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.
This beginning graduate textbook teaches data science and machine learning methods for modeling, prediction, and control of complex systems.
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 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
'This is a cleanly bound, compact book with medium weight coated paper and crisp text. There are many well-composed figures, most of them in color, with good explanatory captions, and sample code for almost all computational examples. While the code is for MATLAB, it is well commented and should not be too difficult to translate to Python or other computer languages ... This is a fine book, and quite good for a first edition. It is clearly written with many examples and informative figures has a very useful bibliography and many good programming examples. I would use it for a course without reservation, and it has a permanent place on my bookshelf as a reference.' John Starrett, Mathematical Association of America Reviews
'Throughout, topics are discussed with theoretical depth and accompanied by a substantial bibliography. The authors also make use of software code snips.' R. S. Stansbury, Choice