  The intersection of machine learning and dynamical systems has generated
considerable interest recently. Neural Ordinary Differential Equations (NODEs)
represent a rich overlap between these fields. In this paper, we develop a
continuous time neural network approach based on Delay Differential Equations
(DDEs). Our model uses the adjoint sensitivity method to learn the model
parameters and delay directly from data. Our approach is inspired by that of
NODEs and extends earlier neural DDE models, which have assumed that the value
of the delay is known a priori. We perform a sensitivity analysis on our
proposed approach and demonstrate its ability to learn DDE parameters from
benchmark systems. We conclude our discussion with potential future directions
and applications.
