Systematic methods for the solution of inverse problems have developed significantly during the last twenty years and have become a powerful tool for analysis and design in engineering. Inverse analysis is nowadays a common practice in which the groups involved with experiments and numerical simulation synergistically collaborate throughout the research work, in order to obtain the maximum of information regarding the physical problem under study. Inverse problems are mathematically classified as ill-posed, that is, their solutions do not satisfy either one of the requirements of existence, uniqueness or stability. The solution approaches generally consist of the reformulation of the inverse problem in terms of an approximate well-posed problem. In this paper we briefly review various approaches for the solution of inverse problems, including those based on classical regularization techniques and those based on the Bayesian statistics. Applications of inverse problems are then presented for cases of practical interest, such as the characterization of non-homogeneous materials and the prediction of the temperature field in oil pipelines.
Well-posed Bayesian geometric inverse problems arising in subsurface flow
