Kooperativer Bibliotheksverbund

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Umfang: 1 online resource (456 pages)

Ausgabe: 1st ed.

ISBN: 3-031-36644-1

Serie: Computational Methods in Engineering and the Sciences Series

Anmerkung: Intro -- Preface -- Contents -- About the Editors -- 1 Machine Learning in Computer Aided Engineering -- 1.1 Introduction -- 1.2 Machine Learning Procedures Employed in CAE -- 1.2.1 Machine Learning Aspects and Classification of Procedures -- 1.2.2 Overview of Classical Machine Learning Procedures Used in CAE -- 1.3 Constraining to, and Incorporating Physics in, Data-Driven Methods -- 1.3.1 Incorporating Physics in, and Learning Physics From, the Dataset -- 1.3.2 Incorporating Physics in the Design of a ML Method -- 1.3.3 Data Assimilation and Correction Methods -- 1.3.4 ML Methods Designed to Learn Physics -- 1.4 Applications of Machine Learning in Computer Aided Engineering -- 1.4.1 Constitutive Modeling and Multiscale Applications -- 1.4.2 Fluid Mechanics Applications -- 1.4.3 Structural Mechanics Applications -- 1.4.4 Machine Learning Approaches Motivated in Structural Mechanics and by Finite Element Concepts -- 1.4.5 Multiphysics Problems -- 1.4.6 Machine Learning in Manufacturing and Design -- 1.5 Conclusions -- References -- 2 Artificial Neural Networks -- 2.1 Introduction -- 2.2 Biological Motivation and Pre-history -- 2.2.1 Memory -- 2.2.2 Learning -- 2.2.3 Parallel Distributed Processing Paradigm -- 2.2.4 The Artificial Neuron -- 2.2.5 The Perceptron -- 2.3 The First Age-The Multi-layer Perceptron -- 2.3.1 Existence of Solutions -- 2.3.2 Uniqueness of Solutions -- 2.3.3 Generalization and Regularization -- 2.3.4 Choice of Output Activations Functions -- 2.4 A First-Age Case Study: Structural Monitoring of an Aircraft Wing -- 2.5 The Second Age-Deep Learning -- 2.5.1 Convolutional Neural Networks (CNNs) -- 2.5.2 A Little More History -- 2.5.3 Other Recent Developments -- 2.6 Conclusions -- References -- 3 Gaussian Processes -- 3.1 Introduction -- 3.1.1 A Visual Introduction To Gaussian Processes -- 3.1.2 Gaussian Process Regression. , 3.1.3 Implementation and Learning of the GP -- 3.2 Beyond the Gaussian Process -- 3.2.1 Large Training Data -- 3.2.2 Non-Gaussian Likelihoods -- 3.2.3 Multiple-Output GPs -- 3.3 A Case Study with Wind Turbine Power Curves -- 3.4 Conclusions -- References -- 4 Machine Learning Methods for Constructing Dynamic Models From Data -- 4.1 Introduction -- 4.2 Modeling Viewpoints -- 4.3 Learning Paradigms: Burgers' Equation -- 4.4 Dynamic Models From Data -- 4.4.1 Dynamic Mode Decomposition -- 4.4.2 Sparse Identification of Nonlinear Dynamics -- 4.4.3 Neural Networks -- 4.5 Joint Discovery of Coordinates and Models -- 4.6 Conclusions -- References -- 5 Physics-Informed Neural Networks: Theory and Applications -- 5.1 Introduction -- 5.2 Basics of Artificial Neural Networks -- 5.2.1 Feed-Forward Neural Networks -- 5.2.2 Activation Functions -- 5.2.3 Training -- 5.2.4 Testing and Validation -- 5.2.5 Optimizers -- 5.3 Physics-Informed Neural Networks -- 5.3.1 Collocation Method -- 5.3.2 Energy Minimization Method -- 5.4 Numerical Applications -- 5.4.1 Forward Problems -- 5.4.2 Inverse Problems -- 5.5 Conclusions -- References -- 6 Physics-Informed Deep Neural Operator Networks -- 6.1 Introduction -- 6.2 DeepONet and Its Extensions -- 6.2.1 Feature Expansion in DeepONet -- 6.2.2 Multiple Input DeepONet -- 6.2.3 Physics-Informed DeepONet -- 6.3 FNO and Its Extensions -- 6.3.1 Feature Expansion in FNO -- 6.3.2 Implicit FNO -- 6.3.3 Physics-Informed FNO -- 6.4 Graph Neural Operators -- 6.4.1 Graph Neural Networks -- 6.4.2 Integral Neural Operators Through Graph Kernel Learning -- 6.5 Neural Operator Theory -- 6.6 Applications -- 6.6.1 Data-Driven Neural Operators -- 6.6.2 Physics-Informed Neural Operators -- 6.7 Summary and Outlook -- References -- 7 Digital Twin for Dynamical Systems -- 7.1 Introduction -- 7.2 Building Blocks and Nominal Model in Digital Twin. , 7.3 Physics-Based Digital Twin for SDOF System -- 7.3.1 Nominal Model -- 7.3.2 The Digital Twin Framework -- 7.3.3 Formulating the Digital Twin -- 7.3.4 Numerical Experiment -- 7.4 Physics ML Fusion: Towards a Predictive Digital Twin -- 7.4.1 Gaussian Process -- 7.4.2 Numerical Experiment -- 7.5 Digital Twin for Nonlinear Stochastic Dynamical Systems -- 7.5.1 Stochastic Nonlinear MDOF System: The Nominal Model -- 7.5.2 Problem Statement -- 7.5.3 The Digital Twin Framework -- 7.5.4 Numerical Examples -- 7.6 Digital Twin for Systems with Misspecified Physics -- 7.6.1 Model Updating Using Input-Output Measurement -- 7.6.2 Model Updating Using Output-Only Measurements -- 7.6.3 Sparse Bayesian Regression -- 7.6.4 Numerical Examples -- 7.7 Conclusions -- References -- 8 Reduced Order Modeling -- 8.1 Introduction -- 8.2 Proper Orthogonal Decomposition -- 8.2.1 Proper Orthogonal Decomposition Applied to Partial Differential Equations -- 8.2.2 Singular Value Decomposition -- 8.3 Reduced Order Modeling Using Proper Orthogonal Decomposition -- 8.3.1 Galerkin Projection -- 8.3.2 Hyperreduction -- 8.3.3 Stabilization Using Variational Multiscale Methods -- 8.4 Non-intrusive Reduced Order Models -- 8.4.1 The General Concept -- 8.4.2 Dynamic Mode Decomposition -- 8.5 Parametric Reduced Order Models -- 8.5.1 Global Basis -- 8.5.2 Local Basis with Interpolation -- 8.6 Machine Learning-Based Reduced Order Models -- 8.6.1 Nonlinear Dimension Reduction -- 8.6.2 Machine Learning Based Non-intrusive Reduced Order Models -- 8.6.3 Closure Modeling -- 8.6.4 Correction Based on Fine Solutions -- 8.6.5 Machine Learning Applied to Parametric Reduced Order Models -- 8.6.6 Physics Informed Machine Learning for Reduced Order Models -- 8.6.7 Reduced System Identification -- 8.7 Concluding Remarks -- References -- 9 Regression Models for Machine Learning -- 9.1 Introduction. , 9.2 Parametric Regression: A Non-Bayesian Perspective -- 9.2.1 Least Square Regression -- 9.2.2 Support Vector Regression -- 9.2.3 Kernel Trick -- 9.3 Regression: A Bayesian Perspective -- 9.3.1 Gaussian Process Regression: A Parametric Space Perspective -- 9.3.2 Gaussian Process Regression: A Functional Space Perspective -- 9.4 Active Learning -- 9.4.1 Active Learning for Bayesian Cubature -- 9.4.2 Active Learning for Bayesian Reliability Assessment -- 9.5 Conclusions -- References -- 10 Overview on Machine Learning Assisted Topology Optimization Methodologies -- 10.1 Introduction -- 10.2 Background -- 10.2.1 Topology Optimization -- 10.2.2 Artificial Intelligence and Neural Networks -- 10.3 Literature Survey -- 10.3.1 Density-Based Methods -- 10.3.2 Image-Based Methods -- 10.4 Conclusions -- References -- 11 Mixed-Variable Concurrent Material, Geometry, and Process Design in Integrated Computational Materials Engineering -- 11.1 Introduction -- 11.2 Mixed-Variable and Constrained Bayesian Optimization -- 11.2.1 Gaussian Processes and Bayesian Optimization -- 11.2.2 Latent Variable Gaussian Process (LVGP) Modeling -- 11.2.3 Constrained Bayesian Optimization -- 11.3 Application to Concurrent Structure and Material Design -- 11.3.1 The Integrated Material-Structure Model -- 11.3.2 Design Variables, Constraints, and Objectives -- 11.3.3 LVGP Modeling and Validation -- 11.3.4 LVGP-CBO Setup and Design Results -- 11.4 Application to Concurrent Material and Process Design -- 11.4.1 The Integrated Process-Structure-Property Model -- 11.4.2 Design Variables, Constraints, and Objectives for SFRP Design -- 11.4.3 LVGP Modeling and Validation -- 11.4.4 LVGP-CBO Setup and Design Results -- 11.5 Conclusions -- References -- 12 Machine Learning Interatomic Potentials: Keys to First-Principles Multiscale Modeling -- 12.1 Introduction. , 12.2 Methods for Exploring Interatomic Forces -- 12.2.1 Quantum Mechanics -- 12.2.2 Empirical Interatomic Potentials -- 12.2.3 Machine Learning Interatomic Potentials -- 12.3 Developing a Machine Learning Interatomic Potential -- 12.3.1 Popular Machine Learning Interatomic Potentials -- 12.3.2 Training of Machine Learning Interatomic Potentials -- 12.3.3 Passive or Active Fitting -- 12.3.4 Current Challenges of MLIPs -- 12.4 Quantum Mechanics and Empirical Interatomic Potentials Challenges -- 12.4.1 Thermal Transport -- 12.4.2 Mechanical Properties -- 12.5 First-Principles Multiscale Modeling -- 12.6 Concluding Remark -- References.

Weitere Ausg.: Print version: Rabczuk, Timon Machine Learning in Modeling and Simulation Cham : Springer International Publishing AG,c2023 ISBN 9783031366437

Sprache: Englisch