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 …

The Koopman operator is a linear but infinite-dimensional operator that governs the
evolution of scalar observables defined on the state space of an autonomous dynamical …

Machine learning has become a widely popular and successful paradigm, especially in data-
driven science and engineering. A major application problem is data-driven forecasting of …

Inference, prediction, and control of complex dynamical systems from time series is
important in many areas, including financial markets, power grid management, climate and …

Information about the behavior of dynamical systems can often be obtained by analyzing the
eigenvalues and corresponding eigenfunctions of linear operators associated with a …

We propose a novel cluster-based reduced-order modelling (CROM) strategy for unsteady
flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt …

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of
coherent vortices. Here we show that such coherent vortices can be extracted as clusters of …

Inference of causality is central in nonlinear time series analysis and science in general. A
popular approach to infer causality between two processes is to measure the information …

How do we capture the breadth of behavior in animal movement, from rapid body twitches to
aging? Using high-resolution videos of the nematode worm Caenorhabditis elegans, we …