## 3 FINM Prediction Model
### GRU Module  
As shown in Figure 3, although the direct modification of the GRU structure may not always reflect significant novelty, the GRU, as a lightweight recurrent neural network variant, still shows a strong time-dependent capture ability when processing sequential data such as passenger flow data. As shown in this Figure, the GRU achieves the effective modeling of complex time series data through its two core components of the reset gate and update gate. The reset gate plays a key role in determining the retention or discarding of past information in the GRU. When the reset door chooses to retain the past information, this implies that the past passenger flow has a significant impact on the future passenger flow; when it chooses to discard past information, this indicates that future traffic is less dependent on past traffic. This mechanism enables the GRU to flexibly handle long-term and short-term dependencies in time series data. The update gate indicates how much of the current state is a copy of the previous state, allowing the GRU to retain relevant past information to influence future predictions. For example, in the case of a steady increase in passenger traffic, the update door may choose to carry information about these rising trends forward to more accurately predict future passenger traffic. GRU neural networks are composed of an input layer, hidden layer, and output layer.  
The hidden layer is the core of a GRU and includes two key components: the update gate and reset gate. For a given passenger flow input matrix, the corresponding hidden layer memory information can be calculated by the following formula:  
\[h_{t}=GRU(x_{t},h_{t-1}) \tag{12}\]  
Here, \(h_{t}\) represents the memory information of the passenger flow obtained by the GRU neural networks in the \(t\) time interval, and \(x_{t}\) represents the passenger flow input in  
Figure 3: GRU model structure diagram.  
the \(t\) time interval. In the \(a\) time interval, the outputs of the update gate and reset gate of the passenger flow obtained by the GRU neural networks are \(z_{a}\) and \(r_{a}\), respectively; that is,  
\[z_{a}=\sigma_{Z}[\omega_{Z}(h_{a},x_{a})+b_{Z}] \tag{13}\]  
\[r_{a}=\sigma_{R}[\omega_{R}(h_{a},x_{a})+b_{R}] \tag{14}\]  
In the formula, \(\sigma_{Z}\) and \(\sigma_{R}\) are the activation functions selected for the update gate and the reset gate, respectively; \(\omega_{Z}\) and \(\omega_{R}\) are the weights selected for the update door and the reset door, respectively; and \(b_{Z}\) and \(b_{R}\) are the bias vectors selected for the update gate and the reset gate, respectively.  
Among them, \(\sigma\) represents the activation function, \(W_{z}\) and \(W_{r}\) are the weight matrices of the update gate and the reset gate, respectively, and \(b_{z}\) and \(b_{r}\) are the bias vectors of the update gate and the reset gate, respectively.  
\(z_{a}\) can be calculated based on \(r_{a}\) and \(\overline{h}_{a+1}\); that is,  
\[\overline{h}_{a+1}=tanh\Big{[}\omega_{\overline{h}_{a+1}}(h_{a}r_{a+1},x_{a+1 })+b_{\overline{h}_{a+1}}+y_{GRU}(a+1)\Big{]} \tag{15}\]  
In the formula, \(\overline{h}_{a+1}\) is the information written to the current candidate set when the reset door controls the previous state; \(\omega_{\overline{h}_{a+1}}\) and \(b_{\overline{h}_{a+1}}\) are the selected weights and bias vectors when calculating \(a+1\), respectively.  
The memory information of the hidden layer is input into the fully connected layer to obtain the passenger flow prediction value \(y_{GRU}(a+1)\) of the GRU neural networks in the Eth time interval; that is,  
\[y_{GRU}(a+1)=\sigma_{GRU}\Big{(}\omega_{GRU}\overline{h}_{a+1}+b_{GRU}\Big{)} \tag{16}\]  
In the formula, \(\sigma_{GRU}\), \(\omega_{GRU}\), and \(b_{GRU}\) are the activation function, weight, and para-noid vector selected by the full connection layer of GRU neural networks, respectively.