Interpretable Physics-Guided Deep Learning Ensemble for Nonisothermal General Rate Model of Chromatography

Each simulation of the ternary nonisothermal General Rate Model (GRM)─governing competitive bi-Langmuir adsorption across two energetically distinct binding-site populations─demands approximately 90 CPU-minutes, rendering iterative process design computationally intractable. A deep learning ensemble trained on 1,375 high-fidelity GRM simulations─spanning near-linear elution through severely overloaded, thermally distorted conditions─jointly predicts 12 chromatographic scalars: retention times, peak geometry, resolution, purity, yield, volumetric productivity, and the column thermal gradient. Twenty-two physics-derived dimensionless ratio features encoding pairwise transport selectivity, bi-Langmuir site competition, and mass-to-thermal coupling were appended to the 31 native GRM parameters, forming a 53-dimensional mechanistically informed input. Four architecturally distinct base learners (TabNet, Residual MLP, Monte Carlo Dropout, FT-Transformer), tuned via Bayesian hyperparameter search, were combined through constrained out-of-fold weight optimization. On a sealed 207-sample test set, the ensemble attained R̅ 2 = 0.9349, statistically exceeding the best single model (FT-Transformer, R̅ 2 = 0.9240; Wilcoxon W = 7374, p = 8.5 × 10 –5 ). A net gain of +0.0325 over a baseline FT-Transformer decomposes into +0.0216 from feature engineering and +0.0109 from ensemble aggregation; the identical augmentation degraded TabNet by −0.0100, establishing that physics-guided input construction is architecture-dependent. SHAP attribution over the 31 physical GRM parameters revealed a physically coherent importance hierarchy: six bi-Langmuir Henry constants account for ≈42.5% of global importance, adsorption enthalpy ranks fifth at 6.5%, and all transport parameters fall below 1.4%─consistent with equilibrium-dominated preparative overloading. Under 10% additive Gaussian noise, median R̅ 2 fell by 0.009, three-to-five times smaller than the degradation reported for comparable tree-based surrogates. The surrogate runs four-to-five orders of magnitude faster than the mechanistic solver.