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 …

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 …

Progress in combustion science and engineering has led to the generation of large amounts
of data from large-scale simulations, high-resolution experiments, and sensors. This corpus …

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

While there is currently a lot of enthusiasm about “big data”, useful data is usually “small”
and expensive to acquire. In this paper, we present a new paradigm of learning partial …

We propose a sparse regression method capable of discovering the governing partial
differential equation (s) of a given system by time series measurements in the spatial …

We put forth a deep learning approach for discovering nonlinear partial differential
equations from scattered and potentially noisy observations in space and time. Specifically …

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 …