Structured Multi-Kernel Heteroscedastic Gaussian Process for Crop Straw-to-Grain Ratio Prediction and Uncertainty Quantification

Crop straw-to-grain ratio (SGR) estimation underpins regional straw resource assessment, yet national inventories rely on fixed coefficients that ignore structured variation across variety, environment, and phenotype. We introduce a Structured Multi-Kernel Heteroscedastic Gaussian Process (GP) framework that models SGR variation through three additive kernels heuristically motivated by the genotype–environment–phenotype (G+E+P) framework—capturing variety-associated variation, spatially structured variation, and environmental and management covariates—and employs an input-dependent noise model for prediction-specific uncertainty quantification. To prevent information leakage, target encoding and feature scaling are recomputed within each cross-validation fold. Evaluated via internal leave-one-out cross-validation on 80 rice samples (42 varieties, six Chinese provinces), the model achieves R2=0.541 with a prediction interval coverage probability of 0.95. Ablation identifies variety-associated variation as the largest contributor among the modeled factors (ΔR2=−0.024) and the multi-kernel design, by incorporating variety-specific information, substantially improves upon a covariate-only RBF GP (ΔR2=0.103). On point-prediction accuracy, Gradient Boosting achieves R2=0.58, slightly ahead of the Heteroscedastic GP (R2=0.54), underscoring that the primary advantage of the GP lies in its input-dependent uncertainty quantification. However, leave-one-county-out validation yields R2≈0 (with σ escalating to 24.4), confirming that the model does not yet generalize to unsampled counties; all reported performance is therefore internal to the nine sampled counties. The framework couples an agronomically motivated additive kernel structure with input-dependent uncertainty quantification, offering a path toward uncertainty-aware prediction from small field datasets.