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 …

Identifying coordinate transformations that make strongly nonlinear dynamics approximately
linear has the potential to enable nonlinear prediction, estimation, and control using linear …

Machine learning (ML) is transforming all areas of science. The complex and time-
consuming calculations in molecular simulations are particularly suitable for an ML …

We consider the frequency domain form of proper orthogonal decomposition (POD), called
spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space …

The Koopman operator is a linear but infinite-dimensional operator that governs the
evolution of scalar observables defined on the state space of an autonomous dynamical …

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