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# Ralph Smith, North Carolina State University – Applied Mathematics Colloquium

## April 5, 2019 @ 4:00 pm - 5:00 pm

**Title:** *Active Subspace Techniques to Construct Surrogate Models for Complex Physical and Biological Models*

**Abstract: **For many complex physical and biological models, the computational cost of high-fidelity simulation codes precludes their direct use for Bayesian model calibration and uncertainty propagation. For example, neutronics and nuclear thermal hydraulics codes can take hours to days for a single run. Furthermore, the models often have tens to thousands of inputs — comprised of parameters, initial conditions, or boundary conditions — many of which are unidentifiable in the sense that they cannot be uniquely determined using measured responses. In this presentation, we will discuss techniques to isolate influential inputs for subsequent surrogate model construction for Bayesian inference and uncertainty propagation. For input selection, we will discuss

advantages and shortcomings of global sensitivity analysis to isolate influential inputs and detail the use of active subspace construction to determine low-dimensional input manifolds. 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, quantum-informed material characterization, and HIV modeling and treatment.

**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 ASMEAdaptive Structures and Material Systems Prize and the SPIE 2017 Smart Structures and Materials Lifetime Achievement, and he was named a SIAM Fellow in 2018. 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.