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Data-driven science and engineering: machine learning, dynamical systems, and control

By: Brunton, Steven L.
Material type: materialTypeLabelBookPublisher: Cambridge Cambridge University Press 2019Edition: 2019.Description: xxii, 472 p. Includes bibliographical references and index.ISBN: 9781108422093.Subject(s): Mathematical analysis | Science - Data processing | Engineering - Data processingDDC classification: 620.00285631 Summary: Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art. • Provides in-depth examples paired with comprehensive, open-source code • Features concise, digestible explanations of complex concepts and their applications • Online supplements include homeworks, video lectures, and code and datasets in MATLAB® and Python https://www.cambridge.org/us/academic/subjects/mathematics/computational-science/data-driven-science-and-engineering-machine-learning-dynamical-systems-and-control?format=HB
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Table of contents

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
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
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
Contents note continued: 3.7.Robust Principal Component Analysis (RPCA)
3.8.Sparse Sensor Placement
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 in Data Mining 2008
6.Neural Networks and Deep Learning
Contents note continued: 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
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
Contents note continued: 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
10.Data-Driven Control
10.1.Nonlinear System Identification for Control
10.2.Machine Learning Control
10.3.Adaptive Extremum-Seeking Control
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
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.

Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.
• Provides in-depth examples paired with comprehensive, open-source code
• Features concise, digestible explanations of complex concepts and their applications
• Online supplements include homeworks, video lectures, and code and datasets in MATLAB® and Python


https://www.cambridge.org/us/academic/subjects/mathematics/computational-science/data-driven-science-and-engineering-machine-learning-dynamical-systems-and-control?format=HB

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