Limits to Nonlinear Inversion

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2012

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For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our ability to produce efficient search algorithms. Such algorithms may be completely problem-independent (which is the case for the so-called 'meta-heuristics' or 'blind-search' algorithms), or they may be designed with the structure of the concrete problem in mind. We show that pure meta-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag.
Original languageEnglish
Title of host publicationApplied Parallel and Scientific Computing. Proceedings of the PARA 2010 Meeting : Revised Selected Papers, Part I
PublisherSpringer
Publication date2012
Pages11-21
ISBN (print)978-3-642-28151-8
StatePublished

Conference

Conference10th International Conference on Applied Parallel and Scientific Computing
CountryIceland
CityReykjavik
Period06/06/1009/06/10
NameLecture Notes in Computer Science
NumberPart 1
Volume7133
ISSN (Print)0302-9743
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