## 1 Introduction  
Crop yield prediction [1] refers to giving the average yield of a particular crop in an area before its crop is harvested. Crop yield prediction is essential for tasks like determining the optimal profile of crops to plant, allocating government resources, effective planning and preparation of aid distribution, and decision making about imports and exports in more commercialized systems and is becoming more important because of the growing concern about food security under the impact of the Russian-Ukrainian War. Based on the development of space satellite technology, remote sensing data are widely used for agricultural applications. The reason for its success is due to large global and temporal availability and easy accessibility. Other traditional methods are based on statistical data that rely heavily on manpower to estimate crop yields based on many characteristics. The labor cost is higher, and the timeliness is poor. However, the characteristics of changes in weather, environment, and other factors can be reflected in remote sensing data captured at different time periods. Therefore, crop yield estimation based on remote sensing data is fast, timely, and has strong application prospects. This is also the starting point of the research content of this article. However, there are many challenges for crop yield prediction based on remote sensing data. Many factors that affect crop yield are shown in Figure 1. Among the factors that can be obtained from remote sensing data are the land temperature and growth of the crop in the area where the crop is grown. However, some factors are still unavailable through remote sensing data, which makes the prediction of crop yield using remote sensing data a challenging problem. Thus, a powerful method is needed to achieve a satisfactory result. Deep learning-based algorithms [2; 3] have shown excellent performance in many fields, and currently, they have become the predominant method in crop prediction. But there are also some difficulties in using deep-learning methods for crop yield estimation:  
1. The inconsistency of the input data's dimensions. The input to a typical crop yield prediction task is a satellite image of a specific region, such as a county. The size of this area can vary greatly. However, the deep-learning method requires that the dimensions of the input data be fixed. Most previous studies have avoided dealing with the full spatiotemporal data directly through various dimensionality reduction techniques. Therefore, a feature embedding method is needed that can map input data with different dimensions to a fixed dimension. 2. Methods with time series processing capabilities are required. The growth of crops is a dynamic process that has to be assessed serially. It is essential to design a method capable of modeling crops' long-term growth dynamics. Some research has shown that the accuracy of the results using CNN is better than those using LSTM [1; 2; 3; 4; 5], indicating that the growth dynamics of crops are so complex that it is not feasible to simply apply time series neural networks to crop yield prediction tasks. 3. Lack of labeled data. Remote sensing data [6; 7] are widely available at a relatively low cost. The scarcity of labeled training data becomes an even more severe issue for deep-learning models that deal with high-dimensional data. However, crop yield data are relatively scarce. For example, crop yield data in the United States are more detailed, while in other regions, especially in developing countries, data are less available and at a coarser granularity (only accurate to the provincial administrative area). In this paper, we propose a crop yield prediction method that uses a 3D convolutional neural network with dimension reduction and metric learning. The proposed method is evaluated on county-level soybean yield prediction in the United States, and the experi  
Figure 1: Graphical analysis of factors affecting crop yield. mental results show the effectiveness of the proposed method.