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 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 …

We investigate the problem of learning an evolution equation directly from some given data.
This work develops a learning algorithm to identify the terms in the underlying partial …

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 …

Optimal sensor and actuator placement is an important unsolved problem in control theory.
Nearly every downstream control decision is affected by these sensor and actuator …

Inferring the structure and dynamics of network models is critical to understanding the
functionality and control of complex systems, such as metabolic and regulatory biological …

Identifying governing equations from data is a critical step in the modeling and control of
complex dynamical systems. Here, we investigate the data-driven identification of nonlinear …