In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …

The ongoing rapid expansion of the Word Wide Web (WWW) greatly increases the
information of effective transmission from heterogeneous individuals to various systems …

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

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

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 …

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 …

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

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 …

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 …