Nonlinear Goal-Oriented Bayesian Inference: Application to Carbon Capture and Storage
Name
Lieberman-2014-Nonlinear goal-orien.pdf
Size
4.37 MB
Format
Adobe PDF
Checksum (MD5)
82536edfa680ca3659b7fe89fc32ac84
Author(s)
Lieberman, Chad E.
Willcox, Karen E.
Date Issued
May 2014
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Lieberman, Chad, and Karen Willcox. “Nonlinear Goal-Oriented Bayesian Inference: Application to Carbon Capture and Storage.” SIAM Journal on Scientific Computing 36, no. 3 (January 2014): B427–B449. © 2014, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
In many engineering problems, unknown parameters of a model are inferred in order to make predictions, to design controllers, or to optimize the model. When parameters are distributed (continuous) or very high-dimensional (discrete) and quantities of interest are low-dimensional, parameters need not be fully resolved to make accurate estimates of quantities of interest. In this work, we extend goal-oriented inference---the process of estimating predictions from observed data without resolving the parameter, previously justified theoretically in the linear setting---to Bayesian statistical inference problem formulations with nonlinear experimental and prediction processes. We propose to learn the joint density of data and predictions offline using Gaussian mixture models. When data are observed online, we condition the representation to arrive at a probabilistic description of predictions given observed data. Our approach enables real-time estimation of uncertainty in quantities of interest and renders tractable high-dimensional PDE-constrained Bayesian inference when there exist low-dimensional output quantities of interest. We demonstrate the method on a realistic problem in carbon capture and storage for which existing methods of Bayesian parameter estimation are intractable.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/130928315
