Dynamic Mode Decomposition:
Dynamic Mode Decomposition by Kutz et al. -- the primary text for this reading group.
Data-Driven Modeling:
Data-Driven Science and Engineering by Kutz and Brunton
The following references serve two purposes: to provide supporting material for the prerequisite knowledge required to study DMD (e.g. linear algebra, nonlinear dynamics), and to provide reading on closely connected topics in (model-based) ML/DL.
Dynamical Systems and Chaos:
Nonlinear Dynamics and Chaos by Strogatz -- standard reference for an upper-division undergraduate course.
Introduction to Dynamical Systems by Brin and Stuck
Chaos in Dynamical Systems by Ott
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by Guckenheimer and Holmes
Chaos and Integrability in Nonlinear Dynamics: An Introduction by Michael Tabor (fmr. chair of Applied Math at UA)
Numerical Algebra and Analysis:
Numerical Linear Algebra by Trefethen and Bau
Numerical Analysis: Mathematics of Scientific Computing by Kincaid and Cheney
Machine Learning:
An Introduction to Statistical Learning by James, Witten, Hastie, and Tibshirani
Deep Learning by Goodfellow, Bengio, and Courville
Physics-Based Deep Learning by Thuerey et al.
Any additional suggestions? Email rferrando at math dot arizona dot edu.