IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

A Bayesian Framework for Uncertainty Quantification with High-Dimensional Data-Driven Inputs

  • May 8, 2012
  • 2 p.m.
  • LeConte 405

Abstract

Uncertainty quantification (UQ) in a broad sense addresses the problem of propagating uncertainty from the input variables to the response of a system governed by differential equations. We are here interested in non-intrusive approaches utilizing expensive deterministic codes. We tackle in a holistic manner the problem of UQ in the presence of high-dimensional, experimentally measured inputs. We will start with a discussion of non-linear model reduction techniques to reduce the dimensionality of the experimentally observed input and estimate its probability density. A Bayesian surrogate of the underlying system will then be introduced using a novel treed Gaussian process model. The tree is adaptively constructed using information conveyed by the observed data about the length scales of the underlying process. On each leaf of the tree, we utilize Bayesian Experimental Design techniques in order to learn a multi-output Gaussian process. The framework effectively quantifies the epistemic uncertainty introduced by the finite number of simulations. Furthermore, the scheme explicitly models correlations between discrete outputs of the code as well as in space and time. We demonstrate the effectiveness of the framework in the solution of some problems in engineering physics governed by stochastic PDEs.

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