Increasing global energy demand and depleting non-renewable resources drive the need for sustainable energy storage. Cement-based energy storage materials that combine structural load bearing and energy storage are well-received due to their low cost and scalability. Cement-based supercapacitors utilize the cement matrix to form electrical double layers as well as enable underpotential deposition (UPD) and highly reversible sorption and redox processes. Though, hardened cement paste has insulating properties, while the continual change in its pore structure is at different concentrations of ions, significantly limiting ions' transport and storage capability. Adding conductive materials to create coupled charge carriers electron and ions can be a solution. The multi-scale complexity of these composites inhibits the ability of classical empirical methods to disentangle the interaction effects among competing effects. In this study, we developed a machine learning framework that could identify hierarchical relationships among structural descriptors, polarization losses and rate conditions, to enable the multi-objective optimization and inverse design of cement-based supercapacitors.

Sixty groups of cement-based positive electrode samples with single and composite conductive phase combinations were fabricated. Raw materials included ordinary Portland cement, three conductive carbons materials (i.e., carbon black (CB), carbon fiber (CF) and carbon nanotube (CNT)), electrolytic α-MnO₂ as an active material, and polycarboxylate superplasticizer for fluidity enhancement. Electrochemical tests employed a two-electrode system in a 1 mol/L ammonium acetate electrolyte at two charge-discharge rates (C-rate), which were 1.0 C and 1.5 C. The internal resistance drop (V_IR). quantifying polarization loss, was defined as a difference between the 1.8 V cut-off and the discharge starting voltage. Electrochemical impedance spectroscopy (EIS) was carried out (i.e., 0.1-10000.0 Hz, 10 mV amplitude) to extract the ohmic resistance (R_s) and charge-transfer resistance (R_ct) of representative samples. A database of 280 valid dates was constructed to predict energy density. In terms of feature engineering, the raw composition descriptors were supplemented by the total carbon mass fraction [w(C_total)], the relative ratios of w(CB), w(CNT) and w(CF), the active-to-conductive ratio w(MnO₂)/w(C_total), and conductive network index (i.e., N_et = a·CNT_ratio + b·CF_ratio + c·CB_ratio). Interaction terms V_IR × N_et, and V_IR × C-rate (i.e., V_IR × 1.0 C and V_IR × 1.5 C) were introduced, and the C-rate was treated as a one-hot categorical variable to represent rate-polarization coupling. Three tree-based regressors, i.e., Random Forest (RF), eXtreme Gradient Boosting (XGBoost) and Extremely Randomized Trees (ExtraTrees), were trained under identical preprocessing using a 5-fold GroupKFold cross-validation scheme based on formulation and voltage descriptors to avoid information leakage. Model accuracy was assessed by the coefficient of determination (R²), the root-mean-square error (RMSE) and the mean absolute error (MAE). The best-performing model was retained for an Optuna-based outer search of the network-index weights under the ordered constraint a≥b≥c≥0, followed by hyper-parameter tuning. Permutation importance and SHapley Additive exPlanations (SHAP) were then applied to interpret the optimized model.

Among the three baseline models, ExtraTrees show the optimum generalization, with an out-of-fold (OOF) R² of 0.7724 and an OOF RMSE of 0.0939. Replacing the empirically assigned weights of the network index with data-driven values increases the OOF R² to 0.8240, and subsequent hyper-parameter tuning gives a final OOF R² of 0.8354 with an RMSE of 0.0793 mW·h·cm^-2. The optimized weights follow an order of CNT (2.084) > CF (1.335) > CB (0.006), indicating that high-aspect-ratio fillers dominate the construction of continuous electron-transport pathways, whereas a particulate CB mainly improves local interfacial contact and contributes little to overall network continuity. This ranking is supported by EIS results on samples with a fixed total carbon content of 10%, in which substituting CNT for CB reduces R_s from 47.90 Ω to 32.68 Ω and R_ct from 45.35 Ω to 28.76 Ω. The SHAP analysis identifies the V_IR as the most influential predictor of energy density and shows that its negative contribution becomes dominant at > 0.5 V. The network index acts as the main positive regulator, and shifts from a restrictive to a reinforcing role once it exceeds 0.5, corresponding to the formation of an effective percolation pathway. The rate-polarization interaction terms give stronger negative SHAP contributions at 1.5 C rather than at 1.0 C, indicating that higher C-rates amplify ohmic losses and narrow the range over that the structural advantage can be exploited. These results indicate a coupled structure-polarization-rate regulation mechanism, in which the energy density is not determined by any single descriptor, but by the matching among conductive network construction, polarization control and rate condition.

A machine learning framework, incorporating an optimizable conductive network index and rate-polarization interaction features, was developed for cement-based supercapacitors. ExtraTrees outperformed RF and XGBoost, and after weight optimization and hyper-parameter tuning, gave a cross-validated R² of 0.8354 for energy density. Data-driven weight learning quantified the relative contributions of the three conductive fillers as CNT > CF > CB, which was consistent with the EIS results. The SHAP interpretation showed that the IR drop could be the primary controlling variable, the network index could be the main positive regulator, and the rate-polarization interaction could be a rate-amplified negative modulator. The energy density of cement-based supercapacitors thus depended on the matching among conductive network construction, polarization control and operating C-rate. The proposed framework could provide a data-driven and mechanism-informed basis for the prediction and optimal design of cement-based energy storage materials.