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The book Data Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control explores how data can be used to discover and learn from patterns in complex systems.

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From the Publisher

Cambridge University Press, Data-Driven Science and Engineering
Cambridge University Press, Data-Driven Science and Engineering

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About the Author Of Data Driven Science And Engineering PDF Free Download


Steven L. Brunton is Associate Professor of Mechanical Engineering at the University of Washington. He is also Adjunct Associate Professor of Applied Mathematics and a Data-Science Fellow at the eScience Institute. His research applies data science and machine learning for dynamical systems and control to fluid dynamics, biolocomotion, optics, energy systems, and manufacturing. He has co-authored two textbooks, received the Army and Air Force Young Investigator awards, and was awarded the University of Washington College of Education teaching award.

J. Nathan Kutz is the Robert Bolles and Yasuko Endo Professor of Applied Mathematics at the University of Washington, and served as department chair until 2015. He is also Adjunct Professor of Electrical Engineering and Physics and a Senior Data-Science Fellow at the eScience Institute. His research interests are in complex systems and data analysis where machine learning can be integrated with dynamical systems and control for a diverse set of applications. He is an author of two textbooks and has received the Applied Mathematics Boeing Award of Excellence in Teaching and an NSF CAREER award. –This text refers to the hardcover edition.

Table Of Content Of Data Driven Science And Engineering PDF Free Download

Preface Common Optimization Techniques, Equations, Symbols, and Acronyms

Part I Dimensionality Reduction and Transforms

page ix xiii 1

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 1.9 Tensor Decompositions and N-Way Data Arrays

3 3 7 10 15 21 25 30 37 41

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 Wavelets and Multi-Resolution Analysis 2.6 2D Transforms and Image Processing

47 47 56 63 69 75 77

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

84 84 88 92 95 98 103 107 110

v

vi

Contents

Part II Machine Learning and Data Analysis

115

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

117 118 123 130 136 140 143 148

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 in Data Mining 2008

154 155 160 164 168 172 176 180 185 190

6

Neural Networks and Deep Learning 6.1 Neural Networks: 1-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 The Diversity of Neural Networks

195 196 199 204 209 212 216 220

Part III Dynamics and Control

227

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

229 230 235 247 257 266

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)

276 277 281 287 292

Contents

8.5 8.6 8.7 8.8

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

vii

296 299 300 308

9

Balanced Models for Control 9.1 Model Reduction and System Identification 9.2 Balanced Model Reduction 9.3 System identification

321 321 322 336

10

Data-Driven Control 10.1 Nonlinear System Identification for Control 10.2 Machine Learning Control 10.3 Adaptive Extremum-Seeking Control

345 346 352 362

Part IV Reduced Order Models

373

11

Reduced Order Models (ROMs) 11.1 POD for Partial Differential Equations 11.2 Optimal Basis Elements: The POD Expansion 11.3 POD and Soliton Dynamics 11.4 Continuous Formulation of POD 11.5 POD with Symmetries: Rotations and Translations

375 375 381 387 391 396

12

Interpolation for Parametric ROMs 12.1 Gappy POD 12.2 Error and Convergence of Gappy POD 12.3 Gappy Measurements: Minimize Condition Number 12.4 Gappy Measurements: Maximal Variance 12.5 POD and the Discrete Empirical Interpolation Method (DEIM) 12.6 DEIM Algorithm Implementation 12.7 Machine Learning ROMs

403 403 409 413 418 423 426 429

Glossary Bibliography Index

436 443 471


Book Description

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