| Abstract: |
| The accurate estimation, physical interpretation, and elimination of parameters in mathematical models often depends on the quantities of interest (QoIs) for which data is available and the structure of the model with respect to its parameters. When data is limited, calibrating models with more than a few parameters can be challenging due to non-identifiabilty of a subset of the model parameters. We present techniques for combining local sensitivity and identifiability analysis with the numerical solution of inverse problems for parameter estimation and model reduction. These techniques are based on a decomposition involving the sensitivity matrix for QoIs tied to the data. Application of these techniques is illustrated for two mathematical models: (i) nonlinear elastic vessel wall deformation in large pulmonary arteries of the cardiovascular system in pulmonary hypertension, and (ii) reaction kinetics for enzyme-mediated polymerization of fibrinogen into insoluble fibrin matrix in a biomimetic wound healing system. In each case, the approach is tailored to the application and the capabilities to preserve or reduce objective cost in the optimization, while also producing reduced models, is demonstrated. |
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