A Two-Stage Hybrid Modeling Approach Integrating Physical Mechanisms and Machine Learning for EC Prediction in Multi-Ion Mixed Fertilizer Solutions

Soilless cultivation and integrated water–fertilizer systems rely on precise control of electrical conductivity (EC) in nutrient solutions. Although EC can be measured online, predicting EC from known ionic composition is valuable for offline formulation screening and feedforward control. Classical extended Debye–Hückel mechanistic models suffer from systematic bias at moderate concentrations because their dilute-solution assumptions cannot capture complex non-ideal ionic interactions and hydration effects. Pure data-driven models, by contrast, lack built-in electrochemical constraints and physical interpretability within the training domain. This study proposes a two-stage hybrid framework: simulated annealing first optimizes the ionic-size parameters of the mechanistic model to mitigate systematic bias, and gradient-boosted regression trees subsequently compensate for nonlinear residuals originating from higher-order ionic interactions, ion pairing, and hydration distortion. The model was developed using 537 samples spanning four mixed nutrient formulations and seven single-salt electrolyte solutions, with EC ranging from 6.6 to 2855 μS/cm across five temperature levels from 15 to 35 °C. On the independent test set, the hybrid model achieved an R2 = 0.9999 and an RMSE = 5.17 μS/cm, reducing prediction error by 89.7–93.9% relative to three benchmark models. The framework simultaneously offers physical interpretability and high in-domain interpolation accuracy.