The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Closed-loop turbulence control is a critical enabler of aerodynamic drag reduction, lift
increase, mixing enhancement, and noise reduction. Current and future applications have …

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 …

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 …

Extracting governing equations from data is a central challenge in many diverse areas of
science and engineering. Data are abundant whereas models often remain elusive, as in …

Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …

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 …