A Bayesian Numerical Homogenization Method for Elliptic Multiscale Inverse Problems

DOI10.1137/18M1187891zbMath1436.62089arXiv1807.10636OpenAlexW3011807816MaRDI QIDQ4960996

Assyr Abdulle, Andrea di Blasio

Publication date: 24 April 2020

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.10636

zbMATH Keywords

inverse problemshomogenizationmultiscale methodsBayesian regularization

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Bayesian inference (62F15) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

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Cites Work

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• The Bayesian formulation of EIT: analysis and algorithms
• A Bayesian level set method for geometric inverse problems
• A multi level Monte Carlo method with control variate for elliptic PDEs with log-normal coefficients
• Approximate boundary-flux calculations
• Hierarchical Bayesian level set inversion
• Reduced basis finite element heterogeneous multiscale method for high-order discretizations of elliptic homogenization problems
• Numerical methods for multiscale inverse problems
• Inverse problems: A Bayesian perspective
• Multiscale Modelling and Inverse Problems
• Dynamic updating of numerical model discrepancy using sequential sampling
• Approximation errors and model reduction with an application in optical diffusion tomography
• Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
• Fine scale uncertainty in parameter estimation for elliptic equations
• Numerical Homogenization and Model Order Reduction for Multiscale Inverse Problems
• Inverse Problem Theory and Methods for Model Parameter Estimation
• On A Priori Error Analysis of Fully Discrete Heterogeneous Multiscale FEM