Residual-hybrid dynamic response-surface/machine-learning framework for predicting malachite green removal and biodegradation by a bacterial consortium

The discharge of dye-containing effluents is a global environmental concern, particularly for synthetic cationic dyes such as malachite green (MG). This study aimed to develop and experimentally validate a hybrid dynamic response-surface/machine-learning framework, coupled with an optimized bacterial consortium, for predicting and enhancing MG removal and elucidating its biodegradation pathway. A four-strain comprising Azotobacter chroococcum, Azotobacter salinestris, Stenotrophomonas maltophilia, and Sphingomonas kyeonggiensis was first optimized by mixture design, where an appropriate proportion of A. chroococcum and S. maltophilia achieved 83.51% MG decolorization. A Box–Behnken design (BBD) was then applied to optimize initial MG concentration, inoculum size, and incubation time; the response-surface model predicted a maximum removal of 96.56% at 100 mg/L, 7% inoculum, and 72 h, in good agreement with the experimental data. The resulting RSM-based dynamic response-surface model used as a baseline, and residual machine-learning regressors were trained on experimentally derived residuals (experimental MG removal minus baseline prediction). Among standalone learners, CatBoost provided the best performance on the exploratory 80/20 train–test split, whereas under leave-one-out cross-validation, the hybrid residual model (dynamic response-surface + Ridge regression) emerged as the most reliable predictor, yielding closer agreement with the experimental MG removal than the baseline model. Biodegradation of MG by the optimized consortium was experimentally validated by Fourier-transform infrared (FTIR) spectroscopy, liquid chromatography–mass spectrometry (LC–MS) and UV–visible spectroscopy, which confirmed disruption of the chromophoric structure and formation of less toxic metabolites. Toxicity assay indicated that the degradation products were non-toxic towards the tested pathogenic bacteria. ISSR molecular typing revealed that primer ISSR-12 exhibited strong discriminatory power, generating nine strain-specific bands, whereas primer ISSR-1 produced a higher proportion of monomorphic bands. This work introduces a small-sample, hybrid dynamic response-surface/machine-learning framework, experimentally validated against MG biodegradation experiments, which integrates an RSM-based baseline as an explicit feature in residual learning. Under leave-one-out cross-validation (N = 17), the RSM baseline achieved R² = 0.988 and RMSE = 2.62% MG removal, while the best hybrid residual model (dynamic response-surface + Ridge regression) yielded R² = 0.987 and RMSE = 2.79%, confirming the robustness of the proposed framework.