Multi-Output Gaussian Process Regression for Rapid Multi-Nutrient Prediction in Soil Using Near-Infrared Spectroscopy

The concentrations of nitrogen (N), phosphorus (P), potassium (K), organic matter (OM), and pH in soil are critical markers of fertility that influence crop growth and yield. Traditional wet-chemical analyses are labor-intensive, time-consuming, and costly, thereby constraining timely soil information acquisition for precision agriculture. This study evaluates whether multi-output Gaussian process regression (MOGPR) can enhance the prediction accuracy of multiple soil nutrients by exploiting their intrinsic correlations, in comparison with single-output Gaussian process regression (SOGPR). Near-infrared (NIR) spectroscopy was applied to 622 typical black soil samples collected from the Farm 855 (45°43′ N, 131°35′ E), Heilongjiang Province, China. Corresponding MOGPR and SOGPR models were developed for systematic performance comparison. Results indicated that MOGPR significantly outperformed SOGPR for nutrients exhibiting moderate-to-strong intercorrelations (N, P, K, and OM), yielding R2 improvements of 0.070.28 and RPD increases of 16–40%, whereas only limited gains were observed for pH due to its weak correlations with other nutrients. These findings indicate that combining NIR spectroscopy with MOGPR offers significant potential for rapid, nondestructive assessment of multiple soil nutrients. This study further establishes a correlation-aware multi-output modeling framework that links shared spectral responses with an inter-nutrient dependency structure, providing methodological guidance for multi-nutrient soil prediction.