基于符号回归与投票集成的高锝酸根在金属有机框架材料上吸附的可解释预测

    Explanatory Prediction of Adsorption of Pertechnetate Ions on MOFs Based on Symbol Regression and Voting Ensemble

    • 摘要: 高锝酸根(\mathrmTcO_4^- )在核废料中具有长期放射性风险,其在金属-有机框架材料(MOF)上的吸附性能预测因实验数据稀缺和机理复杂而面临挑战。本工作提出一种融合特征筛选、消融实验、可解释性分析与符号回归的机器学习框架,旨在小样本条件下实现准确且可解释的\mathrmTcO_4^- 吸附量预测。从公开文献中收集了77条阴离子(\mathrmReO_4^- 、\mathrmCrO_4^2- 、\mathrmMnO_4^- 等)在MOF上的吸附数据,并从对应晶体学文件中提取63个结构描述符。采用七种分类模型(逻辑斯蒂回归、决策树、随机森林、支持向量机、K-近邻、XGBoost、LightGBM)进行二分类任务,通过多模型共识筛选出18个核心特征,分为几何、电荷、金属电子和孔道四类。消融实验表明,移除金属电子或电荷分布特征导致性能下降最显著,证实其主导作用。SHAP分析揭示了关键特征的影响方向:金属电负性与吸附量正相关,孔径呈倒U型关系。在此基础上,利用符号回归为每类特征构建独立的分类规则,并通过投票机制集成四类规则的判断,建立了一个完全可解释的预测模型。该投票模型在测试集上整体准确率达71.4%,对高吸附量样本的召回率达100%。研究表明,\mathrmTcO_4^- 在MOF上的吸附由多类结构因素共同决定,所提机器学习框架在数据稀缺条件下兼顾了预测性能与可解释性,为放射性核素分离材料的高通量筛选提供了新工具。

       

      Abstract: Technetium-99(99Tc) is a major long-lived fission product with a half-life of 2.1×105 years, posing persistent radiological risks in nuclear waste management. In oxidizing environments, technetium exists as the pertechnetate anion(\mathrmTcO_4^- ), which exhibits high aqueous mobility due to its low charge density and small hydration energy, making its efficient removal from radioactive wastewater a critical challenge. Metal-organic frameworks(MOFs) have emerged as promising adsorbents for \mathrmTcO_4^- , but experimental data on \mathrmTcO_4^- adsorption remain extremely scarce(fewer than 100 publicly reported records), hindering the development of predictive models. To overcome this small-sample limitation, we propose a machine learning framework that integrates multi-model feature screening, ablation experiments, SHAP interpretability analysis, and symbolic regression, aiming for accurate and fully interpretable prediction of \mathrmTcO_4^- adsorption on MOFs. A source domain dataset of 77 adsorption records is manually curated from open literature, covering nine structurally or chemically related oxyanions(\mathrmReO_4^- , \mathrmCrO_4^2- , \mathrmMnO_4^-, etc.) on various MOFs. From corresponding crystallographic files(CIF), 63 structural descriptors are automatically extracted, encompassing geometry, charge distribution, metal electronic properties, and pore characteristics. Seven classification models(logistic regression, decision tree, random forest, support vector machine, K-nearest neighbor, XGBoost, LightGBM) were used for binary classification tasks, and 18 core features were selected through multi model consensus screening, divided into four categories: geometry, charge, metal electron, and pore. The ablation experiment shows that the removal of metal electrons or charge distribution characteristics lead to the most significant decrease in performance, confirming the dominant role of these two categories. SHAP analysis reveals the direction of influence of key features: metal electronegativity is positively correlated with adsorption capacity, and pore size exhibits an inverted U-shaped relationship, consistent with the hard-soft acid-base theory. To achieve full explainability, the symbolic regression(PySR) to each of the four feature categories is applied, obtaining explicit mathematical classification rules. These four rules are then integrated via a majority-voting ensemble. Although single-category rules suffer from overfitting(validation accuracy 0.43-0.57), the voting ensemble achieves an overall test accuracy of 71.4%, a recall of 100% for high-adsorption samples(4/4), a precision of 67% for high-adsorption predictions. Notably, the model misclassifies only low-adsorption samples as high, which is acceptable in high-throughput screening where false negatives(missing a promising MOF) are more costly. This framework demonstrates that \mathrmTcO_4^- adsorption on MOFs is governed by synergistic contributions from geometry, charge distribution, metal electronic states, and pore architecture. Although validated on \mathrmReO_4^- as a non-radioactive surrogate, the method is expected to generalize to \mathrmTcO_4^- given their high chemical similarity. To our knowledge, this is the first study to combine symbolic regression with a voting ensemble for interpretable prediction of radionuclide adsorption, providing a practical and data-efficient tool for high-throughput screening of MOF-based adsorbents in radiochemistry.

       

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