The emergence of data methods for the sciences in the last decade has
been enabled by the plummeting costs of sensors, computational power,
and data storage. Such vast quantities of data afford us new
opportunities for data-driven discovery, which has been referred to as
the 4th paradigm of scientific discovery. We demonstrate that we can use
emerging, large-scale time-series data from modern sensors to directly
construct, in an adaptive manner, governing equations, even nonlinear
dynamics, that best model the system measured using modern regression
techniques. Recent innovations also allow for handling multi-scale
physics phenomenon and control protocols in an adaptive and robust way.
The overall architecture is equation-free in that the dynamics and
control protocols are discovered directly from data acquired from
sensors. The theory developed is demonstrated on a number of canonical
example problems from physics, biology and engineering.