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A pseudo-dynamical systems approach to a class of inverse problems in engineering

Banerjee, B and Roy, D and Vasu, RM (2009) A pseudo-dynamical systems approach to a class of inverse problems in engineering. In: Proceedings of the Royal Society A, 465 (2105). pp. 1561-1579.

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Abstract

A pseudo-dynamical approach for a class of inverse problems involving static measurements is proposed and explored. Following linearization of the minimizing functional associated with the underlying optimization problem, the new strategy results in a system of linearized ordinary differential equations (ODEs) whose steady-state solutions yield the desired reconstruction. We consider some explicit and implicit schemes for integrating the ODEs and thus establish a deterministic reconstruction strategy without an explicit use of regularization. A stochastic reconstruction strategy is then developed making use of an ensemble Kalman filter wherein these ODEs serve as the measurement model. Finally, we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest.

Item Type: Journal Article
Additional Information: The copyright of this article belongs to royal society
Keywords: pseudo-dynamical systems; inverse problems; linearization; quasi-Newton methods; ensemble Kalman filters
Department/Centre: Division of Physical & Mathematical Sciences > Instrumentation and Applied Physics (Formally ISU)
Division of Mechanical Sciences > Civil Engineering
Date Deposited: 05 Nov 2009 12:57
Last Modified: 19 Sep 2010 05:30
URI: http://eprints.iisc.ernet.in/id/eprint/19971

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