通过机器学习-符号回归发现可物理解释的数学表达式以预测金属有机框架中的CO₂吸附
Discovering Physically Interpretable Mathematical Expression for Predicting CO2 Adsorption in Metal-Organic Frameworks via Machine Learning-Symbolic Regression
AI总结：
本研究通过ML-SR方法，结合关键结构描述符推导得到可物理解释的CO₂吸附公式，在大规模hMOFs数据集上实现70%以上预测准确率，兼具高效性与机制可解释性。
AI中文摘要：
本研究提出一种机器学习-符号回归（ML-SR）策略，用于构建可物理解释的公式以预测假想金属有机框架（hMOFs）在低压下的CO₂吸附容量。在包含1000个样本的小型数据集上训练了4种机器学习模型，通过SHAP及特征重要性分析确定了5个关键描述符：最大空腔直径、孔限制直径、空隙率、重量表面积和氢原子数量。随后采用符号回归推导得到简洁的吸附公式Q=aA，其中a代表吸附基线（单位为mmol/g），A为无量纲吸附数，整合了4个结构描述符。研究将A解释为吸附结合力与扩散驱动力的比值，揭示了孔拓扑结构与表面化学如何共同影响吸附过程。对包含137652个hMOFs的综合数据集的验证表明，该公式对62448个结构实现了70%以上的预测准确率，证实其在既定结构和操作范围内具有较强适用性。与传统黑箱机器学习模型不同，所提出的物理引导表达式可实现高效预测，并为吸附机制提供更清晰的见解。
英文摘要：
This work presents a machine learning-symbolic regression (ML-SR) strategy to develop a physically interpretable formula for predicting low pressure CO2 adsorption capacity in hypothetical metal-organic frameworks (hMOFs). Four ML models were trained on a small dataset of 1,000 samples, and five key descriptors-largest cavity diameter, pore limiting diameter, void fraction, gravimetric surface area, and number of hydrogen atoms-were identified through SHAP and feature importance analyses. Symbolic regression was then employed to derive a concise adsorption formula, Q=aA, where a represents an adsorption baseline (mmol/g) and A is a dimensionless adsorption number incorporating four structural descriptors. We interpret A as the ratio between an adsorption binding force and a diffusion driving force, revealing how pore topology and surface chemistry jointly influence adsorption. Validation against a comprehensive dataset of 137,652 hMOFs demonstrates that this formula achieves over 70% prediction accuracy for 62,448 structures, confirming strong applicability within defined structural and operational ranges. Unlike conventional black box ML models, the proposed physics-guided expression enables efficient prediction and provides clearer insight into adsorption mechanisms.
