'This is a very timely, comprehensive and well written book in what is now one of the most dynamic and impactful areas of modern applied mathematics. Data science is rapidly taking center stage in our society. The subject cannot be ignored, either by domain scientists or by researchers in applied mathematics who intend to develop algorithms that the community will use. The book by Brunton and Kutz is an excellent text for a beginning graduate student, or even for a more advanced researcher interested in this field. The main theme seems to be applied optimization. The subtopics include dimensional reduction, machine learning, dynamics and control and reduced order methods. These were well chosen and well covered.' Stanley Osher, University of California
'Professors Kutz and Brunton bring both passion and rigor to this most timely subject matter. Data analytics is the important topic for engineering in the twenty-first century and this book covers the far-reaching subject matter with clarity and code examples. Bravo!' Steve M. Legensky, Founder and General Manager, Intelligent Light
'Brunton and Kutz provide a lively and comprehensive treatise on machine learning and data mining algorithms as applied to physical systems arising in science and engineering and their control. They provide an abundance of examples and wisdom that will be of great value to students and practitioners alike.' Tim Colonius, California Institute of Technology
Part I. Dimensionality Reduction and Transforms
1. Singular value decomposition
2. Fourier and wavelet transforms
3. Sparsity and compressed sensing
Part II. Machine Learning and Data Analysis
4. Regression and model selection
5. Clustering and classification
6. Neural networks and deep learning
Part III. Dynamics and Control
7. Data-driven dynamical systems
8. Linear control theory
9. Balanced models for control
10. Data-driven control
Part IV. Reduced-Order Models
11. Reduced-order models (ROMs)
12. Interpolation for parametric ROMs.