Past Event: Oden Institute Seminar

Joint parameter and state dimension reduction for Bayesian ice sheet inverse problems

Noemi Petra, Associate Professor, Applied Mathematics, School of Natural Sciences, University of California at Merced

Abstract

** This seminar is Zoom only**

Solving large-scale Bayesian inverse problems governed by complex forward models suffers from the twin difficulties of the high dimensionality of the uncertain parameters and computationally expensive forward models. In this talk, we focus on joint parameter and state dimension reduction that has the promise to reduce the computational cost when solving these problems.  To reduce the parameter dimension, we exploit the underlying problem structure (e.g., local sensitivity of the data to parameters, the smoothing properties of the forward model, the fact that the data contain limited information about the (infinite-dimensional) parameter field, and the covariance structure of the prior) and identify a likelihood-informed parameter subspace that shows where the change from prior to posterior is most significant. For the state dimension reduction, we employ a proper orthogonal decomposition (POD) combined with the discrete empirical interpolation method (DEIM) to approximate the nonlinear term in the forward model. To account for the model error (due to using a reduced order forward model) we use a Bayesian Approximation Error (BAE) approach which leads to a modified formula for the posterior with a non-diagonal covariance in the likelihood. We illustrate our approach with a model ice sheet inverse problem governed by the nonlinear Stokes equation for which the basal sliding coefficient field is inferred from the surface ice flow velocity. The results show the potential to make the exploration of the full posterior distribution of the parameter or subsequent predictions more tractable.

Biography

Noemi Petra is an Associate Professor of Applied Mathematics in the School of Natural Sciences at the University of California, Merced. She is currently the faculty advisor of the UC Merced SIAM Student Chapter.  Noemi earned her B.Sc. degree in Mathematics and Computer Science from Babeș-Bolyai University, Romania, and her Ph.D. degree in Applied Mathematics from the University of Maryland, Baltimore County. Prior to joining the University of California, Merced she was the recipient of a Peter O’Donnell Jr. (ICES) Postdoctoral Fellowship and later held a Research Associate position at the Oden Institute at The University of Texas at Austin. During Summers 2015 and 2016, she was a Visiting Faculty in the Mathematics and Computer Science Division at Argonne National Laboratory, funded by the Department of Energy (DOE) Visiting Faculty Program (VFP) and during 2017-2018 she served as the secretary of the SIAM Uncertainty Quantification Activity Group (SIAM UQ). As of 2017, Noemi is a recipient of an NSF CAREER grant award. She and her collaborators received the 2019 SIAM Computational Science & Engineering Best Paper Prize. Her research interests include large-scale Bayesian inverse problems governed by differential equation, uncertainty quantification in inference and prediction, and optimal experimental design. Her research is commonly driven by real-world applications such as the dynamics of ice sheets, or power grid.