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

Aerodynamic modeling plays an important role in multiphysics and design problems, in
addition to experiment and numerical simulation, due to its low-dimensional representation …

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 field of fluid mechanics involves a range of rich and vibrant problems with complex
dynamics stemming from instabilities, nonlinearities, and turbulence. The analysis of these …

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 …

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

This article presents a new method to identify the main patterns describing the flow motion in
complex flows. The algorithm is an extension of the higher-order dynamic mode …

Predictive simulations are essential for applications ranging from weather forecasting to
material design. The veracity of these simulations hinges on their capacity to capture the …

A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of
stationary random processes is presented. As new data becomes available, an incremental …