  The success of autonomous systems will depend upon their ability to safely
navigate human-centric environments. This motivates the need for a real-time,
probabilistic forecasting algorithm for pedestrians, cyclists, and other agents
since these predictions will form a necessary step in assessing the risk of any
action. This paper presents a novel approach to probabilistic forecasting for
pedestrians based on weighted sums of ordinary differential equations that are
learned from historical trajectory information within a fixed scene. The
resulting algorithm is embarrassingly parallel and is able to work at real-time
speeds using a naive Python implementation. The quality of predicted locations
of agents generated by the proposed algorithm is validated on a variety of
examples and considerably higher than existing state of the art approaches over
long time horizons.
