# Short-Term Power Load Prediction of VMD-LSTM Based on ISSA Optimization
## 2 Fundamentals of the Model
### Long Short-Term Memory  
Long Short-Term Memory (LSTM) networks were developed to address the challenges of gradient vanishing and gradient explosion that Recurrent Neural Networks (RNNs) confront when processing long sequences. LSTM shares a similar architectural framework with the RNN: the input layer and output layer remain identical to those of the RNN, while the memory cell represents a distinctive structure exclusive to LSTM. The network structure of LSTM is illustrated in Figure 1. The operational principle of the LSTM neural network is elaborated as follows:(1) Forget gate:  
The forget gate integrates contextual information, gradient information derived from the loss function, and historical information to jointly determine the updated long-term memory. This process decides the proportion of key information from the previous time step to be forgotten. The formula is as follows:  
\[f_{t}=\sigma\Big{(}W_{f}\cdot[h_{t-1},x_{t}]+b_{f}\Big{)} \tag{12}\]  
where \(f_{t}\) means the forgetting gate parameter, which affects the proportion of \(C_{t-1}\); \(\sigma\) means the sigmoid function; \(W_{f}\) means the weight matrix of the forget gate; \(h_{t-1}\) means the output of the hidden layer at time step \(t-1\); \(x_{t}\) means the input; and \(b_{f}\) means the bias matrix of the forgetting gate.  
(2) Input gate:  
The input gate governs the amount of new information incorporated into the long-term memory unit. The formula is as follows:  
\[i_{t}=\sigma(W_{i}\cdot[h_{t-1},x_{t}]+b_{i}) \tag{13}\]  
\[\widetilde{C}_{t}=tanh(W_{c}\cdot[h_{t-1},x_{t}]+b_{c}) \tag{14}\]  
\[C_{t}=f_{t}*C_{t-1}+i_{t}*\widetilde{C}_{t} \tag{15}\]  
where \(i_{t}\) is the input gate parameter, serving as the screening factor for new information \(\widetilde{C}_{t}\), \(W_{i}\) is the input gate weight, \(b_{i}\) is the input gate bias matrix, \(tanh\) is the hyperbolic tangent activation function, \(W_{c}\) is the cell state weight, \(b_{c}\) is the bias matrix of the memory cell, \(\widetilde{C}_{t}\) is the input state of the memory cell, \(C_{t-1}\) is the cell state at time step \(t-1\), and \(C_{t}\) is the cell state at the current time step.  
(3) Output gate:  
The output gate extracts the most relevant information for the current time step from the updated long-term information, which is subsequently employed for the prediction at the current time step. The formula is as follows:  
\[O_{t}=\sigma(W_{o}\cdot[h_{t-1},x_{t}]+b_{o}) \tag{16}\]  
\[h_{t}=O_{t}*\tanh(C_{t}) \tag{17}\]  
where \(O_{t}\) is the output gate parameter; \(W_{o}\) is the output gate weight; \(b_{o}\) is the output gate bias matrix; and \(h_{t}\) is the hidden layer output signal at the current moment.  
Given LSTM's capability to correlate past temporal information with current tasks, its consideration of time-series data's temporal correlation, its robust sequential data processing ability, and its excellent nonlinear relationship capturing capacity this paper  
Figure 1: LSTM network structure diagram.  
applies it to load sequence forecasting tasks after VMD and reconstruction. This utilization fully excavates data features to improve the accuracy of short-term power load forecasting.