Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control 2nd Edition, Kindle Edition

✍ Scribed by Steven L. Brunton, J. Nathan Kutz

• Publisher: Cambridge University Press
• Year: 2022
• Tongue: English
• Leaves: 616
• Edition: 2
• Category: Library

✦ Table of Contents

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