  We propose a neural network approach to model general interaction dynamics
and an adjoint based stochastic gradient descent algorithm to calibrate its
parameters. The parameter calibration problem is considered as optimal control
problem that is investigated from a theoretical and numerical point of view. We
prove the existence of optimal controls, derive the corresponding first order
optimality system and formulate a stochastic gradient descent algorithm to
identify parameters for given data sets. To validate the approach we use real
data sets from traffic and crowd dynamics to fit the parameters. The results
are compared to forces corresponding to well-known interaction models such as
the Lighthill-Whitham-Richards model for traffic and the social force model for
crowd motion.
