Algorithm 1 Proposed BiLSTM-GRU with Attention Mechanism

Input: Sequential input data $X=\{x_1,x_2,\dots ,x_T\}$, where each $x_t$ is a feature vector at time t

Output: Predicted output sequence $\widehat{y}=\{y_1,y_2,\dots ,y_T\}$ after applying the BiLSTM-GRU model with attention

1:Initialization: Initialize model weights and biases: $W_{\mathrm{lstm}}$, $U_{\mathrm{lstm}}$, $b_{\mathrm{lstm}}$, $W_{\mathrm{a}}$, $b_{\mathrm{a}}$, $W_{\mathrm{gru}}$, $U_{\mathrm{gru}}$, $b_{\mathrm{gru}}$, $W^{\mathrm{dense}}$, $b^{\mathrm{dense}}$  2:Initialize hidden states and cell states: $h_t^{\to }$, $h_t^{\leftarrow }$, $c_t^{\to }$, $c_t^{\leftarrow }$, $h_{t-1}^{\mathrm{GRU}}$  3:Bidirectional LSTM Layer:  4:for  $(t=0,1,\dots ,T-1)$  do  5: Forward LSTM step: Compute forward hidden state $h_t^{\to }$ and cell state $c_t^{\to }$  6: Backward LSTM step: Compute backward hidden state $h_t^{\leftarrow }$ and cell state $c_t^{\leftarrow }$  7: Concatenate forward and backward hidden states: $H_{\mathrm{BiLSTM}}\left[t\right]$  8:end for  9:Attention Mechanism: 10:for $(t=0,1,\dots ,T-1)$ do 11: Compute attention weights for each time step: $e_t=tanh(W_a{H}_{\mathrm{BiLSTM}}\left[t\right]+b_a)$ 12: Normalize attention weights: ${\alpha }_t=\mathrm{softmax}\left(e_t\right)$ 13: Compute context vector as a weighted sum of hidden states: $c_t={\sum }_{i=0}^{T-1}{\alpha }_i·H_{\mathrm{BiLSTM}}{\left[t\right]}_i$ 14: Concatenate context vector with current BiLSTM hidden state: $h_{\mathrm{att}\_t}=[c_t;H_{\mathrm{BiLSTM}}\left[t\right]]$ 15:end for 16:Gated Recurrent Unit (GRU) Layer: 17:for $(t=0,1,\dots ,T-1)$ do 18: GRU forward step: Compute update gate $z_t$, reset gate $r_t$, candidate hidden state ${\tilde{h}}_t$ 19: Update hidden state: $h_t^{\mathrm{GRU}}$ using $h_{\mathrm{att}\_t}$ as input 20:end for 21:Dense Layer: 22:Perform linear transformation: $z=h_t^{\mathrm{GRU}}·W^{\mathrm{dense}}+b^{\mathrm{dense}}$ 23:Apply activation function: $y=\mathrm{softmax}\left(z\right)$ 24:Training, Evaluation, and Prediction: 25:Train model using backpropagation and optimization algorithm 26:Evaluate model performance using appropriate metrics 27:Make predictions on new sequential data