Thu, Mar 31, 2022 @ 12:30 PM - 01:30 PM
Sonny Astani Department of Civil and Environmental Engineering
Conferences, Lectures, & Seminars
Speaker: Dr. Michael Shields, John Hopkins University
Talk Title: Manifold Learning for High Dimensional Uncertainty Quantification
Uncertainty Quantification (UQ), the systematic and rigorous accounting of uncertainties, has become widely accepted as an essential component of any proper scientific investigation -“ whether computational, experimental, or otherwise. In computational science and engineering, as well as in experimental investigations, we often encounter problems that are parameterized by very high-dimensional quantities and/or result in very high-dimensional quantities of interest. Thanks to the curse of dimensionality, the challenge of solving these problems grows exponentially with the problem dimensions. This explosive growth in complexity has been widely known for decades and may never be truly resolved. However, all hope is not lost. In this presentation, we offer some strategies for addressing high dimensional UQ problems whose uncertainties can be expressed in lower-dimensional latent spaces or on manifolds whose geometry is not necessarily Euclidean. We begin by introducing some concepts in Reimannian geometry and nonlinear dimension reduction, specifically reviewing Grassmann manifolds and diffusion maps, and show how UQ problems with high dimensional solutions can be solved by projecting solution snapshots onto the Grassmann manifold, performing diffusion maps on the manifold, and constructing surrogate models on the resulting low-dimensional space using standard machine learning methods such as Gaussian process regression, polynomial chaos expansions (PCE), or deep neural networks. Next, we consider problems with very high dimensional inputs and present a survey of 13 different unsupervised learning methods for dimension reduction, which are used to identify low-dimensional latent spaces on which PCE surrogates are constructed. Some takeaways from this general approach, termed manifold-PCE, are presented. Finally, we bring the two components together to propose a general framework for UQ in high dimensions that is widely applicable and very flexible.
Biography: Michael D. Shields is an Associate Professor in the Dept. of Civil & Systems Engineering at Johns Hopkins University and holds a secondary appointment in the Dept. of Materials Science and Engineering. Prof. Shields conducts methodological research in uncertainty quantification and stochastic simulation for problems in mechanics, materials science, and physics with applications ranging from multi-scale material modeling to assessing the reliability and safety of large-scale structures. He received his Ph.D. in Civil Engineering and Engineering Mechanics from Columbia University in 2010, after which he was employed as a Research Engineer in applied computational mechanics at Weidlinger Associates, Inc. He joined the faculty at Johns Hopkins in 2013. For his work in UQ, Prof. Shields has been awarded the ONR Young Investigator Award, the NSF CAREER Award, the DOE Early Career Award, and the Johns Hopkins University Catalyst Award. Prof. Shields and his group also develop the open-source UQpy (Uncertainty Quantification with Python) software, which is a general toolbox for UQ in computational, mathematical, and physical systems.
Host: Dr. Roger Ghanem
Webcast: https://usc.zoom.us/j/91873923659 Meeting ID: 918 7392 3659 Pass: 975701
Audiences: Everyone Is Invited
Contact: Evangeline Reyes