Discovering Physically Interpretable Mathematical Expression for Predicting CO2 Adsorption in Metal-Organic Frameworks via Machine Learning-Symbolic Regression

Abstract

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.