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

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 …

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in
many realistic molecular systems, biologically important rare transitions occur on timescales …

We consider the data-driven approximation of the Koopman operator for stochastic
differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the …

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 …

Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to
approximate the Koopman operator for deterministic and stochastic (control) systems. This …

Protein folding is a critical process that determines the functional state of proteins. Proper
folding is essential for proteins to acquire their functional three-dimensional structures and …

Koopman operator theory has been successfully applied to problems from various research
areas such as fluid dynamics, molecular dynamics, climate science, engineering, and …

Slow kinetic processes in molecular systems can be analyzed by computing the dominant
eigenpairs of the Koopman operator or its generator. In this context, the Variational …

Extracting information about dynamical systems from models learned off simulation data has
become an increasingly important research topic in the natural and engineering sciences …