# Energy Consumption Prediction for Drilling Pumps Based on a Long Short-Term Memory Attention Method
## 2 Materials and Methods  
The Long Short-Term Memory (LSTM) network, as illustrated in Figure 1, is designed to address the limitations of traditional Recurrent Neural Networks (RNNs) in handling long-term dependencies and mitigating the issues of vanishing and exploding gradients. The LSTM cell is the fundamental building block of the LSTM network, featuring a unique internal structure that incorporates three key gating mechanisms: the input gate, the forget gate, and the output gate. These gates regulate the flow of information, enabling the model to effectively capture long-term temporal dependencies in sequential data. The following section provides a detailed explanation of the components and functioning of the LSTM network, as depicted in the diagram. The forget gate \(\mathrm{f_{t}}\) determines the extent to which information from the previous cell state \(\mathrm{C_{t-1}}\) should be retained or discarded. It takes the hidden state from the previous time step \(\mathrm{h_{t-1}}\) and the current input \(\mathrm{x_{t}}\) as inputs and computes a forget factor, which ranges between 0 and 1, where 0 indicates complete forgetting and 1 indicates complete  
Figure 1: The structure of the LSTM. retention of the information. This operation is represented in section 1 of the Figure 1. The computation is defined by the following equation:  
\[f_{t}=\sigma(W_{f}\cdot[h_{t-1},x_{t}]+b_{f}) \tag{1}\]  
The input gate \(i_{t}\) controls how much of the new information \(x_{t}\) should be updated in the cell state \(C_{t}\). It consists of two parts: the input gate and the candidate cell state. The input gate, regulated by a sigmoid function, determines the significance of the current input, while the candidate cell state, generated by a tanh function, creates new information \(\widetilde{C}_{t}\) to be potentially added to the cell state. This process is illustrated in section 2 of the Figure 1. The equations for the input gate are as follows:  
\[i_{t}=\sigma(W_{i}\cdot[h_{t-1},x_{t}]+b_{i}) \tag{2}\] \[\widetilde{C}_{t}=\tan h(W_{C}\cdot[h_{t-1},x_{t}]+b_{C})\]  
The cell state \(C_{t}\) is the core component of the LSTM cell, maintaining the memory of the network. The cell state is updated by combining the previous cell state \(C_{t-1}\) and the current candidate cell state \(\widetilde{C}_{t}\), weighted by the forget gate and input gate, respectively. This step is depicted in section 3 of the Figure 1. The cell state update is governed by the following equation:  
\[C_{t}=f_{t}\cdot C_{t-1}+i_{t}\cdot\widetilde{C}_{t} \tag{3}\]  
The output gate \(o_{t}\) determines the value of the hidden state \(h_{t}\) for the current time step, which is subsequently used as input for the next time step. The output gate applies a sigmoid function to control the amount of information from the cell state that is passed to the hidden state. This operation is shown in section 4 of the Figure 1. The output from the hidden state is modulated by the tanh of the updated cell state \(C_{t}\). The equations for the output gate are as follows:  
\[o_{t}=\sigma(W_{o}\cdot[h_{t-1},x_{t}]+b_{o}) \tag{4}\] Figure 1.0  
LSTM networks are highly effective for predicting drilling pump energy consumption due to their ability to capture the temporal dependencies inherent in such data. By leveraging its gated architecture, an LSTM can accurately model the sequential patterns and complex relationships between various operational parameters and energy usage. As illustrated in Figure 2, the attention mechanism is a neural network architecture designed to effectively capture important information within data. It has been widely applied in various fields such as natural language processing and computer vision. The core idea of the attention mechanism is to dynamically adjust the importance of different elements in the input sequence by calculating the similarity between them. The figure depicts the structure of the Scaled Dot-Product Attention mechanism and its computation process.