# Time Series Prediction of Sea Surface Temperature Based on an Adaptive Graph Learning Neural Model
## 2 Materials and Methods
### Time Convolution Module  
The time convolution module contained in the AGLN model proposed in this paper mainly adopts a gated structure and dilated convolution. The gated structure extracts multiple time patterns from the data by adopting multiple convolution modes in each convolution layer so as to effectively control the information flow. By controlling the expansion coefficient, dilatation convolution can enable the model to process longer time series in SST prediction tasks so as to better mine the hidden time correlation of SST data. Figure 2 is the structural schematic diagram of the time convolution module. We design four one-dimensional convolution filters of different sizes as the initial layer of the time convolution module, which can extract the sequence patterns contained in the SST time series data. Then, the tangent hyperbolic activation function, sigmoid activation function, and a gating device are used to control the amount of information transmitted to the downstream task. First of all, in order to simultaneously capture the long and short term signal patterns in SST data, we consider using multiple filters of different sizes to form an initial dilated convolution layer. It is worth noting that we need to choose the appropriate filter size to cover several inherent periods of the time series, such as 3, 7, 9, and 30. According to the periodicity of SST data changes, four filters with sizes of \(1\times 2\), \(1\times 3\), \(1\times 6\) and \(1\times 7\) are selected as a set of standard extended one-dimensional expansion convolution layers. Secondly, in order to enable the model to better deal with long time series data in SST prediction tasks, we need to select an appropriate expansion coefficient. In standard convolutional networks, the field of view increases with the network depth and the number of convolutional kernels. However, SST time series prediction needs to deal with a large field of vision. If we use standard convolution, we have to design a very deep network or a very large filter, which leads to an explosion in model complexity and computation cost. Therefore, in order to avoid such a situation, we use the expansion coefficient \(dn\) to increase the field of view and reduce the computational complexity of the model by changing the input down-sampling frequency. For example, when the expansion coefficient \(dn\) is one, the field size \(V\) of the dilated convolutional network can be calculated by Formula (6). \[V=\frac{(k-1)\Big{(}q^{d}-1\Big{)}}{(q-1)}+1 \tag{6}\]  
where \(V\) is the size of the field of vision of the convolutional network, \(d\) is the depth of the convolutional network, \(k\) is the size of the convolution kernel or the size of the filter, and \(q\) is the growth rate of the expansion coefficient, \(q>1\). As can be seen from Formula (6), in the case of the same number of deep convolution kernels in the network, compared with the standard convolution field with linear growth, the field of field of empty convolution can grow exponentially with the depth of the  
Figure 2: Structure diagram of temporal convolution layer. Tanh and sigmoid denote the tangent hyperbolic activation function and sigmoid activation function, respectively. network. In this way, a longer time series pattern can be captured by processing a larger field. According to the above principle, the initial output of the expansion convolution layer can be calculated by Formula (8). \[X\times f_{1\times k}(t)=\sum_{s=0}^{k-1}(s)X(t-dn\times s) \tag{7}\]  
\[Z=\text{concat}(X\times f_{1\times 2},X\times f_{1\times 3},X\times f_{1\times 6 },X\times f_{1\times 7}) \tag{8}\]  
where \(X\in R^{T}\) is the one-dimensional sequence input, \(s\) is the step size, \(t\) is the time, \(dn\) is the expansion coefficient, and \(f_{1\times 2}\), \(f_{1\times 3}\), \(f_{1\times 6}\), and \(f_{1\times 7}\) are four filters of different sizes. The module truncates the output of the four filters to the same length as the largest filter and then connects a set of filters across the channel dimension to output \(Z\).