# Drilling Parameters Multi-Objective Optimization Method Based on PSO-Bi-LSTM
## 2 Materials and Methods  
### Long Short-Term Memory Model  
Long Short-Term Memory (LSTM) [24], a neural network architecture introduced by [PERSON] and [PERSON] in 1997, has become a prominent solution for retaining and utilizing both short- and long-term information. Over the years, LSTM has undergone significant modifications and refinements by researchers such as [PERSON], [PERSON], and others, resulting in a more comprehensive and robust algorithm. These advancements have propelled LSTM to be widely adopted across diverse domains. LSTM addresses a fundamental challenge in recurrent neural networks (RNNs) by effectively capturing dependencies between short-term and long-term information. Unlike traditional RNNs that often struggle with the vanishing gradient problem, LSTM offers a solution that enables the network to learn and propagate information over extended sequences. The key components of LSTM are the cell state (c\({}^{\text{t}}\)) and the hidden state (h\({}^{\text{t}}\)). The cell state evolves relatively slowly throughout the computation process, while the hidden state exhibits dynamic changes. Each node's output, denoted as c\({}^{\text{t}}\), is computed by combining the previous cell state, c\({}^{\text{t}-1}\), with various input signals. In contrast, the hidden state, h\({}^{\text{t}}\), encapsulates the network's output and undergoes substantial transformations. To facilitate effective information flow and memory management, LSTM employs a specialized structure known as a memory cell. This memory cell incorporates three essential gates: the forgetting gate, the input gate, and the output gate. The forget gate determines which information to discard from the cell state at the current time step. It takes the current input and the previous hidden state as inputs and produces a forget gate activation between 0 and 1. This activation determines what information should be selectively forgotten from the cell state. The input gate controls the addition of new information to the cell state at the current time step. It takes the current input and the previous hidden state as inputs and produces an input gate activation between 0 and 1. This activation determines which new information should be added to the cell state. The output gate regulates how much information should be revealed from the cell state at the current time step. It takes the current input and the previous hidden state as inputs and produces an output gate activation between 0 and 1. This activation determines which information from the cell state should be output to the current time step's hidden state for further computations or predictions. The forget gate, input gate, and output gate are implemented using neural network layers with learnable weights. The gate activations are obtained through a series of computations and activation functions applied to the inputs and hidden states. By adjusting the activations of these gates, LSTM can selectively retain, forget, and output information, allowing the network to better capture and utilize important contextual information in long sequences. Figure 1 depicts the specific structural diagram of LSTM, illustrating the arrangement of gates and connections. In the field of petroleum drilling parameter optimization, traditional RNN methods fail to capture the long-term mapping relationships among drilling parameters. During  
Figure 1: The structure of LSTM. backpropagation, the gradients continuously diminish, leading to the loss of drilling information in long sequences and making the model difficult to train. The gated mechanism of LSTM effectively addresses this issue by enabling the network to better utilize gradient information during training. Additionally, due to the progressive nature of drilling information as a temporal and depth-dependent sequence, the performance of traditional RNNs declines as the sequence length increases. In contrast, LSTM, through its controlled gated mechanism, can adapt more effectively to sequences of varying lengths while maintaining satisfactory performance.