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A Bayesian approach to parameter identification in gas networks

  • The inverse problem of identifying the friction coefficient in an isothermal semilinear Euler system is considered. Adopting a Bayesian approach, the goal is to identify the distribution of the quantity of interest based on a finite number of noisy measurements of the pressure at the boundaries of the domain. First well-posedness of the underlying non-linear PDE system is shown using semigroup theory, and then Lipschitz continuity of the solution operator with respect to the friction coefficient is established. Based on the Lipschitz property, well-posedness of the resulting Bayesian inverse problem for the identification of the friction coefficient is inferred. Numerical tests for scalar and distributed parameters are performed to validate the theoretical results.
Metadaten
Author:Soheil Hajian, Michael Hintermüller, Claudia Schillings, Nikolai Strogies
Parent Title (English):Control and Cybernetics
Document Type:Article
Language:English
Date of Publication (online):2019/12/01
Date of first Publication:2018/01/29
Release Date:2018/01/29
Volume:48
First Page:377
Last Page:402
Institutes:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B02