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

SIMPLE aerodynamic configurations under even modest conditions can exhibit complex
flows with a wide range of temporal and spatial features. It has become common practice in …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and …

The integration of data and scientific computation is driving a paradigm shift across the
engineering, natural, and physical sciences. Indeed, there exists an unprecedented …

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 …

In this work, we explore finite-dimensional linear representations of nonlinear dynamical
systems by restricting the Koopman operator to an invariant subspace spanned by specially …

Spectral decomposition of the Koopman operator is attracting attention as a tool for the
analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular …

In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …

Optimal sensor and actuator placement is an important unsolved problem in control theory.
Nearly every downstream control decision is affected by these sensor and actuator …

Data-driven transformations that reformulate nonlinear systems in a linear framework have
the potential to enable the prediction, estimation, and control of strongly nonlinear dynamics …