  Deep neural networks can be powerful tools, but require careful
application-specific design to ensure that the most informative relationships
in the data are learnable. In this paper, we apply deep neural networks to the
nonlinear spatiotemporal physics problem of vehicle traffic dynamics. We
consider problems of estimating macroscopic quantities (e.g., the queue at an
intersection) at a lane level. First-principles modeling at the lane scale has
been a challenge due to complexities in modeling social behaviors like lane
changes, and those behaviors' resultant macro-scale effects. Following domain
knowledge that upstream/downstream lanes and neighboring lanes affect each
others' traffic flows in distinct ways, we apply a form of neural attention
that allows the neural network layers to aggregate information from different
lanes in different manners. Using a microscopic traffic simulator as a testbed,
we obtain results showing that an attentional neural network model can use
information from nearby lanes to improve predictions, and, that explicitly
encoding the lane-to-lane relationship types significantly improves
performance. We also demonstrate the transfer of our learned neural network to
a more complex road network, discuss how its performance degradation may be
attributable to new traffic behaviors induced by increased topological
complexity, and motivate learning dynamics models from many road network
topologies.
