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Activity Number: 52
Type: Invited
Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract #314601 View Presentation
Title: Quantifying Epistemic Uncertainty in ODE and PDE Numerical Solutions via Gaussian Measures and Feynman-Kac Identities
Author(s): Mark Girolami*
Companies: University of Warwick
Keywords: uncertainty quantification ; epistemic uncertainty ; Gaussian Process
Abstract:

Diaconis and O'Hagan originally suggested the evaluation of a functional can be viewed as an inference problem. This perspective leads to construction of a probability measure describing the epistemic uncertainty associated with the evaluation of functions solving for systems of Differential Equations. By defining a Gaussian Measure on the Hilbert space of functions and their derivatives appearing in an ODE or PDE a stochastic process is constructed. Realisations of this process can be sampled from the associated measure defining "Global" ODE/PDE solutions conditional on a discrete mesh. The sampled realisations are consistent estimates of the function satisfying the ODE or PDE system and the associated measure quantifies our uncertainty in these solutions given a discrete mesh. Likewise an unbiased estimate of the "Local" solutions of certain classes of PDEs, along with the associated probability measure, can be obtained via the Feynman-Kac identities which has advantages over the construction of a Global solution for inverse problems. In this talk I will describe the methodology above and illustrate with various examples of ODEs and PDEs in specific inverse problems.


Authors who are presenting talks have a * after their name.

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