Reduction Approximation Machine Learning Surrogates Emulators And Simulators
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Reduction Approximation Machine Learning Surrogates Emulators And Simulators
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Author : Gianluigi Rozza
language : en
Publisher: Springer Nature
Release Date : 2024-06-24
Reduction Approximation Machine Learning Surrogates Emulators And Simulators written by Gianluigi Rozza and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-24 with Mathematics categories.
This volume is focused on the review of recent algorithmic and mathematical advances and the development of new research directions for Mathematical Model Approximations via RAMSES (Reduced order models, Approximation theory, Machine learning, Surrogates, Emulators, Simulators) in the setting of parametrized partial differential equations also with sparse and noisy data in high-dimensional parameter spaces. The book is a valuable resource for researchers, as well as masters and Ph.D students.
Surrogates
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Author : Robert B. Gramacy
language : en
Publisher: CRC Press
Release Date : 2020-03-10
Surrogates written by Robert B. Gramacy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.
Computer simulation experiments are essential to modern scientific discovery, whether that be in physics, chemistry, biology, epidemiology, ecology, engineering, etc. Surrogates are meta-models of computer simulations, used to solve mathematical models that are too intricate to be worked by hand. Gaussian process (GP) regression is a supremely flexible tool for the analysis of computer simulation experiments. This book presents an applied introduction to GP regression for modelling and optimization of computer simulation experiments. Features: • Emphasis on methods, applications, and reproducibility. • R code is integrated throughout for application of the methods. • Includes more than 200 full colour figures. • Includes many exercises to supplement understanding, with separate solutions available from the author. • Supported by a website with full code available to reproduce all methods and examples. The book is primarily designed as a textbook for postgraduate students studying GP regression from mathematics, statistics, computer science, and engineering. Given the breadth of examples, it could also be used by researchers from these fields, as well as from economics, life science, social science, etc.
The Design And Analysis Of Computer Experiments
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Author : Thomas J. Santner
language : en
Publisher: Springer
Release Date : 2019-01-08
The Design And Analysis Of Computer Experiments written by Thomas J. Santner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
This book describes methods for designing and analyzing experiments that are conducted using a computer code, a computer experiment, and, when possible, a physical experiment. Computer experiments continue to increase in popularity as surrogates for and adjuncts to physical experiments. Since the publication of the first edition, there have been many methodological advances and software developments to implement these new methodologies. The computer experiments literature has emphasized the construction of algorithms for various data analysis tasks (design construction, prediction, sensitivity analysis, calibration among others), and the development of web-based repositories of designs for immediate application. While it is written at a level that is accessible to readers with Masters-level training in Statistics, the book is written in sufficient detail to be useful for practitioners and researchers. New to this revised and expanded edition: • An expanded presentation of basic material on computer experiments and Gaussian processes with additional simulations and examples • A new comparison of plug-in prediction methodologies for real-valued simulator output • An enlarged discussion of space-filling designs including Latin Hypercube designs (LHDs), near-orthogonal designs, and nonrectangular regions • A chapter length description of process-based designs for optimization, to improve good overall fit, quantile estimation, and Pareto optimization • A new chapter describing graphical and numerical sensitivity analysis tools • Substantial new material on calibration-based prediction and inference for calibration parameters • Lists of software that can be used to fit models discussed in the book to aid practitioners
Gaussian Processes For Machine Learning
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Author : Carl Edward Rasmussen
language : en
Publisher: MIT Press
Release Date : 2005-11-23
Gaussian Processes For Machine Learning written by Carl Edward Rasmussen and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-23 with Computers categories.
A comprehensive and self-contained introduction to Gaussian processes, which provide a principled, practical, probabilistic approach to learning in kernel machines. Gaussian processes (GPs) provide a principled, practical, probabilistic approach to learning in kernel machines. GPs have received increased attention in the machine-learning community over the past decade, and this book provides a long-needed systematic and unified treatment of theoretical and practical aspects of GPs in machine learning. The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics. The book deals with the supervised-learning problem for both regression and classification, and includes detailed algorithms. A wide variety of covariance (kernel) functions are presented and their properties discussed. Model selection is discussed both from a Bayesian and a classical perspective. Many connections to other well-known techniques from machine learning and statistics are discussed, including support-vector machines, neural networks, splines, regularization networks, relevance vector machines and others. Theoretical issues including learning curves and the PAC-Bayesian framework are treated, and several approximation methods for learning with large datasets are discussed. The book contains illustrative examples and exercises, and code and datasets are available on the Web. Appendixes provide mathematical background and a discussion of Gaussian Markov processes.
Design And Analysis Of Simulation Experiments
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Author : Jack P.C. Kleijnen
language : en
Publisher: Springer
Release Date : 2015-07-01
Design And Analysis Of Simulation Experiments written by Jack P.C. Kleijnen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with Business & Economics categories.
This is a new edition of Kleijnen’s advanced expository book on statistical methods for the Design and Analysis of Simulation Experiments (DASE). Altogether, this new edition has approximately 50% new material not in the original book. More specifically, the author has made significant changes to the book’s organization, including placing the chapter on Screening Designs immediately after the chapters on Classic Designs, and reversing the order of the chapters on Simulation Optimization and Kriging Metamodels. The latter two chapters reflect how active the research has been in these areas. The validation section has been moved into the chapter on Classic Assumptions versus Simulation Practice, and the chapter on Screening now has a section on selecting the number of replications in sequential bifurcation through Wald’s sequential probability ration test, as well as a section on sequential bifurcation for multiple types of simulation responses. Whereas all references in the original edition were placed at the end of the book, in this edition references are placed at the end of each chapter. From Reviews of the First Edition: “Jack Kleijnen has once again produced a cutting-edge approach to the design and analysis of simulation experiments.” (William E. BILES, JASA, June 2009, Vol. 104, No. 486)
Spaces Speak Are You Listening
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Author : Barry Blesser
language : en
Publisher: MIT Press
Release Date : 2009-09-18
Spaces Speak Are You Listening written by Barry Blesser and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-18 with Architecture categories.
How we experience space by listening: the concepts of aural architecture, with examples ranging from Gothic cathedrals to surround sound home theater. We experience spaces not only by seeing but also by listening. We can navigate a room in the dark, and "hear" the emptiness of a house without furniture. Our experience of music in a concert hall depends on whether we sit in the front row or under the balcony. The unique acoustics of religious spaces acquire symbolic meaning. Social relationships are strongly influenced by the way that space changes sound. In Spaces Speak, Are You Listening?, Barry Blesser and Linda-Ruth Salter examine auditory spatial awareness: experiencing space by attentive listening. Every environment has an aural architecture.The audible attributes of physical space have always contributed to the fabric of human culture, as demonstrated by prehistoric multimedia cave paintings, classical Greek open-air theaters, Gothic cathedrals, acoustic geography of French villages, modern music reproduction, and virtual spaces in home theaters. Auditory spatial awareness is a prism that reveals a culture's attitudes toward hearing and space. Some listeners can learn to "see" objects with their ears, but even without training, we can all hear spatial geometry such as an open door or low ceiling. Integrating contributions from a wide range of disciplines—including architecture, music, acoustics, evolution, anthropology, cognitive psychology, audio engineering, and many others—Spaces Speak, Are You Listening? establishes the concepts and language of aural architecture. These concepts provide an interdisciplinary guide for anyone interested in gaining a better understanding of how space enhances our well-being. Aural architecture is not the exclusive domain of specialists. Accidentally or intentionally, we all function as aural architects.
Reduced Basis Methods For Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2015-08-19
Reduced Basis Methods For Partial Differential Equations written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Mathematics categories.
This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit
Structural Reliability Methods
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Author : O. Ditlevsen
language : en
Publisher: Wiley
Release Date : 1996-06-19
Structural Reliability Methods written by O. Ditlevsen and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-19 with Technology & Engineering categories.
This book addresses probabilistic methods for the evaluation of structural reliability, including the theoretical basis of these methods. Partial safety factor codes under current practice are briefly introduced and discussed. A probabilistic code format for obtaining a formal reliability evaluation system that catches the most essential features of the nature of the uncertainties and their interplay is then gradually developed. The concepts presented are illustrated by numerous examples throughout the text. The modular approach of the book allows the reader to navigate through the different stages of the methods.
Greedy Dictionary Learning Algorithms For Sparse Surrogate Modelling
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Author : Valentin Stolbunov
language : en
Publisher:
Release Date : 2017
Greedy Dictionary Learning Algorithms For Sparse Surrogate Modelling written by Valentin Stolbunov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
In the field of engineering design, numerical simulations are commonly used to forecast system performance before physical prototypes are built and tested. However the fidelity of predictive models has outpaced advances in computer hardware and numerical methods, making it impractical to directly apply numerical optimization algorithms to the design of complex engineering systems modelled with high fidelity. A promising approach for dealing with this computational challenge is the use of surrogate models, which serve as approximations of the high-fidelity computational models and can be evaluated very cheaply. This makes surrogates extremely valuable in design optimization and a wider class of problems: inverse parameter estimation, machine learning, uncertainty quantification, and visualization. This thesis is concerned with the development of greedy dictionary learning algorithms for efficiently constructing sparse surrogate models using a set of scattered observational data. The central idea is to define a dictionary of basis functions either a priori or a posteriori in light of the dataset and select a subset of the basis functions from the dictionary using a greedy search criterion. In this thesis, we first develop a novel algorithm for sparse learning from parameterized dictionaries in the context of greedy radial basis function learning (GRBF). Next, we develop a novel algorithm for general dictionary learning (GGDL). This algorithm is presented in the context of multiple kernel learning with heterogenous dictionaries. In addition, we present a novel strategy, based on cross-validation, for parallelizing greedy dictionary learning and a randomized sampling strategy to significantly reduce approximation costs associated with large dictionaries. We also employ our GGDL algorithm in the context of uncertainty quantification to construct sparse polynomial chaos expansions. Finally, we demonstrate how our algorithms may be adapted to approximate gradient-enhanced datasets. Numerical studies are presented for a variety of test functions, machine learning datasets, and engineering case studies over a wide range of dataset size and dimensionality. Compared to state-of-the-art approximation techniques such as classical radial basis function approximations, Gaussian process models, and support vector machines, our algorithms build surrogates which are significantly more sparse, of comparable or improved accuracy, and often offer reduced computational and memory costs.
A Scientific Machine Learning Approach To Learning Reduced Models For Nonlinear Partial Differential Equations
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Author : Elizabeth Yi Qian
language : en
Publisher:
Release Date : 2021
A Scientific Machine Learning Approach To Learning Reduced Models For Nonlinear Partial Differential Equations written by Elizabeth Yi Qian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
This thesis presents a new scientific machine learning method which learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an enabling technology for many computational algorithms used in engineering settings. The proposed approach generalizes to the PDE setting an Operator Inference method previously developed for systems of ordinary differential equations (ODEs) with polynomial nonlinearities. The method draws on ideas from traditional physics-based modeling to explicitly parametrize the learned model by low-dimensional polynomial operators which reflect the known form of the governing PDE. This physics-informed parametrization is then united with tools from supervised machine learning to infer from data the reduced operators. The Lift & Learn method extends Operator Inference to systems whose governing PDEs contain more general (non-polynomial) nonlinearities through the use of lifting variable transformations which expose polynomial structure in the PDE. The proposed approach achieves a number of desiderata for scientific machine learning formulations, including analyzability, interpretability, and making underlying modeling assumptions explicit and transparent. This thesis therefore provides analysis of the Operator Inference and Lift & Learn methods in both the spatially continuous PDE and spatially discrete ODE settings. Results are proven regarding the mean square errors of the learned models, the impact of spatial and temporal discretization, and the recovery of traditional reduced models via the learning method. Sensitivity analysis of the operator inference problem to model misspecifications and perturbations in the data is also provided. The Lift & Learn method is demonstrated on the compressible Euler equations, the FitzHugh-Nagumo reaction-diffusion equations, and a large-scale three-dimensional simulation of a rocket combustion experiment with over 18 million degrees of freedom. For the first two examples, the Lift & Learn models achieve 2–3 orders of magnitude dimension reduction and match the generalization performance of traditional reduced models based on Galerkin projection of the PDE operators, predicting the system evolution with errors between 0.01% and 1% relative to the original nonlinear simulation. For the combustion application, the Lift & Learn models accurately predict the amplitude and frequency of pressure oscillations as well as the large-scale structures in the flow field’s temperature and chemical variables, with 5–6 orders of magnitude dimension reduction and 6–7 orders of magnitude computational savings. The demonstrated ability of the Lift & Learn models to accurately approximate the system evolution with orders-of-magnitude dimension reduction and computational savings makes the learned models suitable for use in many-query computations used to support scientific discovery and engineering decision-making.