A common way to represent a system's dynamics is to specify how the state evolves in time.
An alternative viewpoint is to specify how functions of the state evolve in time. This evolution …

In many branches of materials science it is now routine to generate data sets of such large
size and dimensionality that conventional methods of analysis fail. Paradigms and tools from …

This paper deals with an extension of dynamic mode decomposition (DMD), which is
appropriate to treat general periodic and quasi-periodic dynamics, and transients decaying …

The prediction of extreme events, from avalanches and droughts to tsunamis and epidemics,
depends on the formulation and analysis of relevant, complex dynamical systems. Such …

In this report, we analyze historical and forecast infections for COVID-19 death based on
Reduced-Space Gaussian Process Regression associated to chaotic Dynamical Systems …

We develop a framework for dimension reduction, mode decomposition, and nonparametric
forecasting of data generated by ergodic dynamical systems. This framework is based on a …

Modern generative machine learning models are able to create realistic outputs far beyond
their training data, such as photorealistic artwork, accurate protein structures or …

Transfer operators such as the Perron–Frobenius or Koopman operator play an important
role in the global analysis of complex dynamical systems. The eigenfunctions of these …

The Koopman operator induced by a dynamical system is inherently linear and provides an
alternate method of studying many properties of the system, including attractor …

Abstract Model reduction methods aim to describe complex dynamic phenomena using only
relevant dynamical variables, decreasing computational cost, and potentially highlighting …