  This paper proposes and develops a physics-inspired neural network (PiNN) for
learning the parameters of commercially implemented adaptive cruise control
(ACC) systems in automotive industry. To emulate the core functionality of
stock ACC systems, which have proprietary control logic and undisclosed
parameters, the constant time-headway policy (CTHP) is adopted. Leveraging the
multi-layer artificial neural networks as universal approximators, the
developed PiNN serves as a surrogate model for the longitudinal dynamics of
ACC-engaged vehicles, efficiently learning the unknown parameters of the CTHP.
The PiNNs allow the integration of physical laws directly into the learning
process. The ability of the PiNN to infer the unknown ACC parameters is
meticulously assessed using both synthetic and high-fidelity empirical data of
space-gap and relative velocity involving ACC-engaged vehicles in platoon
formation. The results have demonstrated the superior predictive ability of the
proposed PiNN in learning the unknown design parameters of stock ACC systems
from different car manufacturers. The set of ACC model parameters obtained from
the PiNN revealed that the stock ACC systems of the considered vehicles in
three experimental campaigns are neither $\mathcal{L}_2$ nor
$\mathcal{L}_\infty$ string stable.
