Optimal Experimental Design for Large-scale Bayesian Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Experimental Design for Large-scale Bayesian Inverse Problems write by Keyi Wu (Ph. D.). This book was released on 2022. Optimal Experimental Design for Large-scale Bayesian Inverse Problems available in PDF, EPUB and Kindle. Bayesian optimal experimental design (BOED)—including active learning, Bayesian optimization, and sensor placement—provides a probabilistic framework to maximize the expected information gain (EIG) or mutual information (MI) for uncertain parameters or quantities of interest with limited experimental data. However, evaluating the EIG remains prohibitive for largescale complex models due to the need to compute double integrals with respect to both the parameter and data distributions. In this work, we develop a fast and scalable computational framework to solve Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with application to optimal sensor placement by maximizing the EIG. We (1) exploit the low-rank structure of the Jacobian of the parameter-to-observable map to extract the intrinsic low-dimensional data-informed subspace, and (2) employ a series of approximations of the EIG that reduce the number of PDE solves while retaining a high correlation with the true EIG. This allows us to propose an efficient offline–online decomposition for the optimization problem, using a new swapping greedy algorithm for both OED problems and goal-oriented linear OED problems. The offline stage dominates the cost and entails precomputing all components requiring PDE solusion. The online stage optimizes sensor placement and does not require any PDE solves. We provide a detailed error analysis with an upper bound for the approximation error in evaluating the EIG for OED and goal-oriented OED linear cases. Finally, we evaluate the EIG with a derivative-informed projected neural network (DIPNet) surrogate for parameter-to-observable maps. With this surrogate, no further PDE solves are required to solve the optimization problem. We provided an analysis of the error propagated from the DIPNet approximation to the approximation of the normalization constant and the EIG under suitable assumptions. We demonstrate the efficiency and scalability of the proposed methods for both linear inverse problems, in which one seeks to infer the initial condition for an advection–diffusion equation, and nonlinear inverse problems, in which one seeks to infer coefficients for a Poisson problem, an acoustic Helmholtz problem and an advection–diffusion–reaction problem. This dissertation is based on the following articles: A fast and scalable computational framework for large-scale and high-dimensional Bayesian optimal experimental design by Keyi Wu, Peng Chen, and Omar Ghattas [88]; An efficient method for goal-oriented linear Bayesian optimal experimental design: Application to optimal sensor placement by Keyi Wu, Peng Chen, and Omar Ghattas [89]; and Derivative-informed projected neural network for large-scale Bayesian optimal experimental design by Keyi Wu, Thomas O’Leary-Roseberry, Peng Chen, and Omar Ghattas [90]. This material is based upon work partially funded by DOE ASCR DE-SC0019303 and DESC0021239, DOD MURI FA9550-21-1-0084, and NSF DMS-2012453
Large-Scale Inverse Problems and Quantification of Uncertainty
Large-Scale Inverse Problems and Quantification of Uncertainty - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Large-Scale Inverse Problems and Quantification of Uncertainty write by Lorenz Biegler. This book was released on 2011-06-24. Large-Scale Inverse Problems and Quantification of Uncertainty available in PDF, EPUB and Kindle. This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
Bayesian Approach to Inverse Problems
Bayesian Approach to Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bayesian Approach to Inverse Problems write by Jérôme Idier. This book was released on 2013-03-01. Bayesian Approach to Inverse Problems available in PDF, EPUB and Kindle. Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational Methods for Inverse Problems write by Curtis R. Vogel. This book was released on 2002-01-01. Computational Methods for Inverse Problems available in PDF, EPUB and Kindle. Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Numerical Analysis and Optimization
Numerical Analysis and Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Analysis and Optimization write by Mehiddin Al-Baali. This book was released on 2015-07-16. Numerical Analysis and Optimization available in PDF, EPUB and Kindle. Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.
