A note on a bilevel problem for parameter learning for inverse problems with the wave equation
type: Item
instance of: scholarly article
title: A note on a bilevel problem for parameter learning for inverse problems with the wave equation
zbMATH Open document ID: 1483.49026
DOI: 10.4171/PM/2073
author: Wiebke Günther
author: Axel Kröner
published in: Portugaliae Mathematica. Nova Série
publication date: 2022-02-22T00:00:00Z
review text: Summary: In this paper we consider a bilevel problem for determining the optimal regularization parameter in an inverse problem with the linear wave equation transferring results from \textit{G. Holler} et al. [Inverse Probl. 34, No. 11, Article ID 115012, 28 p. (2018; Zbl 1400.49046)], where a general function space setting and applications to (bilinear) elliptic problems have been addressed. We analyze the well-posedness and derive the optimality conditions for the bilevel problem for the wave equation. Moreover, for given noisy data the numerical performance of the approach to find the regularization parameter is compared for different choices of priors in the Tikohonov regularization term of the lower level problem.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 49N45
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 7478509
zbMATH Keywords: bilevel optimization
zbMATH Keywords: wave equation
zbMATH Keywords: multi-penalty regularization
zbMATH Keywords: inverse problems
describes a project that uses: FEniCS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7478509