A search grid for parameter optimization as a byproduct of model sensitivity analysis

Inverse problem solving, i.e. the retrieval of optimal values of model parameters from experimental data, remains a bottleneck for modelers. Therefore, a large variety of (heuristic) optimization algorithms has been developed to deal with the inverse problem. However, in some cases, the use of a grid search may be more appropriate or simply more practical. In this paper an approach is presented to improve the selection of the grid points to be evaluated and which does not depend on the knowledge or availability of the underlying model equations. It is suggested that using the information acquired through a sensitivity analysis can lead to better grid search results. Using the sensitivity analysis information, a Gauss–Newton-like matrix is constructed and the eigenvalues and eigenvectors of this matrix are employed to transform naive search grids into better thought-out ones. After a theoretical analysis of the approach, some computational experiments are performed using a simple linear model, as well as more complex nonlinear models.