_applied sciences_  
_Article_  
Dynamic Spatio-Temporal Adaptive Graph Convolutional Recurrent Networks for Vacant Parking Space Prediction  
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Footnote 10: foot  
people often choose to park their vehicles in another parking lot within a tolerable distance from the destination. However, previous VPS prediction methods mainly focused on the time dependency of parking data, neglecting the spatial dependencies among parking lots. In recent years, graph neural networks have been widely used in traffic prediction due to their ability to capture spatial correlations among network nodes [6]. The distribution of parking lots in road networks is typically non-Euclidean, and graph neural networks have advantages in handling non-Euclidean structured data. To model the complex spatio-temporal correlations between multiple parking lots, we propose a dynamic spatio-temporal adaptive graph convolutional recursive network (DSTAGCRN) for predicting available parking spaces in parking lots. In contrast to previous methods, DSTAGCRN considers hidden dependencies between different parking lots from both periodic and spatial perspectives. Specifically, we decompose the parking history data into trend and seasonal components as inputs using data decomposition. We combine daily and weekly information with node embeddings using a dynamic parameter-learning module (DPLM) to generate dynamic adaptive graphs. We design a parameter-learning graph convolutional recursive module (PLGCRM) that integrates gated recurrent units (GRUs) and the DPLM to infer the spatio-temporal dependencies at each time step. Meanwhile, we use a multihead attention mechanism module to automatically allocate relatively more attention to valuable information, enabling more effective predictions of parking availability. Under our improvement, the proposed dynamic spatio-temporal adaptive graph convolutional recursive network (DSTAGCRN) method has the following main advantages compared with existing methods:  
1. Dynamic Graph Generation  
Existing methods mostly rely on static predefined graphs to model spatial dependencies between parking lots, such as ASTGCN and AGCRN. These static images cannot capture the dynamic relationship between parking lots. Our DSTAGCRN method utilizes a dynamic parameter-learning module (DPLM) to combine daily and weekly information to generate dynamic graphs, thereby better capturing the implicit dependency relationships between parking lots over time. 2. Spatio-temporal Feature Fusion  
Traditional methods, such as LSTM and DCRNN, mainly focus on temporal dependencies while ignoring spatial correlations between parking lots. Our method utilizes a parameter-learning graph convolutional recursive module (PLGCRM), combined with a multihead attention mechanism, to not only capture temporal dependencies but also effectively integrate temporal and spatial dependencies, making our model more robust  
Figure 1: Schematic diagram of hidden relationships in multiple parking lots. and accurate when facing complex spatio-temporal data and improving the prediction accuracy of the model. (3) Dynamic Adaptive Ability  
Due to the functional role of dynamic graphs, our model can automatically adjust weights based on real-time changes in parking lot data, thereby better reflecting the dynamic spatial correlation between different parking lots. This dynamic adaptive ability enables our model to maintain high predictive performance when facing different time periods and spatial layouts. In addition, we have validated the proposed DSTAGCRN model on various parking lot datasets of different scales and characteristics, such as Zurich, Guangzhou, and Singapore, to demonstrate its strong applicability and scalability and its ability to adapt to different parking lot network scenarios. The rest of this paper is organized as follows: Section 2 provides a brief review of related work.