Parameter estimation for partial differential equations using stochastic methods

Tanase, Roxana Elena (2016) Parameter estimation for partial differential equations using stochastic methods. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

The aim of this thesis is to compare the efficiency of different algorithms on estimating parameters
that arise in partial differential equations: Kalman Filters (Ensemble Kalman Filter,
Stochastic Collocation Kalman Filter, Karhunen-Lo`eve Ensemble Kalman Filter, Karhunen-
Lo`eve Stochastic Collocation Kalman Filter), Markov-Chain Monte Carlo sampling schemes
and Adjoint variable-based method.
We also present the theoretical results for stochastic optimal control for problems constrained
by partial differential equations with random input data in a mixed finite element form. We
verify experimentally with numerical simulations using Adjoint variable-based method with
various identification objectives that either minimize the expectation of a tracking cost functional
or minimize the difference of desired statistical quantities in the appropriate Lp norm.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID Tanase, Roxana Elena tanase.roxana@gmail.com ROT26
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee CoChair Yotov, Ivan yotov@math.pitt.edu YOTOV Committee CoChair Trenchea, Catalin trenchea@pitt.edu TRENCHEA Committee Member Swigon, David swigon@pitt.edu SWIGON Committee Member Clermont, Gilles clermontg@ccm.upmc.edu
Date:	15 June 2016
Date Type:	Publication
Defense Date:	22 March 2016
Approval Date:	15 June 2016
Submission Date:	11 April 2016
Access Restriction:	No restriction; Release the ETD for access worldwide immediately.
Number of Pages:	142
Institution:	University of Pittsburgh
Schools and Programs:	Dietrich School of Arts and Sciences > Mathematics
Degree:	PhD - Doctor of Philosophy
Thesis Type:	Doctoral Dissertation
Refereed:	Yes
Uncontrolled Keywords:	parameter estimation, Kalman Filter, Stochastic Collocation, Markov Chain Monte Carlo, Adjoint variable
Date Deposited:	15 Jun 2016 21:10
Last Modified:	15 Nov 2016 14:32
URI:	http://d-scholarship.pitt.edu/id/eprint/27640

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