Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

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

Dynamic mode decomposition (DMD) describes complex dynamic processes through a
hierarchy of simpler coherent features. DMD is regularly used to understand the …

Koopman operators are infinite‐dimensional operators that globally linearize nonlinear
dynamical systems, making their spectral information valuable for understanding dynamics …

Dynamic mode decomposition (DMD) is a popular technique for modal decomposition, flow
analysis, and reduced-order modeling. In situations where a system is time varying, one …

The Koopman theory, a concept to globally model nonlinear signals by a linear Hamiltonian,
has been at the frontier of fluid mechanics research for the last decade. Wind engineering …

High-fidelity blood flow modelling is crucial for enhancing our understanding of
cardiovascular disease. Despite significant advances in computational and experimental …

This paper distills the serial work of Li et al., 2020a, Li et al., 2021, Li et al., 2022a, Li et al.,
2022b, Li et al., 2022c, Li et al., 2023a, Li et al., 2023b into a practice guide for the Dynamic …

In this paper, we consider the Koopman operator associated with the discrete and the
continuous-time random dynamical system (RDS). We provide results that characterize the …

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