| Abstract: |
| We consider inverse problems governed by systems of differential equations that contain uncertain parameters in addition to the parameters being estimated. For example, while the goal may be estimating some coefficients or coefficient functions, one might have uncertainties in initial conditions or source terms. In such problems, it is important to understand the sensitivity of the solution of the inverse problem to the uncertain model parameters. It is also of interest to understand the sensitivity of the inverse problem solution to different types of measurements or parameters describing the experimental setup. Hyper-differential sensitivity analysis (HDSA) is a sensitivity analysis approach that provides tools for such tasks. In this talk, we discuss HDSA for systems governed by ordinary differential equations with a focus on illustrative model problems in epidemiology. We will also discuss uncertainty analysis in the class of parameterized inverse problems under study. |
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