@article{stevens_sunseri_alexanderian_2022, title={Hyper-differential sensitivity analysis for inverse problems governed by ODEs with application to COVID-19 modeling}, volume={351}, ISSN={["1879-3134"]}, DOI={10.1016/j.mbs.2022.108887}, abstractNote={We consider inverse problems governed by systems of ordinary differential equations (ODEs) that contain uncertain parameters in addition to the parameters being estimated. In such problems, which are common in applications, 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. We extend existing HDSA methods by developing methods for quantifying the uncertainty in the estimated parameters. Specifically, we propose a linear approximation to the solution of the inverse problem that allows efficiently approximating the statistical properties of the estimated parameters. We also explore the use of this linear model for approximate global sensitivity analysis. As a driving application, we consider an inverse problem governed by a COVID-19 model. We present comprehensive computational studies that examine the sensitivity of this inverse problem to several uncertain model parameters and different types of measurement data. Our results also demonstrate the effectiveness of the linear approximation model for uncertainty quantification in inverse problems and for parameter screening.}, journal={MATHEMATICAL BIOSCIENCES}, author={Stevens, Mason and Sunseri, Isaac and Alexanderian, Alen}, year={2022}, month={Sep} }
 @article{alexanderian_petra_stadler_sunseri_2021, title={Optimal Design of Large-scale Bayesian Linear Inverse Problems Under Reducible Model Uncertainty: Good to Know What You Don't Know}, volume={9}, ISSN={["2166-2525"]}, DOI={10.1137/20M1347292}, abstractNote={We consider optimal design of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations that contain secondary reducible model uncertainties, in addition to the uncertainty in the inversion parameters. By reducible uncertainties we refer to parametric uncertainties that can be reduced through parameter inference. We seek experimental designs that minimize the posterior uncertainty in the primary parameters, while accounting for the uncertainty in secondary parameters. We accomplish this by deriving a marginalized A-optimality criterion and developing an efficient computational approach for its optimization. We illustrate our approach for estimating an uncertain time-dependent source in a contaminant transport model with an uncertain initial state as secondary uncertainty. Our results indicate that accounting for additional model uncertainty in the experimental design process is crucial.}, number={1}, journal={SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION}, author={Alexanderian, Alen and Petra, Noemi and Stadler, Georg and Sunseri, Isaac}, year={2021}, pages={163–184} }
 @article{sunseri_hart_bloemen waanders_alexanderian_2020, title={Hyper-differential sensitivity analysis for inverse problems constrained by partial differential equations}, volume={36}, ISSN={["1361-6420"]}, DOI={10.1088/1361-6420/abaf63}, abstractNote={Abstract}, number={12}, journal={INVERSE PROBLEMS}, author={Sunseri, Isaac and Hart, Joseph and Bloemen Waanders, Bart and Alexanderian, Alen}, year={2020}, month={Dec} }