A computational framework for the regularization of adjoint analysis in multiscale PDE systems
Journal of Computational Physics
Journal of Computational Physics
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We study model nonlinearity and sensitivity for parameter estimation problems. Previous work has revealed a correlation between high nonlinearity, low sensitivity, and short scale for an ODE model. In this paper, we investigate whether this correlation is valid for a larger class of model functions. We set forth a proposition that says, in essence, that the correlation holds when the forward model output is an integral. Solutions to ODEs and PDEs can be viewed as integral models. If the proposition is true, it may explain an apparent conflict between earlier works on uncertainty analysis for parameter estimation problems. It could also have impact on the choice of solution algorithm for such problems. The validity of the proposition is assessed by studying nonlinearity and sensitivity for fairly general nonlinear models, and corresponding integrals of these models. Theory is developed and its predictions are tested through numerical examples. The focus is on general effects for the model classes (integrated/nonintegrated), i.e., effects that do not depend on any specific choice of model function within each class.