  We develop a deep learning model to predict traffic flows. The main
contribution is development of an architecture that combines a linear model
that is fitted using $\ell_1$ regularization and a sequence of $\tanh$ layers.
The challenge of predicting traffic flows are the sharp nonlinearities due to
transitions between free flow, breakdown, recovery and congestion. We show that
deep learning architectures can capture these nonlinear spatio-temporal
effects. The first layer identifies spatio-temporal relations among predictors
and other layers model nonlinear relations. We illustrate our methodology on
road sensor data from Interstate I-55 and predict traffic flows during two
special events; a Chicago Bears football game and an extreme snowstorm event.
Both cases have sharp traffic flow regime changes, occurring very suddenly, and
we show how deep learning provides precise short term traffic flow predictions.
