  This paper introduces RACER, the Rational Artificial Intelligence
Car-following model Enhanced by Reality, a cutting-edge deep learning
car-following model, that satisfies partial derivative constraints, designed to
predict Adaptive Cruise Control (ACC) driving behavior while staying
theoretically feasible. Unlike conventional models, RACER effectively
integrates Rational Driving Constraints (RDCs), crucial tenets of actual
driving, resulting in strikingly accurate and realistic predictions. Against
established models like the Optimal Velocity Relative Velocity (OVRV), a
car-following Neural Network (NN), and a car-following Physics-Informed Neural
Network (PINN), RACER excels across key metrics, such as acceleration,
velocity, and spacing. Notably, it displays a perfect adherence to the RDCs,
registering zero violations, in stark contrast to other models. This study
highlights the immense value of incorporating physical constraints within AI
models, especially for augmenting safety measures in transportation. It also
paves the way for future research to test these models against human driving
data, with the potential to guide safer and more rational driving behavior. The
versatility of the proposed model, including its potential to incorporate
additional derivative constraints and broader architectural applications,
enhances its appeal and broadens its impact within the scientific community.
