Nonlinearity, Scale, and Sensitivity for Parameter Estimation Problems

Abstract

Both sensitivity and nonlinearity are important for the efficiency of an estimation algorithm. Knowledge of a general nature on sensitivity and/or nonlinearity for some class of models can perhaps be utilized to improve the estimation efficiency for this class.For an ODE model, a correlation between high nonlinearity, low sensitivity, and small-scale perturbations, has been reported. Also, it was found that representing the unknown function by a multi-scale basis lead to faster estimation convergence than use of a single-scale local basis. This was explained referring to the above-mentioned correlation. Recently, the existence of such a correlation for a large class of nonlinear models, including the above-mentioned ODE model, was found.Here, we further investigate into utilization of the correlation Address all correspondence to this author. † Now with Nansen Environmental and Remote Sensing Center, Edvard Griegsvei 3a, N-5037 Solheimsviken, Norway, E-mail: karib@nrsc.no ‡ Now with RF-Rogaland Research, Thormøhlensgt. 55, Norway, between nonlinearity, scale, and sensitivity within parameter estimation. Results from numerical experiments with alternative optimizers on ODE and PDE models describing flow in porous media, are presented.

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