Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB®, Python, Julia, and R - available on databookuw.com.

Contenu

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.