J. Nathan Kutz

TL;DR: This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.

TL;DR: In this paper, the authors define dynamic mode decomposition (DMD) as the eigendecomposition of an approximating linear operator, and propose sampling strategies that increase computational efficiency and mitigate the effects of noise.

TL;DR: In this paper, the authors propose a sparse regression method for discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain, which relies on sparsitypromoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models.

TL;DR: A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.

TL;DR: This first book to address the DMD algorithm presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development, and blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses.