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 …

We introduce a data-driven forecasting method for high-dimensional chaotic systems using
long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural …

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

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 …

We establish the convergence of a class of numerical algorithms, known as dynamic mode
decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite …

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 …