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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 (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Tanase, Roxana Elenatanase.roxana@gmail.comROT26
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee CoChairYotov, Ivanyotov@math.pitt.eduYOTOV
Committee CoChairTrenchea, Catalintrenchea@pitt.eduTRENCHEA
Committee MemberSwigon, Davidswigon@pitt.eduSWIGON
Committee MemberClermont,
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


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