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arXiv · 1804.04542

Regula falsi based automatic regularization method for PDE constrained optimization

Nick Schenkels·Wim Vanroose
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Abstract

Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the mismatch between the observed data and the model predictions, including an extra regularization term, and use the PDE as a constraint. Often, a suitable regularization parameter is determined by solving the problem for a whole range of parameters -- e.g. using the L-curve -- which is computationally very expensive. In this paper we derive two methods that simultaneously solve the inverse problem and determine a suitable value for the regularization parameter. The first one is a direct generalization of the Generalized Arnoldi Tikhonov method for linear inverse problems. The second method is a novel method based on similar ideas, but with a number of advantages for nonlinear problems.

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Nick Schenkels, Wim Vanroose. 2018-04-12. Regula falsi based automatic regularization method for PDE constrained optimization. https://doi.org/10.1016/j.cam.2018.08.050

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