Step-by-step explanation of the data pipeline, imputation strategy, ensemble learning architecture, and SHAP explainability approach used across all five Abelmoschus esculentus application domains.
Experimental datasets extracted from literature often contain missing values for unreported conditions. MICE preserves inter-feature correlations during imputation.
Multivariate Imputation by Chained Equations (MICE) imputes each missing variable by fitting a predictive model conditional on all other variables, iterating until convergence. Unlike mean/median imputation, MICE produces statistically consistent estimates that reflect the joint distribution of the data.
Features like Icorr, Rct, and ΞH are physically correlated (higher Icorr β lower Rct). Mean imputation would break these relationships, inflating artificial correlation structures and biasing model training. MICE respects these dependencies by conditioning on all available features simultaneously.
IterativeImputer (scikit-learn) with max_iter=10dataset_imputation_comparison.csvMICE imputation increased usable dataset size by allowing rows with partial measurements to be retained. The five imputed CSVs form the training set for all ML models. Domain-specific missing rates ranged from <5% (corrosion) to ~30% (composites thermomechanical properties).
Three complementary tree-based learners are combined via soft (averaged probability) voting to reduce variance and improve generalization.
Bagging of decision trees with random feature subsets. Low variance, moderate bias. Robust to outliers.
n_estimators: 100
max_features: sqrt
Sequential boosting of weak learners with gradient descent on loss. Low bias, moderate variance. Best single-model for adsorption.
n_estimators: 100
learning_rate: 0.1
Extremely Randomized Trees β random split thresholds reduce variance further at the cost of slight bias. Fastest to train.
n_estimators: 100
max_features: sqrt
Each base model has different inductive biases and error patterns. Combining them via averaging reduces the risk of any one model's systematic error dominating. This is especially effective for small experimental datasets where individual models can overfit.
The ensemble outperformed every individual model on all four predictable domains. The largest improvement was in adsorption: Ensemble RΒ²=0.8987 vs. GBM best=0.8841 (+1.6 pp). In electrochemistry, ensemble closed the gap between RF (0.8146) and GBM (0.8693), achieving 0.8951.
SHAP (SHapley Additive exPlanations) decomposes each model prediction into individual feature contributions, providing transparent, physics-consistent explanations.
For each prediction, SHAP computes the contribution of each feature by averaging over all possible feature orderings (Shapley values from cooperative game theory). The mean absolute SHAP value across all samples provides a global feature importance ranking that is additive and consistent.
SHAP results were checked against known electrochemical and adsorption theory. Icorr dominance in corrosion matches the FaradayβButler-Volmer formalism (IE = 1 β Icorr/Icorr_blank). ΞH dominance in adsorption aligns with van't Hoff thermodynamics. These findings increase confidence in model validity.
| Domain | Rank | Feature | Mean |SHAP| | Interpretation |
|---|---|---|---|---|
| Corrosion Inhibition | 1 β | Icorr_uAcm2 | 12.2479 | Electrochemical inhibition baseline; directly tracks IE% |
| 2 | Inhibitor_Concentration_ppm | 7.0209 | Log-saturation concentration response (Langmuir-like) | |
| 3 | Rct_ohm_cm2 | 1.7263 | Charge-transfer resistance reflects adsorbed inhibitor film | |
| Adsorption / Pollutant Removal | 1 β | Thermodynamic_DH_kJ_mol | 0.9148 | Exothermic ΞH β high qe; thermodynamic driving force |
| 2 | Thermodynamic_DG_kJ_mol | 0.1734 | Spontaneity of adsorption (negative ΞG = favorable) | |
| 3 | Thermodynamic_DS_J_mol_K | 0.1550 | Entropy change reflects adsorbent surface randomness | |
| Biopolymers & Composites | 1 β | Secondary_Reinforcement_wt_percent | 2.3588 | CHB content drives tensile improvement most strongly |
| 2 | Secondary_Reinforcement (type) | 1.9340 | Identity of secondary filler determines matrix compatibility | |
| 3 | Okra_Fiber_Content_wt_percent | 0.7558 | Fiber loading improves strength up to optimal threshold | |
| Electrochemistry / Carbon | 1 β | Current_Density_A_g | 24.6369 | Rate capability: higher J β lower accessible capacitance |
| 2 | Measurement_Configuration | 12.3361 | 3-electrode β« 2-electrode by ~47% (cell geometry effect) | |
| 3 | Electrolyte | 7.9384 | Ion size, viscosity, and voltage window determine charge storage | |
| Nanoparticle Synthesis Not predicted |
1 | Target_Organism | 0.3971 | Biological target modulates inhibition zone size |
| 2 | Nanoparticle_Size_nm | 0.3716 | Smaller NPs β greater surface area β higher antimicrobial activity | |
| 3 | Dose_ug_mL | 0.3276 | Dose-response relationship for inhibition zone |
All metrics are mean 5-fold CV scores. MAE and RMSE units: IE% for corrosion, log(mg/g+1) for adsorption, MPa for composites, F/g for electrochemistry, mm for nanoparticles.
| Domain | Model | CV RΒ² | CV MAE | CV RMSE | Assessment |
|---|---|---|---|---|---|
| Corrosion Inhibition | Random Forest | 0.8424 | 5.364 | 10.859 | Good |
| Gradient Boosting | 0.8226 | 5.309 | 11.521 | Good | |
| Extra Trees | 0.8408 | 4.759 | 10.912 | Good | |
| π Heterogeneous Voting | 0.8422 | 4.911 | 10.865 | Best | |
| Adsorption / Pollutant Removal | Random Forest | 0.8774 | 0.350 | 0.468 | Good |
| Gradient Boosting | 0.8841 | 0.301 | 0.455 | Good | |
| Extra Trees | 0.8691 | 0.321 | 0.484 | Good | |
| π Heterogeneous Voting | 0.8987 | 0.283 | 0.426 | Best | |
| Biopolymers & Composites | Random Forest | 0.5591 | 2.880 | 4.113 | Moderate |
| Gradient Boosting | 0.5735 | 2.906 | 4.046 | Moderate | |
| Extra Trees | 0.5360 | 2.995 | 4.220 | Moderate | |
| π Heterogeneous Voting | 0.5744 | 2.915 | 4.041 | Best/Moderate | |
| Electrochemistry / Carbon | Random Forest | 0.8146 | 12.231 | 17.598 | Good |
| Gradient Boosting | 0.8693 | 10.123 | 14.772 | Good | |
| Extra Trees | 0.8290 | 10.754 | 16.897 | Good | |
| π Heterogeneous Voting | 0.8951 | 8.974 | 13.234 | Best | |
| Nanoparticle Green Synthesis | Random Forest | β0.1999 | 1.178 | 2.017 | Poor |
| Gradient Boosting | β0.8028 | 1.430 | 2.472 | Poor | |
| Extra Trees | β0.7525 | 1.412 | 2.438 | Poor | |
| Heterogeneous Voting | β0.5268 | 1.292 | 2.275 | Poor |
The adsorption capacity target (qe) spans three orders of magnitude (3.9β1132 mg/g), making it highly right-skewed. Log-transforming the target (log(qe+1)) normalizes the distribution, improving model performance. MAE reported in log units; predictions are back-transformed via exp(Β·)β1 for display.
The composites dataset covers mechanically distinct systems (polyester, PP, CMC) with varying test protocols and loading directions. Pooling these into a single model introduces heterogeneity. Additionally, the small dataset (n<50) limits generalization. RΒ²=0.57 is respectable for cross-system mechanical property prediction from processing parameters alone.