The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and …

Generation and analysis of time-series data is relevant to many quantitative fields ranging
from economics to fluid mechanics. In the physical sciences, structures such as metastable …

Nonlinear dynamical systems are ubiquitous in science and engineering, yet analysis and
prediction of these systems remains a challenge. Koopman operator theory circumvents …

Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …

This paper presents a randomized algorithm for computing the near-optimal low-rank
dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to …

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal
patterns from multi-dimensional time series, and it has been used successfully in a wide …

We study numerical approaches to computation of spectral properties of composition
operators. We provide a characterization of Koopman Modes in Banach spaces using …

Understanding the flow in urban environments is an increasingly relevant problem due to its
significant impact on air quality and thermal effects in cities worldwide. In this review we …

Higher Order Dynamic Mode Decomposition and Its Applications provides detailed
background theory, as well as several fully explained applications from a range of industrial …