A Sequential Sensor Selection Strategy for Hyper-Parameterized Linear Bayesian Inverse Problems

Nicole Aretz-Nellesen, Peng Chen, Martin Grepl, Karen Veroy

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This model variability needs to be taken into account for the experimental design to guarantee that the Bayesian inverse solution is uniformly informative. In this work we link the numerical stability of the maximum a posterior point and A-optimal experimental design to an observability coefficient that directly describes the influence of the chosen sensors. We propose an algorithm that iteratively chooses the sensor locations to improve this coefficient and thereby decrease the eigenvalues of the posterior covariance matrix. This algorithm exploits the structure of the solution manifold in the hyper-parameter domain via a reduced basis surrogate solution for computational efficiency. We illustrate our results with a steady-state thermal conduction problem.
Original languageEnglish
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2019
EditorsFred J. Vermolen, Cornelis Vuik
Place of PublicationCham, Switzerland
PublisherSpringer
Pages489-497
Volume139
ISBN (Electronic)978-3-030-55874-1
ISBN (Print)978-3-030-55873-4
DOIs
Publication statusPublished - 2021
Externally publishedYes
EventEuropean Conference on Numerical Mathematics and Advanced Applications 2019 - Hotel Zuiderduin, Egmond aan Zee, Netherlands
Duration: 30 Sep 20194 Oct 2019
https://www.enumath2019.eu/

Publication series

NameLecture Notes in Computational Science and Engineering
PublisherSpringer International Publishing
Volume139
ISSN (Print)1439-7358

Conference

ConferenceEuropean Conference on Numerical Mathematics and Advanced Applications 2019
Abbreviated titleENUMATH 2019
CountryNetherlands
CityEgmond aan Zee
Period30/09/194/10/19
Internet address

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