Flow-Through Tensors: A Unified Computational Graph Architecture for Multi-Layer Transportation Network Optimization

TL;DR

Flow Through Tensors (FTT) introduces a unified tensor-based framework for multi-layer transportation network optimization, enabling gradient optimization, multidimensional analysis, and scalable real-time control for integrated mobility systems.

Contribution

It presents a novel tensor-based architecture that unifies diverse transportation modeling elements and supports scalable, real-time, multi-modal network optimization.

Findings

Enables gradient-based optimization across transportation models

Supports multidimensional traffic analysis over time, space, and user groups

Maintains computational efficiency for large-scale applications

Abstract

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.