Variational Methods for Uncertainty Quantification - 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 Variational Methods for Uncertainty Quantification write by David Neckels. This book was released on 2005. Variational Methods for Uncertainty Quantification available in PDF, EPUB and Kindle.
Uncertainty Quantification in Variational Inequalities
Uncertainty Quantification in Variational Inequalities - 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 Uncertainty Quantification in Variational Inequalities write by Joachim Gwinner. This book was released on 2021-12-24. Uncertainty Quantification in Variational Inequalities available in PDF, EPUB and Kindle. Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature
Spectral Methods for Uncertainty Quantification
Spectral Methods for Uncertainty Quantification - 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 Spectral Methods for Uncertainty Quantification write by Olivier Le Maitre. This book was released on 2010-03-11. Spectral Methods for Uncertainty Quantification available in PDF, EPUB and Kindle. This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations
Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations - 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 Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations write by Peng Chen. This book was released on 2014. Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations available in PDF, EPUB and Kindle. Uncertainty propagation (UP) in physical systems governed by PDEs is a challenging problem. This thesis addresses the development of a number of innovative techniques that emphasize the need for high-dimensionality modeling, resolving discontinuities in the stochastic space and considering the computational expense of forward solvers. Both Bayesian and non-Bayesian approaches are considered. Applications demonstrating the developed techniques are investigated in the context of flow in porous media and reservoir engineering applications. An adaptive locally weighted projection method (ALWPR) is firstly developed. It adaptively selects the needed runs of the forward solver (data collection) to maximize the predictive capability of the method. The methodology effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics. It could provide predictions and confidence intervals at any query input and can deal with multi-output responses. A probabilistic graphical model framework for uncertainty quantification is next introduced. The high dimensionality issue of the input is addressed by a local model reduction framework. Then the conditional distribution of the multi-output responses on the low dimensional representation of the input field is factorized into a product of local potential functions that are represented non-parametrically. A nonparametric loopy belief propagation algorithm is developed for studying uncertainty quantification directly on the graph. The nonparametric nature of the model is able to efficiently capture non-Gaussian features of the response. Finally an infinite mixture of Multi-output Gaussian Process (MGP) models is presented to effectively deal with many of the difficulties of current UQ methods. This model involves an infinite mixture of MGP's using Dirichlet process priors and is trained using Variational Bayesian Inference. The Bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations. The automatic detection of the mixture components by the Variational Inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions. Finally, correlations between the components of multi-variate responses are captured by the underlying MGP model in a natural way. A summary of suggestions for future research in the area of uncertainty quantification field are given at the end of the thesis.
Model Validation and Uncertainty Quantification, Volume 3
Model Validation and Uncertainty Quantification, Volume 3 - 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 Model Validation and Uncertainty Quantification, Volume 3 write by Zhu Mao. This book was released on 2022-01-01. Model Validation and Uncertainty Quantification, Volume 3 available in PDF, EPUB and Kindle. Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Inverse Problems and Uncertainty Quantification Controlling Uncertainty Validation of Models for Operating Environments Model Validation & Uncertainty Quantification: Decision Making Uncertainty Quantification in Structural Dynamics Uncertainty in Early Stage Design Computational and Uncertainty Quantification Tools
