scholarly journals Parameter and State Model Reduction for Large-Scale Statistical Inverse Problems

2010 ◽  
Vol 32 (5) ◽  
pp. 2523-2542 ◽  
Author(s):  
Chad Lieberman ◽  
Karen Willcox ◽  
Omar Ghattas
Keyword(s):  
Inverse Problems ◽  
Model Reduction ◽  
Large Scale ◽  
State Model ◽  
Statistical Inverse Problems

A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion

2012 ◽  
Vol 34 (3) ◽  
pp. A1460-A1487 ◽  
Author(s):  
James Martin ◽  
Lucas C. Wilcox ◽  
Carsten Burstedde ◽  
Omar Ghattas
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Seismic Inversion ◽  
Mcmc Method ◽  
Statistical Inverse Problems

scholarly journals Learning physics-based models from data: perspectives from inverse problems and model reduction

Acta Numerica ◽  
2021 ◽  
Vol 30 ◽  
pp. 445-554
Author(s):  
Omar Ghattas ◽  
Karen Willcox
Keyword(s):  
Inverse Problems ◽  
Model Reduction ◽  
Large Scale ◽  
Dimensional Subspace ◽  
Dimensional Solution ◽  
Scale Models ◽  
Recent Developments ◽  
Engineered Systems ◽  
Low Dimensional ◽  
Solution Manifold

This article addresses the inference of physics models from data, from the perspectives of inverse problems and model reduction. These fields develop formulations that integrate data into physics-based models while exploiting the fact that many mathematical models of natural and engineered systems exhibit an intrinsically low-dimensional solution manifold. In inverse problems, we seek to infer uncertain components of the inputs from observations of the outputs, while in model reduction we seek low-dimensional models that explicitly capture the salient features of the input–output map through approximation in a low-dimensional subspace. In both cases, the result is a predictive model that reflects data-driven learning yet deeply embeds the underlying physics, and thus can be used for design, control and decision-making, often with quantified uncertainties. We highlight recent developments in scalable and efficient algorithms for inverse problems and model reduction governed by large-scale models in the form of partial differential equations. Several illustrative applications to large-scale complex problems across different domains of science and engineering are provided.

An object-oriented optimization framework for large-scale inverse problems

2021 ◽  
pp. 104790
Author(s):  
Ettore Biondi ◽  
Guillaume Barnier ◽  
Robert G. Clapp ◽  
Francesco Picetti ◽  
Stuart Farris
Keyword(s):  
Inverse Problems ◽  
Large Scale ◽  
Object Oriented ◽  
Optimization Framework

Model Reduction and Clusterization of Large-Scale Bidirectional Networks

2014 ◽  
Vol 59 (1) ◽  
pp. 48-63 ◽  
Author(s):  
Takayuki Ishizaki ◽  
Kenji Kashima ◽  
Jun-ichi Imura ◽  
Kazuyuki Aihara
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Bidirectional Networks
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