A Bayesian approach to parameter identification in gas networks

Abstract

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.