## 3 Symbol Definitions and Problem Description  
### Symbols and Relevant Definitions  
In this section, we provide an overview of the symbols and relevant definitions used in this paper. The symbols and their meanings are listed in Table 1.  
Time Interval: The temporal scope within the research domain is partitioned into \(T\) time intervals, with minutes as the smallest unit of time.  
Bike-Sharing Static Multi-Graph: Assuming there are \(N\) stations in the research area, the static network of bike-sharing is represented by a graph \(G(V,~{}E,~{}A)\). Nodes \(V=\{v_{1},~{}v_{2},~{}\cdots,~{}v_{N}\}\) represent the set of bike-sharing stations, edges between two nodes \(E=\{e(i,j)|i,j=1,2,\ldots,N\}\) represent the connections between stations, and the adjacency matrix \(A=\{a(i,j)|i,j=1,2,\ldots,N\}\in\mathbb{R}^{N\times N}\) represents the degree of connection between stations. Based on three different location semantic information, the graph \(G\) is assigned different weights, resulting in the static multi-graph \(\mathbf{G}=\left\{G_{dis},G_{this},G_{poi}\right\}\). It includes three types of graphs: distance graph \(G_{dis}(V,\ E,\ A_{dis})\), historical connectivity graph \(G_{his}(V,\ E,\ A_{his})\), and POI Similarity graph \(G_{poi}(V,\ E,\ A_{poi})\).  
Bike-Sharing Dynamic Multi-Graph: Due to resource optimization, bike-sharing managers make irregular adjustments to stations, leading to station additions or closures. Therefore, based on the static multi-graph \(\mathbf{G}\), dynamic graphs are created for each time period to characterize station dynamics. \(\mathbf{G}^{t}\) is used to represent the dynamic multi-graph in each time period, where \(\mathbf{G}^{t}\) includes \(G^{t}_{dis},\ G^{t}_{dis}\) and \(G^{t}_{poi},\ G^{t}_{dis}=\left\{G^{t}_{dis},\ G^{t}_{dis},\ G^{t}_{dis},\ \cdots,\ G^{t}_{dis}\right\}\), \(G^{t}_{his}=\left\{G^{1}_{his},\ G^{2}_{his},\ \cdots,\ G^{t}_{his}\right\}\), \(G^{t}_{poi}=\left\{G^{1}_{poi},\ G^{2}_{poi},\ \cdots,\ G^{t}_{poi}\right\}\), \(t=1,\ 2,\ \cdots,\ T\).  
Bike-Sharing Riding Record: A record of a bike-sharing journey from one station to another, denoted as \(R(SS,\ ES,\ ST,\ ET)\), where \(SS\) represents the start station, \(ES\) represents the end station, \(ST\) represents the start time, and \(ET\) represents the end time.  
Bike-Sharing Flow: The flow of bike-sharing within a time, divided into output flow and input flow, represented by \(X^{O}=\left\{x^{O}_{1},\ x^{O}_{2},\ \cdots,\ x^{O}_{T}\right\}\) and \(X^{I}=\left\{x^{I}_{1},\ x^{I}_{2},\ \cdots,\ x^{I}_{T}\right\}\), respectively. In this research, we focus on predicting bike-sharing demand (output flow), denoted as \(X=\left\{x_{1},\ x_{2},\ \cdots,\ x_{T}\right\}\in\mathbb{R}^{T\times N}\). The demand for shared bicycles within a specific time interval \(t\) can be represented by \(\mathbf{x}_{t}=\left\{x^{1}_{t},\ x^{2}_{t},\ \cdots,\ x^{N}_{t}\right\}\in\mathbb{R}^{N}\), which can be calculated by Formula (1).  
\[\mathbf{x}_{t}=\sum\
olimits_{n=1}^{N}\lvert\{R(SS,\ ES,\ ST,\ ET)|SS=n\wedge ST =t\}\rvert \tag{1}\]  
Confirmed COVID-19 Cases: This study also considers the important external influencing factor of confirmed COVID-19 cases, denoted as \(COV=\left\{\text{cov}_{1},\ \text{cov}_{2},\ \cdots,\ \text{cov}_{D}\right\}\in \mathbb{R}^{D}\), where \(D\) represents the total number of days in the research time frame.  
Time Features: Includes time semantic features for weekdays, weekends, and holidays, represented by \(TF=\left\{tf_{1},\ tf_{2},\ \cdots,\ tf_{D}\right\}\in\mathbb{R}^{D}\).  
Weather Condition: Includes temperature, humidity, wind speed, and atmospheric pressure, represented by \(W=\left\{w_{1},\ w_{2},\ \cdots,\ w_{T}\right\}\in\mathbb{R}^{T}\).