09-23-2026, 07:58 PM
Data-Driven Methods for Dynamic Systems by Jason J. Bramburger is a 2024 SIAM book that introduces modern data-driven techniques for analyzing and modeling dynamical systems. Its central theme is the combination of classical dynamical-systems mathematics with computational methods from data science and machine learning. The book covers dynamic mode decomposition (DMD), the Koopman operator, sparse/nonlinear modeling, polynomial optimization, neural networks, and autoencoders, showing how these tools can extract information about differential equations and time-dependent phenomena directly from experimental or simulated data.
A major message is that machine learning does not simply replace traditional mathematical modeling; instead, it can complement it by discovering useful representations, forecasting dynamics, and extracting system-level properties from data. The book discusses the limitations of purely linear approaches such as DMD and then introduces nonlinear methods and neural networks capable of better generalization.
It also uses Koopman-operator methods and polynomial/semidefinite optimization to study complex systems without necessarily constructing an explicit model. Numerous MATLAB scripts and Jupyter notebooks accompany the examples, making the book particularly practical for graduate students and researchers working at the intersection of dynamical systems, differential equations, applied mathematics, and AI/data science.
BOOK
A major message is that machine learning does not simply replace traditional mathematical modeling; instead, it can complement it by discovering useful representations, forecasting dynamics, and extracting system-level properties from data. The book discusses the limitations of purely linear approaches such as DMD and then introduces nonlinear methods and neural networks capable of better generalization.
It also uses Koopman-operator methods and polynomial/semidefinite optimization to study complex systems without necessarily constructing an explicit model. Numerous MATLAB scripts and Jupyter notebooks accompany the examples, making the book particularly practical for graduate students and researchers working at the intersection of dynamical systems, differential equations, applied mathematics, and AI/data science.
BOOK
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