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Order Valium 10 Mg Uk Cover Half-title Endorsements Title page Copyright information Contents Preface Acknowledgments Common Optimization Techniques, Equations, Symbols, and Acronyms Part I Dimensionality Reduction and Transforms 1 Singular Value Decomposition (SVD) 1.1 Overview 1.2 Matrix Approximation 1.3 Mathematical Properties and Manipulations 1.4 Pseudo-Inverse, Least-Squares, and Regression 1.5 Principal Component Analysis (PCA) 1.6 Eigenfaces Example 1.7 Truncation and Alignment 1.8 Randomized Singular Value Decomposition Randomized Linear Algebra Randomized SVD Algorithm Oversampling Power Iterations Guaranteed Error Bounds Choice of Random Matrix P Example of Randomized SVD 1.9 Tensor Decompositions and N-Way Data Arrays 2 Fourier and Wavelet Transforms 2.1 Fourier Series and Fourier Transforms 2.2 Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) 2.3 Transforming Partial Differential Equations 2.4 Gabor Transform and the Spectrogram 2.5 Laplace Transform 2.6 Wavelets and Multi-Resolution Analysis 2.7 Two-Dimensional Transforms and Image Processing 3 Sparsity and Compressed Sensing 3.1 Sparsity and Compression 3.2 Compressed Sensing 3.3 Compressed Sensing Examples 3.4 The Geometry of Compression 3.5 Sparse Regression 3.6 Sparse Representation 3.7 Robust Principal Component Analysis (RPCA) 3.8 Sparse Sensor Placement Part II Machine Learning and Data Analysis 4 Regression and Model Selection 4.1 Classic Curve Fitting 4.2 Nonlinear Regression and Gradient Descent 4.3 Regression and Ax = b: Over- and Under-Determined Systems 4.4 Optimization as the Cornerstone of Regression 4.5 The Pareto Front and Lex Parsimoniae 4.6 Model Selection: Cross-Validation 4.7 Model Selection: Information Criteria 5 Clustering and Classification 5.1 Feature Selection and Data Mining 5.2 Supervised versus Unsupervised Learning 5.3 Unsupervised Learning: k-Means Clustering 5.4 Unsupervised Hierarchical Clustering: Dendrogram 5.5 Mixture Models and the Expectation-Maximization Algorithm 5.6 Supervised Learning and Linear Discriminants 5.7 Support Vector Machines (SVM) 5.8 Classification Trees and Random Forest 5.9 Top 10 Algorithms of Data Mining circa 2008 (Before the Deep Learning Revolution) 6 Neural Networks and Deep Learning 6.1 Neural Networks: Single-Layer Networks 6.2 Multi-Layer Networks and Activation Functions 6.3 The Backpropagation Algorithm 6.4 The Stochastic Gradient Descent Algorithm 6.5 Deep Convolutional Neural Networks 6.6 Neural Networks for Dynamical Systems 6.7 Recurrent Neural Networks 6.8 Autoencoders 6.9 Generative Adversarial Networks (GANs) 6.10 The Diversity of Neural Networks Part III Dynamics and Control 7 Data-Driven Dynamical Systems 7.1 Overview, Motivations, and Challenges 7.2 Dynamic Mode Decomposition (DMD) 7.3 Sparse Identification of Nonlinear Dynamics (SINDy) 7.4 Koopman Operator Theory 7.5 Data-Driven Koopman Analysis 8 Linear Control Theory 8.1 Closed-Loop Feedback Control 8.2 Linear Time-Invariant Systems 8.3 Controllability and Observability 8.4 Optimal Full-State Control: Linear–Quadratic Regulator (LQR) 8.5 Optimal Full-State Estimation: the Kalman Filter 8.6 Optimal Sensor-Based Control: Linear–Quadratic Gaussian (LQG) 8.7 Case Study: Inverted Pendulum on a Cart 8.8 Robust Control and Frequency-Domain Techniques 9 Balanced Models for Control 9.1 Model Reduction and System Identification 9.2 Balanced Model Reduction 9.3 System Identification Part IV Advanced Data-Driven Modeling and Control 10 Data-Driven Control 10.1 Model Predictive Control (MPC) 10.2 Nonlinear System Identification for Control 10.3 Machine Learning Control 10.4 Adaptive Extremum-Seeking Control 11 Reinforcement Learning 11.1 Overview and Mathematical Formulation 11.2 Model-Based Optimization and Control 11.3 Model-Free Reinforcement Learning and Q-Learning 11.4 Deep Reinforcement Learning 11.5 Applications and Environments 11.6 Optimal Nonlinear Control 12 Reduced-Order Models (ROMs) 12.1 Proper Orthogonal Decomposition (POD) for Partial Differential Equations 12.2 Optimal Basis Elements: the POD Expansion 12.3 POD and Soliton Dynamics 12.4 Continuous Formulation of POD 12.5 POD with Symmetries: Rotations and Translations 12.6 Neural Networks for Time-Stepping with POD 12.7 Leveraging DMD and SINDy for Galerkin–POD 13 Interpolation for Parametric Reduced-Order Models 13.1 Gappy POD 13.2 Error and Convergence of Gappy POD 13.3 Gappy Measurements: Minimize Condition Number 13.4 Gappy Measurements: Maximal Variance 13.5 POD and the Discrete Empirical Interpolation Method (DEIM) 13.6 DEIM Algorithm Implementation 13.7 Decoder Networks for Interpolation 13.8 Randomization and Compression for ROMs 13.9 Machine Learning ROMs 14 Physics-Informed Machine Learning 14.1 Mathematical Foundations 14.2 SINDy Autoencoder: Coordinates and Dynamics 14.3 Koopman Forecasting 14.4 Learning Nonlinear Operators 14.5 Physics-Informed Neural Networks (PINNs) 14.6 Learning Coarse-Graining for PDEs 14.7 Deep Learning and Boundary Value Problems Glossary References Index