  The estimation of origin-destination (OD) matrices is a crucial aspect of
Intelligent Transport Systems (ITS). It involves adjusting an initial OD matrix
by regressing the current observations like traffic counts of road sections
(e.g., using least squares). However, the OD estimation problem lacks
sufficient constraints and is mathematically underdetermined. To alleviate this
problem, some researchers incorporate a prior OD matrix as a target in the
regression to provide more structural constraints. However, this approach is
highly dependent on the existing prior matrix, which may be outdated. Others
add structural constraints through sensor data, such as vehicle trajectory and
speed, which can reflect more current structural constraints in real-time. Our
proposed method integrates deep learning and numerical optimization algorithms
to infer matrix structure and guide numerical optimization. This approach
combines the advantages of both deep learning and numerical optimization
algorithms. The neural network(NN) learns to infer structural constraints from
probe traffic flows, eliminating dependence on prior information and providing
real-time performance. Additionally, due to the generalization capability of
NN, this method is economical in engineering. We conducted tests to demonstrate
the good generalization performance of our method on a large-scale synthetic
dataset. Subsequently, we verified the stability of our method on real traffic
data. Our experiments provided confirmation of the benefits of combining NN and
numerical optimization.
