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. 2025 Jul 28;25(15):4663. doi: 10.3390/s25154663

Algorithm 1 LSTM-based Encoder–Attention–Decoder.

Input: Input sequence $X \in R^{B \times T \times D_{e}}$
Encoder:

1:
$E \leftarrow LinearEncoder (Flatten (X))$ ▹ $(B \times T, D_{r})$
2:
$E \leftarrow Reshape {(E, (B, T, D_{r}))}^{⊺}$ ▹ $(T, B, D_{r})$
3:
Initialize $h_{0} \in R^{L \times B \times H}$
4:
$(O_{e}, h_{1}) \leftarrow LSTM (E, h_{0})$ ▹ $(T, B, H)$

Attention:

5:
$A \leftarrow O_{e}^{⊺}$ ▹ $(B, T, H)$
6:
$Q, K, V \leftarrow A \cdot W_{q}, A \cdot W_{k}, A \cdot W_{v}$ ▹ $W_{\cdot} \in R^{H \times d}$
7:
$Attn \leftarrow softmax (\frac{Q K^{⊤}}{\sqrt{d}}) V$ ▹ $(B, T, H)$
8:
$S \leftarrow {Attn}^{⊺}$ ▹ $(T, B, H)$

Decoder:

9:
$O_{d} \leftarrow LSTMDecoder (S)$ ▹ $(T, B, H)$
10:
$Y_{r} \leftarrow LinearDecoder (O_{d})$ ▹ $(T, B, D_{d})$
11:
$Y_{m} \leftarrow MLP (Flatten (S))$

Fusion:

12:
$Y \leftarrow \frac{1}{2} (Y_{r} + Y_{m})$
13:
if use_residual then
14:
$Y \leftarrow Y + X^{⊺}$
15:
end if
16:
$Y \leftarrow Y^{⊺}$ ▹ $(B, T, D_{d})$

Output: Prediction $Y \in R^{B \times T \times D_{d}}$