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

2025-06-30

AI Summary

Existing traffic modeling approaches—such as sensor-based forecasting, reinforcement learning, classical optimization, and demand modeling—are fragmented and lack a unified framework supporting cross-module gradient optimization, multi-dimensional and multi-modal joint analysis, and large-scale deployment. This paper proposes Flow-Through Tensors (FTT), a tensor-based unified computational graph architecture that jointly models traffic flow, route choice, and travel time. Its key contributions are: (1) a differentiable unified mathematical structure enabling end-to-end gradient propagation; (2) fine-grained spatiotemporal and demographic joint analysis; and (3) efficient tensor decomposition ensuring real-time computation on million-node networks. Experiments demonstrate that FTT significantly improves collaborative optimization efficiency and control responsiveness while strictly satisfying physical constraints.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Learning to Search
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile 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.

Problem

• Unifies isolated transportation modeling methods into one framework
• Enables gradient-based optimization across diverse network elements
• Supports scalable real-time control for multi-modal transport systems

Innovation

• Unified computational graph for multi-layer networks
• Gradient-based optimization across modeling elements
• Tensor decomposition for large-scale applications