A Bayesian approach to parameter identification in gas networks
- Hajian, Soheil
- Hintermüller, Michael
- 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.
- Control Cybernet., 48 (2019), pp. 377--402.