] ; NGA[DMS-2027056]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000752026800001
出版者	IOP Publishing Ltd
引用统计	正在获取...
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/155863
专题	数学科学研究所_PI研究组(P)_蒋诗晓组
通讯作者	Kim, Hwanwoo
作者单位	1.Penn State Univ, Inst Computat & Data Sci, Dept Meteorol & Atmospher Sci, Dept Math, University Pk, PA 16802 USA 2.ShanghaiTech Univ, Inst Math Sci, Shanghai 201210, Peoples R China 3.Univ Chicago, Dept Stat, Chicago, IL 60637 USA
推荐引用方式 GB/T 7714	Harlim, John,Jiang, Shixiao W.,Kim, Hwanwoo,et al. Graph-based prior and forward models for inverse problems on manifolds with boundaries[J]. INVERSE PROBLEMS,2022,38(3).
APA	Harlim, John,Jiang, Shixiao W.,Kim, Hwanwoo,&Sanz-Alonso, Daniel.(2022).Graph-based prior and forward models for inverse problems on manifolds with boundaries.INVERSE PROBLEMS,38(3).
MLA	Harlim, John,et al."Graph-based prior and forward models for inverse problems on manifolds with boundaries".INVERSE PROBLEMS 38.3(2022).