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

Summary

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 derived a concise adsorption formula, Q=aA, where a is an adsorption baseline (mmol/g) and A is a dimensionless adsorption number incorporating four structural descriptors. The authors interpret A as the ratio between adsorption binding force and diffusion driving force, revealing joint effects of pore topology and surface chemistry. Validation against 137,652 hMOFs achieved over 70% prediction accuracy for 62,448 structures, confirming applicability within defined structural and operational ranges. Unlike black-box ML models, this physics-guided expression enables efficient prediction and clearer mechanistic insight.