Machine Learning, Dynamical Systems, and Control
Data-driven methods have become an essential part of the methodological portfolio of fluid dynamicists, motivating students and practitioners to gather practical knowledge from a diverse range of disciplines. These fields include computer science,...
This is the first textbook on a generally applicable control strategy for turbulence and other complex nonlinear systems. The approach of the book employs powerful methods of machine learning for optimal nonlinear control laws. This machine learni...
'Finally, a book that introduces data science in a context that will make any mechanical engineer feel comfortable. Data science is the new calculus, and no engineer should graduate without a thorough understanding of the topic.' Hod Lipson, Columbia University
'This book is a must-have for anyone interested in data-driven modeling and simulations. The readers as diverse as undergraduate STEM students and seasoned researchers would find it useful as a guide to this rapidly evolving field. Topics covered by the monograph include dimension reduction, machine learning, and robust control of dynamical systems with uncertain/random inputs. Every chapter contains codes and homework problems, which make this treaties ideal for the classroom setting. The book is supplemented with online lectures, which are not only educational but also entertaining to watch.' Daniel M. Tartakovsky, Stanford University
'Engineering principles will always be based on physics, and the models that underpin engineering will be derived from these physical laws. But in the future models based on relationships in large datasets will be as important and, when used alongside physics-based models, will lead to new insights and designs. Brunton and Kutz will equip students and practitioners with the tools they will need for this exciting future.' Greg Hyslop, Boeing
'Brunton and Kutz's book is fast becoming an indispensable resource for machine learning and data-driven learning in science and engineering. The second edition adds several timely topics in this lively field, including reinforcement learning and physics-informed machine learning. The text balances theoretical foundations and concrete examples with code, making it accessible and practical for students and practitioners alike.' Tim Colonius, California Institute of Technology
'This is a must read for those who are interested in understanding what machine learning can do for dynamical systems! Steve and Nathan have done an excellent job in bringing everyone up to speed to the modern application of machine learning on these complex dynamical systems.' Shirley Ho, Flatiron Institute/New York University
Steven L. Brunton is the James B. Morrison Professor of Mechanical Engineering at the University of Washington and Associate Director of the NSF AI Institute in Dynamic Systems. He is also Adjunct Professor of Applied Mathematics and Computer Science and a Data-Science Fellow at the eScience Institute. His research merges data science and machine learning with dynamical systems and control, with applications in fluid dynamics, biolocomotion, optics, energy systems, and manufacturing. He is an author of three textbooks, and received the UW College of Engineering Teaching award, the Army and Air Force Young Investigator Program (YIP) awards, and the Presidential Early Career Award for Scientists and Engineers (PECASE) award. J. Nathan Kutz is the Robert Bolles and Yasuko Endo Professor of Applied Mathematics at the University of Washington and Director of the NSF AI Institute in Dynamic Systems. He is also Adjunct Professor of Electrical and Computer Engineering, Mechanical Engineering, and Physics and Senior Data-Science Fellow at the eScience Institute. His research interests lie at the intersection of dynamical systems and machine learning. He is an author of three textbooks and has received the Applied Mathematics Boeing Award of Excellence in Teaching and an NSF CAREER award.
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; Part IV. Advanced Data-Driven Modeling and Control: 10. Data-Driven Control; 11. Reinforcement Learning; 12. Reduced Order Models (ROMs); 13. Interpolation for Parametric ROMs; 14. Physics-Informed Machine Learning.