  In vehicle trajectory prediction, physics models and data-driven models are
two predominant methodologies. However, each approach presents its own set of
challenges: physics models fall short in predictability, while data-driven
models lack interpretability. Addressing these identified shortcomings, this
paper proposes a novel framework, the Physics-Enhanced Residual Learning (PERL)
model. PERL integrates the strengths of physics-based and data-driven methods
for traffic state prediction. PERL contains a physics model and a residual
learning model. Its prediction is the sum of the physics model result and a
predicted residual as a correction to it. It preserves the interpretability
inherent to physics-based models and has reduced data requirements compared to
data-driven methods. Experiments were conducted using a real-world vehicle
trajectory dataset. We proposed a PERL model, with the Intelligent Driver Model
(IDM) as its physics car-following model and Long Short-Term Memory (LSTM) as
its residual learning model. We compare this PERL model with the physics
car-following model, data-driven model, and other physics-informed neural
network (PINN) models. The result reveals that PERL achieves better prediction
with a small dataset, compared to the physics model, data-driven model, and
PINN model. Second, the PERL model showed faster convergence during training,
offering comparable performance with fewer training samples than the
data-driven model and PINN model. Sensitivity analysis also proves comparable
performance of PERL using another residual learning model and a physics
car-following model.
