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Author: Felix Fritzen Publisher: MDPI ISBN: 3039214098 Category : Technology & Engineering Languages : en Pages : 254
Book Description
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 Publisher: MDPI ISBN: 3039214098 Category : Technology & Engineering Languages : en Pages : 254
Book Description
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 Publisher: ISBN: 9783039214105 Category : Electronic books Languages : en Pages : 1
Book Description
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: Publisher: Elsevier ISBN: 0443239851 Category : Mathematics Languages : en Pages : 590
Book Description
Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on the Numerical Analysis Meets Machine Learning
Author: Alfio Quarteroni Publisher: Springer ISBN: 3319020900 Category : Mathematics Languages : en Pages : 338
Book Description
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: Marc Peter Deisenroth Publisher: Cambridge University Press ISBN: 1108569323 Category : Computers Languages : en Pages : 392
Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.
Author: Steven L. Brunton Publisher: Cambridge University Press ISBN: 1009098489 Category : Computers Languages : en Pages : 615
Book Description
A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Author: Qizhi He Publisher: ISBN: Category : Languages : en Pages : 289
Book Description
Physics-based numerical simulation remains challenging as the complexity of today's high-fidelity models has dramatically increased. Model order reduction (MOR) and data-driven modeling, based on the emerging techniques of data learning and physical modeling, present a promising way to tackle the computational bottleneck related to the computational intensity and model complexity. Nevertheless, MOR has proven to be significantly more difficult for parameterized mechanics systems that exhibit a wide variety of parameter-dependent nonlinear behaviors or that involve localized essential features. The first objective of this work is to develop robust, physics-preserving MOR methods. As constructing a low-dimensional MOR model can be considered as the hybrid data-physics approach, one can optimize it through a learning process using both data and physical models. As such, we first propose a MOR method based on decomposed reduced-order projections that well preserve the essential near-tip characteristic for fracture mechanics. Moreover, we develop an enhanced reduced-order basis to construct a low-dimensional subspace, deriving from a generalized manifold learning framework that allows the employment of local information in the data structure during the learning phase. This approach can yield a robust reduced-order model against noise and outliers and is well suited for parameterized nonlinear physical systems. Finally, a nonlinear MOR for a meshfree Galerkin formulation with the stabilized conforming nodal integration (SCNI) scheme is developed to yield a pure node based MOR that is particularly effective for hyper-reduction techniques. A numerical example of two-phase hyperelastic solid with perturbed loading conditions is used to validate the effectiveness of the proposed reduction method. The second goal of the dissertation is to develop a robust data-driven computational framework, which provides an alternative to conventional scientific computing for complex materials. This framework aims at performing physical simulation by directly interacting with material data via machine learning procedures instead of employing phenomenological constitutive models, and especially addressing the robustness issue associated with noisy and scarce data. To this end, we propose to search data solutions from a locally reconstructed convex hull associated with the k-nearest neighbor points, which leads to robustness to noisy data and ensures convergence stability. The accuracy and robustness of the proposed data-driven approach are demonstrated in the modeling of linear and nonlinear elasticity problems. In addition, we present a preliminary result of data-driven modeling of biological tissue using material data collected from laboratory testing on heart valve tissue, showing the potential of data-driven simulation by integrating physical modeling and machine learning techniques.
Author: Felix Fritzen
Author: Felix Fritzen
Author: Felix Fritzen
Author: 
Author: Gianluigi Rozza
Author: Alfio Quarteroni
Author: Michel Bergmann
Author: Marc Peter Deisenroth
Author: Steven L. Brunton
Author: David Ryckelynck
Author: Qizhi He