Global optimization in inverse problems: A comparison of Kriging and radial basis functions

TL;DR

This paper compares Kriging and Radial Basis Function methods for global optimization in ill-posed inverse problems, highlighting the advantages of RBF adaptation for non-linear inverse problems with expensive evaluations.

Contribution

It provides a comparative analysis of Kriging and RBF techniques, proposing RBF adaptation as the most promising approach for non-linear inverse problems.

Findings

RBF-based methods are more adaptable for inverse problems.

Kriging offers credible stopping rules but less flexibility.

RBF adaptation shows promising results in complex inverse scenarios.

Abstract

We study global optimization (GOP) in the framework of non-linear inverse problems with a unique solution. These problems are in general ill-posed. Evaluation of the objective function is often expensive, as it implies the solution of a non-trivial forward problem. The ill-posedness of these problems calls for regularization while the high evaluation cost of the objective function can be addressed with response surface techniques. The global optimization using Radial Basis Function (RBF) as presented by Gutmann (2001) is a response surface global optimization technique with regularizing aspects. Alternatively, several publications put forward global optimization using a probabilistic approach based upon Kriging as an efficient technique for non-linear multi modal objective functions, thereby providing a credible stopping rule (Jones2001). After comparing both concepts, we argue that in case of non-linear inverse problems an adaptation of the RBF algorithm seems to be the most promising approach.