IGPP is pleased to invite you to join its Spring 2022 Seminar Series presentation featuring UC Merced's Noemi Petra. Dr. Petra's talk, "Exploiting Low-dimensional Structure in Bayesian Inverse Problems Governed by a Nonlinear Stokes Ice Sheet Flow Model" will be available via Zoom on Tuesday, April 26, 2022, starting at 12:00pm. Zoom: https://ucsd.zoom.us/j/99001964180?pwd=cmFOcFVBM0JRTmJwU1B1N1Rlbm1BQT09. Password: smallModel
Time: 12:00 pm, Pacific Time
Note: This meeting will be recorded. Please make sure that you are comfortable with this before registering.
Abstract: 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.