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

Koopman operators globally linearize nonlinear dynamical systems and their spectral
information is a powerful tool for the analysis and decomposition of nonlinear dynamical …

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

The development of data-informed predictive models for dynamical systems is of
widespread interest in many disciplines. We present a unifying framework for blending …

This paper provides a unifying mean field based framework for the derivation and analysis of
ensemble Kalman methods. Both state estimation and parameter estimation problems are …

Research in modern data-driven dynamical systems is typically focused on the three key
challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode …

Data-driven modeling has become a key building block in computational science and
engineering. However, data that are available in science and engineering are typically …

Enforcing sparse structure within learning has led to significant advances in the field of data-
driven discovery of dynamical systems. However, such methods require access not only to …

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 …

We develop an algebraic framework for sequential data assimilation of partially observed
dynamical systems. In this framework, Bayesian data assimilation is embedded in a …