Physics-Informed Generative Modeling for Sparse OD Matrix Forecasting: A Dual-Head VAE-GMM Approach With a Single Time Step Input

Abstract

Accurate passenger flow prediction is crucial to the development of efficient public transit systems, enabling optimal resource allocation, dynamic route planning, and robust congestion mitigation. However, forecasting highly sparse origin-destination (OD) matrices remains a persistent challenge due to extreme data overdispersion and the “zero convergence” problem, where models gravitate toward predicting zeros to minimize global error at the expense of edge-level accuracy. Traditional sequential forecasting models often exacerbate these issues by relying on extensive historical data sequences, which compounds memory overhead and limits real-time scalability. In order to address these limitations, this study proposes a novel, compact, physics-informed generative framework (the Dual-Head VAE-GMM) capable of forecasting transit demands using only a single historical time step as input. The proposed architecture incorporates a Gaussian Mixture Model (GMM) latent prior to capture multi-modal mobility regimes and utilizes a dual-head decoder that explicitly decouples binary network topology edge prediction from continuous volume regression. To ensure predictions align with real-world flow dynamics, the model is governed by a composite objective function that integrates physics-informed graph spectral regularizers and domain-aware mass conservation laws into a generalized variational lower bound. Evaluations on a comprehensive smart card dataset from the 748-station Seoul metropolitan subway network indicate that the proposed approach successfully mitigates zero-inflation and performs significantly better than traditional parametric and deep-learning baselines. The model achieves a mean absolute error of under two passengers with an inference latency of about 57 milliseconds for a 60-minute forecasting horizon.