Flow-through tensors: A unified computational graph architecture for multi-layer transportation network optimization

Modern transportation network modeling increasingly involves the integration of diverse methodologies – including sensor-based forecasting, reinforcement learning , classical flow optimization, and demand modeling – that have traditionally been developed in isolation. This paper introduces Flow Through Tensors (FTT), a unified computational graph architecture that connects origin destination flows, path probabilities, and link travel times as interconnected tensors. Our framework makes three key contributions: first, it establishes a consistent mathematical structure that enables gradient-based optimization across previously separate modeling elements; second, it supports multidimensional analysis of traffic patterns over time, space, and user groups with precise quantification of system efficiency ; third, it implements tensor decomposition techniques that maintain computational tractability for large scale applications. These innovations collectively enable real time control strategies , efficient coordination between multiple transportation modes and operators, and rigorous enforcement of physical network constraints. The FTT framework bridges the gap between theoretical transportation models and practical deployment needs, providing a foundation for next generation integrated mobility systems.