# Yield Prediction of Winter Wheat at Different Growth Stages Based on Machine Learning
## 1 Introduction  
Accurate crop yield prediction is vital for ensuring food security and promoting sustainable agricultural development [1]. Wheat, one of the world's three major staple crops, constitutes 40% of the global food supply, thus playing a pivotal role in global food security [2]. With the rapid advancement of satellite-based Earth observation technologies, the significance of utilizing remote sensing techniques in the research of large-scale winter wheat yield prediction has become increasingly apparent. Crop yield is influenced by various factors such as weather, climate, soil, and field management practices [3]. Crop yield prediction commonly employs both physical and statistical modeling approaches. Physical models typically utilize crop growth models to simulate the dynamic changes in crop growth and the formation of yield [4, 5]. However, the complexity of parameters required by physical models, including crop varieties, soil types, and climate variables, limits their application in large-scale predictions [6, 7]. Statistical models predict yields by establishing relationships between crop production and inherent crop and environmental characteristics [8]. Remote sensing technology provides the data foundation for the establishment of statistical models [9]. Remote sensing data have the advantages of wide coverage and spectral range, which can capture a variety of crop characteristics, such as monitoring crop growth [10], identifying crop pests and diseases [11, 12], and estimating weed density [13]. The vegetation index (VI), derivedfrom remote sensing data, is more common in crop yield forecasting. VI is more sensitive to vegetation conditions than the original reflectance values and can better capture changes in vegetation conditions, such as crop growth and health status [14]. Temperature and evapotranspiration data can characterize crop health or stress [15]. Remote sensing products within various spectral ranges have been extensively employed in crop yield prediction. These include vegetation indices (VIs) [16; 17; 18], surface reflectance (SR) [19], leaf area index (LAI) [20], fraction of photosynthetically active radiation (FPAR) [21], solar-induced fluorescence (SIF) [9], land surface temperature (LST) [22], and gross primary productivity (GPP) [23], among others. Data-driven statistical models have the advantage of data detection and are widely used for crop yield prediction on a large scale [19; 24; 25]. Although remote sensing data provide type-rich data for crop yield prediction, crop yield, crop biochemical information, and growth condition information are usually nonlinear, and statistical models constructed using only linear relationships are poorly fitted at large scales [26]. Machine learning possesses the ability to discern nonlinear relationships between target and feature variables, effectively aiding quantitative remote sensing research [27]. Currently, various machine learning algorithms, such as ridge regression (RR), Gaussian process regression (GPR), random forest (RF), Lasso regression (Lasso), support vector machine (SVM), and gradient boosting, among others, are extensively applied in crop yield prediction driven by remote sensing data [28; 29; 30; 31; 32]. However, single machine learning algorithms exhibit instability in crop yield prediction. For instance, [PERSON] et al. employed the random forest (RF) algorithm with high-resolution imagery, meteorological variables, and yield data to predict wheat yields in the southeastern region of Australia, where the predictive performance in one planting area significantly lagged behind that of the other two areas [30]. Similarly, [PERSON] et al. utilized remote sensing data and climate variables, employing the RF, SVM, and Lasso algorithms for yield prediction in winter wheat planting areas in China, revealing substantial disparities in the predictive accuracy among the three machine learning algorithms [33].