# Logistics Transportation Vehicle Supply Forecasting Based on Improved Informer Modeling
## 3 Problem Description and Model Design
### Improved Informer Modeling
#### 3.3.2 Spatiotemporal Convolutional Network to Extract Spatiotemporal Features  
The concatenated features are fed into the Informer model, with model parameters configured to accommodate the concatenated spatiotemporal data, including the sizes of the encoder and decoder, the attention mechanism, and the sequence length. This setup aims to further enhance the accuracy and fitting capability of time series predictions. As illustrated in Figure 3, this paper proposes a spatiotemporal convolutional network (STCN module) that applies spatiotemporal convolution to the output values of the Informer model's decoder, facilitating the extraction of spatiotemporal features from the data. The STCN module comprises four main convolutional layers, each designed to extract features across different spatiotemporal dimensions.  
Figure 3: Spatiotemporal convolutional network (STCN module).  
Figure 2: Position encoding.  
The local spatial convolutional layer (st_region_convs) employs a standard convolutional kernel to capture the spatial information of the domain around each data point. To maintain the consistency of spatial dimensions, the inputs and outputs apply a padding strategy that sets the padding size to (1, 1) to extract local spatial features. Let \(X\) be the input feature matrix \(X\in R^{H\times W\times C}\), where \(H,W\), and \(C\) denote the height, width, and number of channels, respectively, and the convolution kernel \(K_{s}\) using \(3\times 3\), where the st_region_convs layer is represented as shown in Equation (12). Immediately after that, the spatial feature extraction convolutional layer (st_pair_t_convs) and temporal feature extraction convolutional layer (st_pair_n_convs) are set up to optimize for spatial and temporal dimensions, respectively. The st_pair_t_convs layer uses a convolution kernel of \(1\times 3\) that focuses on capturing the temporal continuum without changing the spatial dimensions and applies a convolution, maintaining a single length in the spatial dimension, helping in understanding the dynamics of the time series in more detail, as shown in Equations (13) and (14). The st_pair_n_convs layer employs a convolution kernel of \(3\times 1\), aiming to strengthen the spatial relationships within a single time step and enhance the model's understanding of the spatial dynamics by expanding the spatial context, as shown below.  
\[Y_{s}=X*K_{s}+b_{s} \tag{12}\]  
\[Y_{t}=X*K_{t}+b_{t} \tag{13}\]  
\[Y_{n}=X*K_{n}+b_{n} \tag{14}\]  
\(*\) denotes the convolution operation, \(b_{s}\) denotes the bias top, \(Y_{s}\in R^{H\times X\times C}\), \(Y_{t}\in R^{H\times W\times C}\), \(Y_{n}\in R^{H\times W\times C}\), \(K_{s}\in R^{1\times 3\times C}\), and\(K_{n}\in R^{3\times 1\times C}\). To synthesize the features extracted from different convolutional layers and reduce the feature dimensions, a feature compression convolutional layer (st_condense) is designed, which uses a convolutional kernel of \(1\times 1\) to fuse the features of the three aforementioned convolutional layers and map the features to a lower dimensionality space, realizing the compression and integration of the features, reducing the computational complexity, and retaining key spatiotemporal information, as shown below.  
\[Y_{c}=(Y_{s}\oplus Y_{t}\oplus Y_{n})*K_{c}+b_{c} \tag{15}\]  
\(\oplus\) denotes the feature splicing operation and \(Y_{c}\in R^{H\times W\times C}\) is the compressed output feature matrix. In this section, through the spatiotemporal convolutional network design, the spatiotemporal features are effectively extracted and fused while keeping the spatial structure of the time series data unchanged, which provides an informative and computationally efficient feature representation for the subsequent time series prediction task.