## 3 Method  
### Informer Model  
The transformer model based on the self-attention structure was proposed by [PERSON] in 2017 [29]. The transformer model uses the self-attention mechanism rather than the sequential structure of RNNs, which has efficient parallel computing and can capture global information. Compared with RNN models, transformer-based models have superior performance in solving long-sequence time-series forecasting problems [43]. However, traditional transformer-based models need expensive costs of computation and dozens of CPUs owing to the self-attention mechanism and architecture. Therefore, it is unaffordable for the transformer models to solve realistic problems. To overcome the deficiencies of transformer models and improve prediction performance, the Informer model, which can achieve better efficiency and overcome resource consumption, was proposed by [PERSON] et al. [43].  
We present the architecture of the Informer model for rice yield prediction in Figure 2. The Informer model consists of an input layer, two encoder layers, one decoder layer, and an output layer. The canonical self-attention [29] is replaced by the ProbSparse self-attention mechanism in the Informer model. The ProbSparse self-attention can efficiently reduce the time complexity and memory usage. The encoder consists of two identical multihead attention layers formed by combining multiple self-attention. The encoder module is designed to handle longer sequential inputs under memory usage limitations by using the self-attention distilling operation. The self-attention distilling operation can extract dominating attention and reduce the network size sharply, which is beneficial for receiving long-sequence inputs. The decoder used in the Informer model is a standard decoder structure containing a stack of two identical multihead attention layers [29]. Then, the output of the decoder is aggregated into the fully connected layer, and the fully connected layer acquires the final output. The detailed architecture of Informer can be referred to in a study by [PERSON] et al. [43].  
To obtain the best performance of the Informer model, we set the dimension of the model to 512, the number of heads to 8, the dimension of the fully connected layer to 2048, the ProbSparse attention factor to 5, the experiment times to 3, the train epochs to 10, the batch size to 16, the early stopping patience to 3, and the optimizer learning rate to 0.0001. The number of encoder and decoder layers was set to 2 and 1, respectively. The Informer model was implemented using the open-source PyTorch library in Python 3.6.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number of the**} & \multicolumn{2}{c}{**Start Date**} & \multicolumn{2}{c}{**End Date**} \\ \cline{2-5}  & **Normal Year** & **Leap Year** & **Normal Year** & **Leap Year** \\ \hline
1 & 25 May & 24 May & 9 June & 8 June \\
2 & 10 June & 9 June & 25 June & 24 June \\
3 & 26 June & 25 June & 11 July & 10 July \\
4 & 12 July & 11 July & 27 July & 26 July \\
5 & 28 July & 27 July & 12 August & 11 August \\
6 & 13 August & 12 August & 28 August & 27 August \\
7 & 29 August & 28 August & 13 September & 12 September \\
8 & 14 September & 13 September & 29 September & 28 September \\
9 & 30 September & 29 September & 15 October & 14 October \\
10 & 16 October & 15 October & 31 October & 30 October \\
11 & 01 November & 31 October & 16 November & 15 November \\
12 & 17 November & 16 November & 2 December & 1 December \\ \hline \hline \end{tabular}
\end{table}
Table 2: The start dates and end dates of the 12 time intervals.