2026-09-19T15:58:21Zhttps://dspace.mit.edu/server/oai/request

oai:dspace.mit.edu:1721.1/653222022-01-13T07:54:53Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023

Youssef Marzouk. Parno, Matthew David Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program 2011-08-18T19:18:37Z 2011-08-18T19:18:37Z 2011 2011 http://hdl.handle.net/1721.1/65322 746081025 Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2011. Page 118 blank. Cataloged from PDF version of thesis. Includes bibliographical references (p. 112-117). The Bayesian approach to inference problems provides a systematic way of updating prior knowledge with data. A likelihood function involving a forward model of the problem is used to incorporate data into a posterior distribution. The standard method of sampling this distribution is Markov chain Monte Carlo which can become inefficient in high dimensions, wasting many evaluations of the likelihood function. In many applications the likelihood function involves the solution of a partial differential equation so the large number of evaluations required by Markov chain Monte Carlo can quickly become computationally intractable. This work aims to reduce the computational cost of sampling the posterior by introducing a multiscale framework for inference problems involving elliptic forward problems. Through the construction of a low dimensional prior on a coarse scale and the use of iterative conditioning technique the scales are decouples and efficient inference can proceed. This work considers nonlinear mappings from a fine scale to a coarse scale based on the Multiscale Finite Element Method. Permeability characterization is the primary focus but a discussion of other applications is also provided. After some theoretical justification, several test problems are shown that demonstrate the efficiency of the multiscale framework. by Matthew David Parno. S.M. 118 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Computation for Design and Optimization Program. A multiscale framework for Bayesian inference in elliptic problems Thesis application/pdf false Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="0166be22-5529-480c-b150-ef686d581698"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>A multiscale framework for Bayesian inference in elliptic problems</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2011</PublicationDate> <Authors> <Author> <DisplayName>Parno, Matthew David</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Computation for Design and Optimization Program.</Keyword> <Abstract>The Bayesian approach to inference problems provides a systematic way of updating prior knowledge with data. A likelihood function involving a forward model of the problem is used to incorporate data into a posterior distribution. The standard method of sampling this distribution is Markov chain Monte Carlo which can become inefficient in high dimensions, wasting many evaluations of the likelihood function. In many applications the likelihood function involves the solution of a partial differential equation so the large number of evaluations required by Markov chain Monte Carlo can quickly become computationally intractable. This work aims to reduce the computational cost of sampling the posterior by introducing a multiscale framework for inference problems involving elliptic forward problems. Through the construction of a low dimensional prior on a coarse scale and the use of iterative conditioning technique the scales are decouples and efficient inference can proceed. This work considers nonlinear mappings from a fine scale to a coarse scale based on the Multiscale Finite Element Method. Permeability characterization is the primary focus but a discussion of other applications is also provided. After some theoretical justification, several test problems are shown that demonstrate the efficiency of the multiscale framework.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>