Download or read book Model Order Reduction Techniques for Uncertainty Quantification Problems written by Chen Peng and published by . This book was released on 2014 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantification of Uncertainty Improving Efficiency and Technology written by Marta D'Elia and published by Springer Nature. This book was released on 2020-07-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Reduced Order Methods for Modeling and Computational Reduction written by Alfio Quarteroni and published by Springer. This book was released on 2014-06-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Download or read book Encyclopedia of Computational Mechanics written by Erwin Stein and published by . This book was released on 2004 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.

Download or read book Interpolatory Methods for Model Reduction written by A. C. Antoulas and published by SIAM. This book was released on 2020-01-13 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Download or read book Model Order Reduction Theory Research Aspects and Applications written by Wilhelmus H. Schilders and published by Springer Science & Business Media. This book was released on 2008-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem and published by Springer. This book was released on 2016-05-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Model Reduction and Approximation written by Peter Benner and published by SIAM. This book was released on 2017-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Download or read book Uncertainty Quantification for Maxwell s Equations Using Stochastic Collocation and Model Order Reduction written by Peter Benner and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Modeling and simulation are important for the design process of new semiconductor structures. Difficulties proceed from shrinking structures, increasing working frequencies, and uncertainties of materials and geometries. Therefore, we consider the time-harmonic Maxwell\'s equations for the simulation of a coplanar waveguide with uncertain material parameters. To analyze the uncertainty of the system, we use stochastic collocation with Stroud and sparse grid points. The results are compared to a Monte Carlo simulation. Both methods rely on repetitive runs of a deterministic solver. Hence, we compute a reduced model by means of proper orthogonal decomposition to reduce the computational cost. The Monte Carlo simulation and the stochastic collocation are both applied to the full and the reduced model. All results are compared concerning accuracy and computation time.

Download or read book Large Scale Inverse Problems and Quantification of Uncertainty written by Lorenz Biegler and published by John Wiley & Sons. This book was released on 2011-06-24 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.

Download or read book High order Retractions for Reduced order Modeling and Uncertainty Quantification written by Aaron Solomon Charous and published by . This book was released on 2021 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though computing power continues to grow quickly, our appetite to solve larger and larger problems grows just as fast. As a consequence, reduced-order modeling has become an essential technique in the computational scientist’s toolbox. By reducing the dimensionality of a system, we are able to obtain approximate solutions to otherwise intractable problems. And because the methodology we develop is sufficiently general, we may agnostically apply it to a plethora of problems, whether the high dimensionality arises due to the sheer size of the computational domain, the fine resolution we require, or stochasticity of the dynamics. In this thesis, we develop time integration schemes, called retractions, to efficiently evolve the dynamics of a system’s low-rank approximation. Through the study of differential geometry, we are able to analyze the error incurred at each time step. A novel, explicit, computationally inexpensive set of algorithms, which we call perturbative retractions, are proposed that converge to an ideal retraction that projects exactly to the manifold of fixed-rank matrices. Furthermore, each perturbative retraction itself exhibits high-order convergence to the best low-rank approximation of the full-rank solution. We show that these high-order retractions significantly reduce the numerical error incurred over time when compared to a naive Euler forward retraction. Through test cases, we demonstrate their efficacy in the cases of matrix addition, real-time data compression, and deterministic and stochastic differential equations.

Download or read book Sub structure Coupling for Dynamic Analysis written by Hector Jensen and published by Springer. This book was released on 2019-03-26 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines a model reduction technique with an efficient parametrization scheme for the purpose of solving a class of complex and computationally expensive simulation-based problems involving finite element models. These problems, which have a wide range of important applications in several engineering fields, include reliability analysis, structural dynamic simulation, sensitivity analysis, reliability-based design optimization, Bayesian model validation, uncertainty quantification and propagation, etc. The solution of this type of problems requires a large number of dynamic re-analyses. To cope with this difficulty, a model reduction technique known as substructure coupling for dynamic analysis is considered. While the use of reduced order models alleviates part of the computational effort, their repetitive generation during the simulation processes can be computational expensive due to the substantial computational overhead that arises at the substructure level. In this regard, an efficient finite element model parametrization scheme is considered. When the division of the structural model is guided by such a parametrization scheme, the generation of a small number of reduced order models is sufficient to run the large number of dynamic re-analyses. Thus, a drastic reduction in computational effort is achieved without compromising the accuracy of the results. The capabilities of the developed procedures are demonstrated in a number of simulation-based problems involving uncertainty.

Download or read book Uncertainty Quantification in Multiscale Materials Modeling written by Yan Wang and published by Woodhead Publishing Limited. This book was released on 2020-03-12 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.

Download or read book Uncertainty Modeling for Engineering Applications written by Flavio Canavero and published by Springer. This book was released on 2018-12-29 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of state-of-the-art uncertainty quantification (UQ) methodologies and applications, and covers a wide range of current research, future challenges and applications in various domains, such as aerospace and mechanical applications, structure health and seismic hazard, electromagnetic energy (its impact on systems and humans) and global environmental state change. Written by leading international experts from different fields, the book demonstrates the unifying property of UQ theme that can be profitably adopted to solve problems of different domains. The collection in one place of different methodologies for different applications has the great value of stimulating the cross-fertilization and alleviate the language barrier among areas sharing a common background of mathematical modeling for problem solution. The book is designed for researchers, professionals and graduate students interested in quantitatively assessing the effects of uncertainties in their fields of application. The contents build upon the workshop “Uncertainty Modeling for Engineering Applications” (UMEMA 2017), held in Torino, Italy in November 2017.

Download or read book Model Order Reduction Techniques with Applications in Finite Element Analysis written by Zu-Qing Qu and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardware, simulations are often extremely computationally intensive and time-consuming when full-blown models are under consideration. The need to reduce the computational cost involved when dealing with high-order/many-degree-of-freedom models can be offset by adroit computation. In this light, model-reduction methods have become a major goal of simulation and modeling research. Model reduction can also ameliorate problems in the correlation of widely used finite-element analyses and test analysis models produced by excessive system complexity. Model Order Reduction Techniques explains and compares such methods focusing mainly on recent work in dynamic condensation techniques: - Compares the effectiveness of static, exact, dynamic, SEREP and iterative-dynamic condensation techniques in producing valid reduced-order models; - Shows how frequency shifting and the number of degrees of freedom affect the desirability and accuracy of using dynamic condensation; - Answers the challenges involved in dealing with undamped and non-classically damped models; - Requires little more than first-engineering-degree mathematics and highlights important points with instructive examples. Academics working in research on structural dynamics, MEMS, vibration, finite elements and other computational methods in mechanical, aerospace and structural engineering will find Model Order Reduction Techniques of great interest while it is also an excellent resource for researchers working on commercial finite-element-related software such as ANSYS and Nastran.

Download or read book IUTAM Symposium on Model Order Reduction of Coupled Systems Stuttgart Germany May 22 25 2018 written by Jörg Fehr and published by Springer. This book was released on 2019-07-19 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the IUTAM Symposium on Model Order Reduction of Coupled System, held in Stuttgart, Germany, May 22–25, 2018. For the understanding and development of complex technical systems, such as the human body or mechatronic systems, an integrated, multiphysics and multidisciplinary view is essential. Many problems can be solved within one physical domain. For the simulation and optimization of the combined system, the different domains are connected with each other. Very often, the combination is only possible by using reduced order models such that the large-scale dynamical system is approximated with a system of much smaller dimension where the most dominant features of the large-scale system are retained as much as possible. The field of model order reduction (MOR) is interdisciplinary. Researchers from Engineering, Mathematics and Computer Science identify, explore and compare the potentials, challenges and limitations of recent and new advances.