Physics-grounded machine learning for inverse design of TiO2/CuInGaS2/rGO–CuxS quantum-dot solar cells using surrogate modeling and SCAPS-based validation

Abstract The inverse design of multilayer heterojunction solar cells is difficult because device efficiency depends on coupled structural and electronic parameters, while extensive SCAPS-1D parameter sweeps become costly as the design space grows. This work develops a physics-grounded machine-learning framework for TiO 2 /CuInGaS 2 /rGO-Cu x S quantum-dot solar cells, using SCAPS-1D both to generate the simulation dataset and to directly re-evaluate selected inverse-designed candidates. The dataset contains 2925 valid SCAPS configurations obtained by varying five design variables: TiO 2 thickness, CuInGaS 2 thickness, CuInGaS 2 bandgap energy, rGO-Cu x S bandgap energy, and rGO-Cu x S thickness. Ridge Regression, Random Forest, and Gradient Boosting were evaluated under a definitive random-split interpolation protocol and a separate CuInGaS 2 -bandgap interior-gap holdout. In the random-split workflow, the Gradient Boosting estimator selected directly by three-fold achieved the strongest test performance, with $$R^2=0.999674$$ , MAE = 0.036424, and RMSE = 0.053531 percentage points. When the 1.64 and 1.76 eV absorber-bandgap levels were excluded completely from fitting, the same model class reached $$R^2=0.853967$$ , MAE = 0.904670, and RMSE = 1.102763 on 1000 untouched configurations. The reduced holdout performance indicates that the high random-split accuracy mainly characterizes interpolation within the structured SCAPS design space rather than unrestricted generalization. Gradient Boosting was retained for interpretation and inverse design because it was the strongest surrogate under the definitive random-split protocol. SHAP analysis, partial dependence, large-scale screening, clustering, and local perturbation analysis were then used to characterize high-efficiency design regions. Screening 100,000 random-split candidates retained 61,867 configurations with $$\hat{\eta }\ge 18\%$$ and produced a maximum surrogate prediction of 21.170918%. The interior-gap holdout workflow retained 61,443 of 100,000 candidates and reached a maximum predicted efficiency of 20.401503%. In both workflows, $$k=4$$ was retained as a prespecified compact engineering representation, although the highest tested silhouette score occurred at $$k=8$$ . Direct SCAPS re-evaluation was expanded from the original eight cases to 50 candidates, comprising 25 random-split and 25 interior-gap holdout designs. Across these 50 directly evaluated configurations, the surrogate–SCAPS comparison gives MAE = 0.4147 and RMSE = 0.5590 percentage points. The highest directly SCAPS-computed efficiency remains 21.2588%, which exceeds the 16.6150% baseline by 4.6438 percentage points. Relative to the best original SCAPS-grid efficiency of 21.1580%, the increase is 0.1008 percentage points, corresponding to 0.4764%. The expanded campaign is used as a targeted physics-based consistency check of selected high-efficiency designs. The reported MAE and RMSE are descriptive agreement measures for the 50 directly evaluated configurations and are not interpreted as population-level error estimates for either complete 100,000-candidate screening pool. The definitive cluster representatives remain surrogate-selected unless their complete parameter vectors coincide with directly re-evaluated cases.