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 …

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

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

Physics is a field of science that has traditionally used the scientific method to answer
questions about why natural phenomena occur and to make testable models that explain the …

This review discusses Operator Inference, a nonintrusive reduced modeling approach that
incorporates physical governing equations by defining a structured polynomial form for the …

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

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 …

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

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 …