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

In this work, we demonstrate how physical principles—such as symmetries, invariances and
conservation laws—can be integrated into the dynamic mode decomposition (DMD). DMD is …

This review presents a modern perspective on dynamical systems in the context of current
goals and open challenges. In particular, our review focuses on the key challenges of …

Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of
reduced-order models for a variety of scientific and engineering tasks. However, it is …

The dynamic mode decomposition (DMD) is a powerful data-driven modeling technique that
reveals coherent spatiotemporal patterns from dynamical system snapshot observations …

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to
understand and describe their behavior. However, there is a scarcity of plasma models of …

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 …

Dynamic mode decomposition (DMD) provides a regression framework for adaptively
learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal …

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal
patterns from multi-dimensional time series, and it has been used successfully in a wide …

The advent of data-driven/machine-learning based methods and the increase in data
available from high-fidelity simulations and experiments has opened new pathways toward …