Abstract: Engineering and biological models generally have a number of parameters which are nonidentifiable in the sense that they are not uniquely determined by measured responses. Furthermore, the computational cost of high-fidelity simulation codes often precludes their direct use for Bayesian model calibration and uncertainty propagation. In this presentation, we will discuss techniques to isolate influential parameters for subsequent surrogate model construction, Bayesian inference and uncertainty propagation. For parameter selection, we will discuss advantages and shortcomings of global sensitivity analysis to isolate influential inputs and detail the use of parameter subset selection and active subspace techniques as an alternative. We will also discuss the manner in which Bayesian calibration on active subspaces can be used to quantify uncertainties in physical parameters. These techniques will be illustrated for models arising in nuclear power plant design and quantitative systems pharmacology (QSP), as well as models for transductive materials.
Biography: Ralph C. Smith joined the North Carolina State University faculty in 1998 where he is presently a Distinguished University Professor of Mathematics. He is co-author of the research monograph Smart Material Structures: Modeling, Estimation and Control and author of the books Smart Material Systems: Model Development and Uncertainty Quantification: Theory, Implementation, and Applications. He is on the editorial boards of the Journal of Intelligent Material Systems and Structures and the SIAM/ASA Journal on Uncertainty Quantification. He is the recipient of the 2016 ASME Adaptive Structures and Material Systems Prize and the SPIE 2017 Smart Structures and Materials Lifetime Achievement, and he was named a SIAM Fellow in 2018 and an ASME Fellow in 2022. His research areas include mathematical modeling of smart material systems, numerical analysis and methods for physical systems, Bayesian model calibration, sensitivity analysis, control, and uncertainty quantification for physical and biological systems.