Machine Learning Low Rank Approximations And Reduced Order Modeling In Computational Mechanics

Author : Felix Fritzen,David Ryckelynck
Publisher : MDPI
Page : 254 pages
File Size : 51,9 Mb
Release : 2019-09-18
Category : Technology & Engineering
ISBN : 9783039214099

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Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by Felix Fritzen,David Ryckelynck Pdf

The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

Author : Felix Fritzen,David Ryckelynck
Publisher : Unknown
Page : 1 pages
File Size : 48,6 Mb
Release : 2019
Category : Electronic books
ISBN : 3039214101

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Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by Felix Fritzen,David Ryckelynck Pdf

The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

Author : Ivan Markovsky
Publisher : Springer Science & Business Media
Page : 260 pages
File Size : 53,6 Mb
Release : 2011-11-19
Category : Technology & Engineering
ISBN : 9781447122272

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Low Rank Approximation by Ivan Markovsky Pdf

Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation; machine learning for information retrieval and clustering; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; and psychometrics for factor analysis. Software implementation of the methods is given, making the theory directly applicable in practice. All numerical examples are included in demonstration files giving hands-on experience and exercises and MATLAB® examples assist in the assimilation of the theory.

Author : Michel Bergmann,Laurent Cordier,Traian Iliescu
Publisher : Frontiers Media SA
Page : 178 pages
File Size : 46,6 Mb
Release : 2023-01-05
Category : Science
ISBN : 9782832510704

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Data-driven modeling and optimization in fluid dynamics: From physics-based to machine learning approaches by Michel Bergmann,Laurent Cordier,Traian Iliescu Pdf

Author : Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong
Publisher : Cambridge University Press
Page : 391 pages
File Size : 46,6 Mb
Release : 2020-04-23
Category : Computers
ISBN : 9781108470049

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Mathematics for Machine Learning by Marc Peter Deisenroth,A. Aldo Faisal,Cheng Soon Ong Pdf

Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.

Author : Alfio Quarteroni,Gianluigi Rozza
Publisher : Springer
Page : 338 pages
File Size : 48,6 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9783319020907

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Reduced Order Methods for Modeling and Computational Reduction by Alfio Quarteroni,Gianluigi Rozza Pdf

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.

Author : Genki Yagawa,Atsuya Oishi
Publisher : Springer Nature
Page : 233 pages
File Size : 47,6 Mb
Release : 2021-02-26
Category : Technology & Engineering
ISBN : 9783030661113

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Computational Mechanics with Neural Networks by Genki Yagawa,Atsuya Oishi Pdf

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

Author : Gianluigi Rozza,Giovanni Stabile,Max Gunzburger,Marta D'Elia
Publisher : Springer
Page : 0 pages
File Size : 42,8 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 3031550595

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Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators by Gianluigi Rozza,Giovanni Stabile,Max Gunzburger,Marta D'Elia Pdf

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.

Author : Stefan Kollmannsberger,Davide D'Angella,Moritz Jokeit,Leon Herrmann
Publisher : Springer
Page : 0 pages
File Size : 53,7 Mb
Release : 2022-08-07
Category : Technology & Engineering
ISBN : 303076589X

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Deep Learning in Computational Mechanics by Stefan Kollmannsberger,Davide D'Angella,Moritz Jokeit,Leon Herrmann Pdf

This book provides a first course on deep learning in computational mechanics. The book starts with a short introduction to machine learning’s fundamental concepts before neural networks are explained thoroughly. It then provides an overview of current topics in physics and engineering, setting the stage for the book’s main topics: physics-informed neural networks and the deep energy method. The idea of the book is to provide the basic concepts in a mathematically sound manner and yet to stay as simple as possible. To achieve this goal, mostly one-dimensional examples are investigated, such as approximating functions by neural networks or the simulation of the temperature’s evolution in a one-dimensional bar. Each chapter contains examples and exercises which are either solved analytically or in PyTorch, an open-source machine learning framework for python.

Author : Erwin Stein,René de Borst,Thomas J. R. Hughes
Publisher : Unknown
Page : 870 pages
File Size : 53,5 Mb
Release : 2004
Category : Dynamics
ISBN : UOM:39015060085126

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Encyclopedia of Computational Mechanics by Erwin Stein,René de Borst,Thomas J. R. Hughes Pdf

The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.

Author : Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban
Publisher : Springer
Page : 504 pages
File Size : 42,5 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9783319587868

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Model Reduction of Parametrized Systems by Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban Pdf

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Author : Alfio Quarteroni,Andrea Manzoni,Federico Negri
Publisher : Springer
Page : 296 pages
File Size : 48,9 Mb
Release : 2015-08-19
Category : Mathematics
ISBN : 9783319154312

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Reduced Basis Methods for Partial Differential Equations by Alfio Quarteroni,Andrea Manzoni,Federico Negri Pdf

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

Author : Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
Publisher : Springer
Page : 131 pages
File Size : 48,7 Mb
Release : 2015-08-20
Category : Mathematics
ISBN : 9783319224701

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Certified Reduced Basis Methods for Parametrized Partial Differential Equations by Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm Pdf

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.

Author : Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk
Publisher : John Wiley & Sons
Page : 403 pages
File Size : 44,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9781119957584

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Large-Scale Inverse Problems and Quantification of Uncertainty by Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk Pdf

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.

Author : Justin Solomon
Publisher : CRC Press
Page : 400 pages
File Size : 48,7 Mb
Release : 2015-06-24
Category : Computers
ISBN : 9781482251890

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Numerical Algorithms by Justin Solomon Pdf

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig