# Deep Learning-Driven Bus Short-Term OD Demand Prediction via a Physics-Guided Adaptive Graph Spatio-Temporal Attention Network

## TL;DR

This paper introduces a new deep learning model for predicting bus origin-destination demand using spatiotemporal data and physics-guided mechanisms.

## Contribution

The novel contribution is a physics-guided adaptive graph spatio-temporal attention network (PAG-STAN) that improves prediction accuracy with a masked physics-guided loss function.

## Key findings

- PAG-STAN outperforms other models with reductions of 6.19% in RMSE and 8.20% in WMAPE.
- One-layer BiLSTMs perform better than multi-layer ones in the model architecture.
- The model achieves a 1.13% improvement in R2 compared to suboptimal models.

## Abstract

This study develops a recent model proposed by Zhang et al. to predict bus short-term origin-destination (OD) demand based on a small-scale dataset (i.e., one week’s data per 30 mins’ collecting interval). We distinctively use sole input sequence by introducing a multi-head attention mechanism while simultaneously ensuring prediction accuracy. Extensive experiments demonstrate that one-layer bidirectional LSTMs (BiLSTMs) perform better than multi-layer ones. A modified deep learning model integrating physics-guided mechanisms, adaptive graph convolution, attention networks, and spatiotemporal encoder–decoder is constructed. We retained the original name, i.e., physics-guided adaptive graph spatio-temporal attention network (PAG-STAN) model. The model uses an encoder–decoder architecture, where the encoder captures spatiotemporal correlations via an adaptive graph convolutional LSTM (AGC-LSTM), enhanced by an attention mechanism that adjusts the importance of different spatiotemporal features. The decoder utilizes bidirectional LSTM to reconstruct the periodic patterns and predict the full OD matrix for the next interval. A masked physics-guided loss function, which embeds the quantitative relationship between boarding passenger volume and OD demand, is adopted for training. The Adam optimizer and early stopping technique are used to enhance training efficiency and avoid overfitting. Experimental results show that PAG-STAN outperforms other deep learning models in prediction accuracy. Compared with the suboptimal model, the proposed model achieved reductions of 6.19% in RMSE, 6.59% in MAE, and 8.20% in WMAPE, alongside a 1.13% improvement in R2.