Data-driven
discovery of governing equations and physical laws

Nathan Kutz, University of Washington

Nathan Kutz, University of Washington

Abstract:

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 and PDEs, that best
model the system measured using modern regression and machine
learning techniques. We can also discover nonlinear
embeddings of the dynamics using Koopman theory and deep neural
network architectures. 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.