Development of Machine Learning Models for Predicting the Fertilizer Suction Characteristics of an Asymmetric Venturi Injector

The fertilizer suction performance of Venturi injectors is jointly governed by fertilizer-solution properties and hydraulic boundary conditions, resulting in multivariable and potentially nonlinear responses that may be difficult to characterize using simplified empirical relationships. In this study, a fixed-geometry downward-eccentric Venturi injector was investigated. Separate single-output models were developed for fertilizer suction flow rate and fertilizer suction efficiency using dynamic viscosity, density, inlet pressure, and pressure differential as input variables. Based on 567 observations obtained from 189 unique experimental conditions, with three replicate measurements per condition, separate RF, SVR, and BPNN models were developed for fertilizer suction flow rate and fertilizer suction efficiency. Under the observation-level random partition used in the present analysis, BPNN achieved the lowest numerical error for fertilizer suction flow-rate prediction, whereas SVR achieved the lowest numerical error for fertilizer suction-efficiency prediction. Because replicates from the same experimental condition were not explicitly grouped during the original partition, these performance estimates should be interpreted as replicate-level predictive agreement within the investigated domain rather than as definitive validation for completely unseen operating conditions. SVR was therefore used only as a provisionally selected working model for the subsequent exploratory analyses. Predictive performance was evaluated using the coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The BPNN model achieved the best performance for fertilizer suction flow-rate prediction, with an R2 of 0.9871 and an RMSE of 5.7688 L·h−1. SVR achieved the highest accuracy for fertilizer suction-efficiency prediction, with an R2 of 0.9953 and an RMSE of 0.0310 percentage points. Considering the four evaluation metrics for both response variables, SVR was selected as the overall preferred model because it achieved the best performance for fertilizer suction-efficiency prediction while maintaining high predictive accuracy for fertilizer suction flow rate. Permutation-importance analysis indicated that the fitted SVR predictions of fertilizer suction flow rate depended most strongly on pressure differential, whereas the predictions of fertilizer suction efficiency depended most strongly on inlet pressure. External validation using actual fertilizer solutions further demonstrated the potential engineering applicability of the developed model.