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 domain. The …

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 …

The integration of data and scientific computation is driving a paradigm shift across the
engineering, natural, and physical sciences. Indeed, there exists an unprecedented availability of …

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

It was only a matter of time before deep neural networks (DNNs) – deep learning – made
their mark in turbulence modelling, or more broadly, in the general area of high-dimensional, …

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 …

We develop a new method which extends dynamic mode decomposition (DMD) to incorporate
the effect of control to extract low-order models from high-dimensional, complex systems. …

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

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 …

Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling
and control efforts, providing a tremendous opportunity to extend the reach of model …