Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureHoofdstukAcademicpeer review

Samenvatting

These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a notion of optimal performance in terms of the smallest reconstruction error that any reconstruction algorithm can achieve, the notes present practical numerical algorithms based on nonlinear reduced models for which one can prove that they can deliver a performance close to optimal. We also discuss algorithms for sensor placement. The proposed concepts may be viewed as exploring alternatives to Bayesian inversion in favor of more deterministic notions of accuracy quantification.

Originele taal-2Engels
TitelModel Order Reduction and Applications Cetraro, Italy 2021
RedacteurenMaurizio Falcone, Gianluigi Rozza
UitgeverijSpringer
Pagina's73-124
Aantal pagina's52
ISBN van elektronische versie978-3-031-29563-8
ISBN van geprinte versie978-3-031-29562-1
DOI's
StatusGepubliceerd - 2023

Publicatie series

NaamLecture Notes in Mathematics
Volume2328
ISSN van geprinte versie0075-8434
ISSN van elektronische versie1617-9692

Bibliografische nota

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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