  This study aims to discover the governing mathematical expressions of
car-following dynamics from trajectory data directly using deep learning
techniques. We propose an expression exploration framework based on deep
symbolic regression (DSR) integrated with a variable intersection selection
(VIS) method to find variable combinations that encourage interpretable and
parsimonious mathematical expressions. In the exploration learning process, two
penalty terms are added to improve the reward function: (i) a complexity
penalty to regulate the complexity of the explored expressions to be
parsimonious, and (ii) a variable interaction penalty to encourage the
expression exploration to focus on variable combinations that can best describe
the data. We show the performance of the proposed method to learn several
car-following dynamics models and discuss its limitations and future research
directions.
