Data driven science and engineering

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Preface Acknowledgments Optimization, Equations, Symbols, and Acronyms I Dimensionality Reduction and Transforms Singular Value Decomposition (SVD) Overview Matrix Approximation Mathematical Properties and Manipulations Pseudo-Inverse, Least-Squares, and Regression Principal Component Analysis (PCA) Eigenfaces Example Truncation and Alignment Randomized Singular Value Decomposition Tensor Decompositions and N-Way Data Arrays Fourier and Wavelet Transforms Fourier Series and Fourier Transforms Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) Transforming Partial Differential Equations Gabor Transform and the Spectrogram Laplace Transform Wavelets and Multi-Resolution Analysis Two-Dimensional Transforms and Image Processing Sparsity and Compressed Sensing Sparsity and Compression Compressed Sensing Compressed Sensing Examples The Geometry of Compression Sparse Regression Sparse Representation Robust Principal Component Analysis (RPCA) Sparse Sensor Placement II Machine Learning and Data Analysis Regression and Model Selection Classic Curve Fitting Nonlinear Regression and Gradient Descent Regression and Ax=b: Over- and Under-Determined Systems Optimization as the Cornerstone of Regression The Pareto Front and Lex Parsimoniae Model Selection: Cross-Validation Model Selection: Information Criteria Clustering and Classification Feature Selection and Data Mining Supervised versus Unsupervised Learning Unsupervised Learning: k-Means Clustering Unsupervised Hierarchical Clustering: Dendrogram Mixture Models and the Expectation-Maximization Algorithm Supervised Learning and Linear Discriminants Support Vector Machines (SVM) Classification Trees and Random Forest Top 10 Algorithms of Data Mining circa 2008 (Before the Deep Learning Revolution) Neural Networks and Deep Learning Neural Networks: Single-Layer Networks Multi-Layer Networks and Activation Functions The Backpropagation Algorithm The Stochastic Gradient Descent Algorithm Deep Convolutional Neural Networks Neural Networks for Dynamical Systems Recurrent Neural Networks Autoencoders Generative Adversarial Networks (GANs) The Diversity of Neural Networks III Dynamics and Control Data-Driven Dynamical Systems Overview, Motivations, and Challenges Dynamic Mode Decomposition (DMD) Sparse Identification of Nonlinear Dynamics (SINDy) Koopman Operator Theory Data-Driven Koopman Analysis Linear Control Theory Closed-Loop Feedback Control Linear Time-Invariant Systems Controllability and Observability Optimal Full-State Control: Linear–Quadratic Regulator (LQR) Optimal Full-State Estimation: the Kalman Filter Optimal Sensor-Based Control: Linear–Quadratic Gaussian (LQG) Case Study: Inverted Pendulum on a Cart Robust Control and Frequency-Domain Techniques Balanced Models for Control Model Reduction and System Identification Balanced Model Reduction System Identification IV Advanced Data-Driven Modeling and Control Data-Driven Control Model Predictive Control (MPC) Nonlinear System Identification for Control Machine Learning Control Adaptive Extremum-Seeking Control Reinforcement Learning Overview and Mathematical Formulation Model-Based Optimization and Control Model-Free Reinforcement Learning and Q-Learning Deep Reinforcement Learning Applications and Environments Optimal Nonlinear Control Reduced-Order Models (ROMs) Proper Orthogonal Decomposition (POD) for Partial Differential Equations Optimal Basis Elements: the POD Expansion POD and Soliton Dynamics Continuous Formulation of POD POD with Symmetries: Rotations and Translations Neural Networks for Time-Stepping with POD Leveraging DMD and SINDy for POD-Galerkin Interpolation for Parametric Reduced-Order Models Gappy POD Error and Convergence of Gappy POD Gappy Measurements: Minimize Condition Number Gappy Measurements: Maximal Variance POD and the Discrete Empirical Interpolation Method (DEIM) DEIM Algorithm Implementation Decoder Networks for Interpolation Randomization and Compression for ROMs Machine Learning ROMs Physics-Informed Machine Learning Mathematical Foundations SINDy Autoencoder: Coordinates and Dynamics Koopman Forecasting Learning Nonlinear Operators Physics-Informed Neural Networks (PINNs) Learning Coarse-Graining for PDEs Deep Learning and Boundary Value Problems Glossary References Index