Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 3
Book Description
Enabling Efficient Uncertainty Quantification Using Adjoint-based Techniques
Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 3
Book Description
Coupled Flow Systems, Adjoint Techniques and Uncertainty Quantification
Author: Vikram Vinod GargPublisher:
ISBN:
Category :
Languages : en
Pages : 394
Book Description
Coupled systems are ubiquitous in modern engineering and science. Such systems can encompass fluid dynamics, structural mechanics, chemical species transport and electrostatic effects among other components, all of which can be coupled in many different ways. In addition, such models are usually multiscale, making their numerical simulation challenging, and necessitating the use of adaptive modeling techniques. The multiscale, multiphysics models of electrosomotic flow (EOF) constitute a particularly challenging coupled flow system. A special feature of such models is that the coupling between the electric physics and hydrodynamics is via the boundary. Numerical simulations of coupled systems are typically targeted towards specific Quantities of Interest (QoIs). Adjoint-based approaches offer the possibility of QoI targeted adaptive mesh refinement and efficient parameter sensitivity analysis. The formulation of appropriate adjoint problems for EOF models is particularly challenging, due to the coupling of physics via the boundary as opposed to the interior of the domain. The well-posedness of the adjoint problem for such models is also non-trivial. One contribution of this dissertation is the derivation of an appropriate adjoint problem for slip EOF models, and the development of penalty-based, adjoint-consistent variational formulations of these models. We demonstrate the use of these formulations in the simulation of EOF flows in straight and T-shaped microchannels, in conjunction with goal-oriented mesh refinement and adjoint sensitivity analysis. Complex computational models may exhibit uncertain behavior due to various reasons, ranging from uncertainty in experimentally measured model parameters to imperfections in device geometry. The last decade has seen a growing interest in the field of Uncertainty Quantification (UQ), which seeks to determine the effect of input uncertainties on the system QoIs. Monte Carlo methods remain a popular computational approach for UQ due to their ease of use and "embarassingly parallel" nature. However, a major drawback of such methods is their slow convergence rate. The second contribution of this work is the introduction of a new Monte Carlo method which utilizes local sensitivity information to build accurate surrogate models. This new method, called the Local Sensitivity Derivative Enhanced Monte Carlo (LSDEMC) method can converge at a faster rate than plain Monte Carlo, especially for problems with a low to moderate number of uncertain parameters. Adjoint-based sensitivity analysis methods enable the computation of sensitivity derivatives at virtually no extra cost after the forward solve. Thus, the LSDEMC method, in conjuction with adjoint sensitivity derivative techniques can offer a robust and efficient alternative for UQ of complex systems. The efficiency of Monte Carlo methods can be further enhanced by using stratified sampling schemes such as Latin Hypercube Sampling (LHS). However, the non-incremental nature of LHS has been identified as one of the main obstacles in its application to certain classes of complex physical systems. Current incremental LHS strategies restrict the user to at least doubling the size of an existing LHS set to retain the convergence properties of LHS. The third contribution of this research is the development of a new Hierachical LHS algorithm, that creates designs which can be used to perform LHS studies in a more flexibly incremental setting, taking a step towards adaptive LHS methods.
Spectral Methods for Uncertainty Quantification
Author: Olivier Le MaitrePublisher: Springer Science & Business Media
ISBN: 9048135206
Category : Science
Languages : en
Pages : 542
Book Description
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.
Handbook of Uncertainty Quantification
Author: Roger GhanemPublisher: Springer
ISBN: 9783319123844
Category : Mathematics
Languages : en
Pages : 0
Book Description
The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.
Quantification of Uncertainty: Improving Efficiency and Technology
Author: Marta D'EliaPublisher: Springer Nature
ISBN: 3030487210
Category : Mathematics
Languages : en
Pages : 290
Book Description
This book explores four guiding themes – reduced order modelling, high dimensional problems, efficient algorithms, and applications – by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book’s content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.
Uncertainty Quantification
Author: Ralph C. SmithPublisher: SIAM
ISBN: 1611973228
Category : Computers
Languages : en
Pages : 400
Book Description
The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.
Advances in Uncertainty Quantification and Optimization Under Uncertainty with Aerospace Applications
Author: Massimiliano VasilePublisher: Springer Nature
ISBN: 3030805425
Category : Technology & Engineering
Languages : en
Pages : 448
Book Description
The 2020 International Conference on Uncertainty Quantification & Optimization gathered together internationally renowned researchers in the fields of optimization and uncertainty quantification. The resulting proceedings cover all related aspects of computational uncertainty management and optimization, with particular emphasis on aerospace engineering problems. The book contributions are organized under four major themes: Applications of Uncertainty in Aerospace & Engineering Imprecise Probability, Theory and Applications Robust and Reliability-Based Design Optimisation in Aerospace Engineering Uncertainty Quantification, Identification and Calibration in Aerospace Models This proceedings volume is useful across disciplines, as it brings the expertise of theoretical and application researchers together in a unified framework.
Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics
Author: Bernhard EisfeldPublisher: Springer Science & Business Media
ISBN: 3642361854
Category : Science
Languages : en
Pages : 344
Book Description
This volume reports results from the German research initiative MUNA (Management and Minimization of Errors and Uncertainties in Numerical Aerodynamics), which combined development activities of the German Aerospace Center (DLR), German universities and German aircraft industry. The main objective of this five year project was the development of methods and procedures aiming at reducing various types of uncertainties that are typical of numerical flow simulations. The activities were focused on methods for grid manipulation, techniques for increasing the simulation accuracy, sensors for turbulence modelling, methods for handling uncertainties of the geometry and grid deformation as well as stochastic methods for quantifying aleatoric uncertainties.
Adjoint-Based a Posteriori Error Estimation and Uncertainty Quantification for Transient Nonlinear Problems with Discontinuous Solutions
Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 73
Book Description
The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology, Volume II
Author: Dan Gabriel CacuciPublisher: Springer
ISBN: 9783031196379
Category : Science
Languages : en
Pages : 0
Book Description
This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called “curse of dimensionality” in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. This Volume Two, the second of three, presents the large-scale application of the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.
