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 …

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 is rapidly advancing, driven by unprecedented volumes of data
from experiments, field measurements, and large-scale simulations at multiple …

In the context of science, the well-known adage" a picture is worth a thousand words" might
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …

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

Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

The discovery of governing equations from scientific data has the potential to transform data-
rich fields that lack well-characterized quantitative descriptions. Advances in sparse …