Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

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

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 …

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 …

Soft robots promise improved safety and capability over rigid robots when deployed near
humans or in complex, delicate, and dynamic environments. However, infinite degrees of …

In a paper by Willems et al., it was shown that persistently exciting data can be used to
represent the input-output behavior of a linear system. Based on this fundamental result, we …

In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

This paper presents a class of linear predictors for nonlinear controlled dynamical systems.
The basic idea is to lift (or embed) the nonlinear dynamics into a higher dimensional space …

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 …