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 However, this approach is highly dependent on the existing prior matrix, which may be outdated.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.

翻译：起点-终点（OD）矩阵的估计是智能交通系统（ITS）的一个关键方面。它涉及通过回归当前观测数据（如路段交通流量，例如利用最小二乘法）来调整初始OD矩阵。然而，OD估计问题缺乏足够的约束条件，在数学上属于欠定问题。为缓解该问题，部分研究者将先验OD矩阵作为回归目标引入，以提供更多结构性约束。但该方法高度依赖现有先验矩阵，而后者可能已经过时。另有研究者通过传感器数据（如车辆轨迹和速度）添加结构性约束，这类数据能够实时反映更具时效性的结构性约束。我们提出的方法融合了深度学习与数值优化算法，用于推断矩阵结构并指导数值优化过程。该方案结合了深度学习与数值优化算法的双重优势。神经网络（NN）通过学习从探测车流量中推断结构性约束，消除了对先验信息的依赖并实现实时性能。此外，由于神经网络的泛化能力，该方法在工程应用中具有经济性。我们通过在大型合成数据集上的测试验证了该方法的良好泛化性能，随后在真实交通数据上检验了方法的稳定性。实验证实了神经网络与数值优化相结合的优势。