WIAS Preprint No. 2537, (2018)

A Bayesian approach to parameter identification in gas networks


  • Hajian, Soheil
  • Hintermüller, Michael
    ORCID: 0000-0001-9471-2479
  • Schillings, Claudia
  • Strogies, Nikolai

2010 Mathematics Subject Classification

  • 35L40 65C50 65M32


  • Bayesian inversion, distributed friction coefficient, gas network/pipeline, hyperbolic PDE system




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.

Appeared in

  • Control Cybernet., 48 (2019), pp. 377--402.

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