Reconstruction algorithm for unknown cavities via Feynman–Kac type formula

Hajime Kawakami ()

Computational Optimization and Applications, 2015, vol. 61, issue 1, 133 pages

Abstract: In this paper, we consider an inverse problem of identifying one or more unknown cavities in a heat conductor. We propose an algorithm for reconstructing the position and shape of the unknown cavities using the measured surface temperature of the heat conductor. The heat conductor is discretized into small components, and we attempt to determine the components of the unknown cavities. Each of the components of the cavities is encoded as $$0,$$ 0 , and each of the other components is encoded as $$1.$$ 1 . Thus, the inverse problem is translated into a binary optimization problem. Our algorithm is based on a discrete probabilistic representation of a solution of an initial boundary value problem for the heat equation, which we call a discrete Feynman–Kac type formula. It uses a set of sample paths generated by the Monte-Carlo method. We can use this formula to naturally transform the binary optimization problem to an optimization problem with continuous variables. This continuous approach is used by the algorithm. Although the algorithm comprises some iterations, each iteration step can use a common set of sample paths. Thus, we only need one round of the Monte-Carlo-based simulation to obtain the set of sample paths. Our experiments suggest that the algorithm has an acceptable performance when there are one or two cavities. Copyright Springer Science+Business Media New York 2015

Keywords: Inverse problem; Heat equation; Nonlinear integer programming; Binary variables; Continuous approach; Monte-Carlo method (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-014-9706-4 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:61:y:2015:i:1:p:101-133

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-014-9706-4

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().