Targeted adsorbent preparation under data-limited conditions: a transfer learning-driven inverse optimization...

Despite extensive studies on the use of drinking water treatment sludge (DWS) for heavy metal adsorption, its application remains constrained by limited data availability in metal-specific DWS adsorption datasets and the lack of operating parameter determination under target concentration requirements. To address these challenges, a data-driven inverse optimization framework was developed to identify adsorption operating parameters of modified DWS under predefined equilibrium concentration targets. A machine learning-based forward prediction model incorporating transfer learning was trained using literature-derived adsorption datasets, and Bayesian optimization was employed to inversely screen feasible parameter combinations within a practically relevant parameter space, aiming to identify conditions capable of achieving predefined equilibrium concentration targets. Batch adsorption experiments demonstrated that the optimized conditions achieved complete removal of Pb²⁺ and Cr³⁺, while reducing Cd²⁺ concentration from 2 mg/L to 0.004 mg/L, corresponding to a removal efficiency of 99.8 %. Comparative tests indicated that additional activated carbon did not further enhance adsorption performance under the investigated conditions. Further results showed that Pb-optimized DWS maintained stable and efficient removal of Pb²⁺, Cr³⁺, and Cd²⁺ in binary and ternary systems under near-neutral conditions (pH ≈ 6.4). Competitive adsorption and cyclic experiments suggested that Pb²⁺ and Cr³⁺ exhibited stronger surface binding characteristics, while Cd²⁺ adsorption was more sensitive to background ions and repeated use. These results demonstrate that integrating transfer learning with inverse optimization provides a preliminary framework for parameter-oriented design of waste-derived adsorbents under small-sample conditions.