Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems.
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While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role i…
Inverse problems in subsurface flow are generally challenging due to the need for a large number of expensive numerical solutions to partial di↵erential equations (PDEs). Inverse modeling typically consists of generating realizations of the unknown model parameters and matching …
This thesis may be broadly divided into 4 parts. In the first part, we do a literature review of the state of the art in misspecification in Macroeconomics, and what so far has been the contribution of a relatively new area of research called Uncertainty Quantification to the Ma…
This thesis proposes a novel method for solving inverse thermal systems problems based on stigmergy. Inverse problems are those problems that have a desired output but the inputs required to achieve that output are unknown. The example problem examined is an established inverse …
To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exac…
