The Library
Multiscale modelling and inverse problems
Tools
Pavliotis, Greg and Stuart, A. M. (2010) Multiscale modelling and inverse problems. In: London Mathematical Society - EPSRC Durham Symposium : Numerical Analysis of Multiscale Problems, Durham, 5-15 July 2010 (Unpublished)
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://www.maths.dur.ac.uk/events/Meetings/LMS/201...
Abstract
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters which are functions, such as constitutive tensors, initial conditions and forcing can be estimated on the basis of observed data. The resulting inverse problems are often ill-posed and some form of regularization is required. When the function being estimated has a multiscale structure a number of natural questions arise, in particular: (i) how should the data be used, and the regularization chosen, if only an averaged or homogenized solution to the inverse problem is required; (ii) how should the data be used, and the regularization chosen, if the details of the multiscale structure are important. We will devote three lectures to a development of the mathematics required to address these questions. We adopt a probabilistic approach to the inverse problems, based on the Bayesian viewpoint, and show how the choice of prior measure is intimately related to answering questions (i) and (ii). The ideas will be illustrated throughout in the context of simple models for groundwater flow.
The lectures will be pedagogical in style and accesible to an audience with basic knowledge of differential equations and probability.
Item Type: | Conference Item (Paper) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Official Date: | July 2010 | ||||
Dates: |
|
||||
Status: | Not Peer Reviewed | ||||
Publication Status: | Unpublished | ||||
Description: | Three lectures in a series, delivered at the same conference |
||||
Conference Paper Type: | Paper | ||||
Title of Event: | London Mathematical Society - EPSRC Durham Symposium : Numerical Analysis of Multiscale Problems | ||||
Type of Event: | Conference | ||||
Location of Event: | Durham | ||||
Date(s) of Event: | 5-15 July 2010 |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |