Machine learning-enhanced breakthrough modeling of malachite green adsorption onto superparamagnetic activated carbon

• Magnetic activated carbon was used for fixed-bed adsorption of MG dye • Adams–Bohart, Thomas, Yoon–Nelson, Clark, and BDST models were used • Optimum conditions: Z=2 cm, Q =4.2 mL/min, C 0 = 40 mg/L resulted q e = 108.06 mg/g • CatBoost and Support Vector Regression achieved R 2 > 0.99 accuracy • SHapley Additive exPlanations and Partial Dependence Plots showed time dominance The efficient removal of toxic dyes from industrial effluents remains a persistent environmental challenge, necessitating the development of high-performance and recyclable adsorbents. In this study, a superparamagnetic activated carbon derived from Spathodea campanulata flowers (SCMAC) was synthesized via a sustainable low-temperature carbonization–magnetization route and employed for the fixed-bed adsorption of Malachite Green (MG) dye. The influence of key operational parameters, including bed height (1–3 cm), flow rate (3–5 mL/min), and inlet concentration (20–60 mg/L), was systematically investigated. Increasing the bed height from 1 to 3 cm prolonged the breakthrough time and enhanced dye removal (34.32 to 50.37%), while higher flow rates and feed concentrations accelerated saturation. The optimal conditions (Z = 2 cm, Q = 4.2 mL/min, C 0 = 40 mg/L), yielded a maximum equilibrium adsorption capacity of 108.06 mg/g. Breakthrough modeling using the Thomas, Yoon–Nelson, Adams–Bohart, Clark, and Bed Depth Service Time models showed excellent agreement with experimental data, validating the adsorption kinetics and mass-transfer dynamics. To further improve predictive capability, advanced machine-learning models were developed, with CatBoost (R 2 = 0.9965) identified as the most accurate predictor. SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP) analyses revealed time as the dominant parameter influencing MG breakthrough behavior. These findings establish SCMAC as a magnetically separable, high-efficient adsorbent and introduce a data-driven modeling framework for optimizing continuous adsorption systems for dye-laden wastewater remediation.