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Bayesian approach to parameter identification in gas networks

Hajian Soheil, Hintermüller Michael, Schillings Claudia, Strogies Nikolai

Control and Cybernetics

2019

Vol. 48, No. 2

377--402

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 wellposedness 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.

Bayesian approach to tomographic imaging of rock-mass velocity heterogeneities

Dębski W.

Acta Geophysica

2013

Vol. 61, no. 6

1395--1436

Detailed imaging of the Earth subsurface structure has both scientific and practical aspects. From a scientific point of view knowledge of the Earth’s structure is necessary for understanding various processes. Practical aspects include such issues as localization and description of natural resources deposits. Although huge progress has been made in this field, there are still a lot of questions not answered yet. One of them is the question of a relation between observed seismicity and the earth’s structure. In this paper we address this issue and argue that the probabilistic (Bayesian) approach should be used. Since this inversion method introduces some additional complexity to the already difficult seismic tomography technique, we decided to describe the basic steps of Bayesian tomographic imaging from data preparation to analysis of imaging results. The methodological considerations are illustrated by examples of imaging for four mining regions within the Rudna (Poland) copper mine.