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

Abstract

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.