Adaptive Learning Framework in Prediction and Validation of Gibbs Free Energy for Inorganic Crystalline Solids

Gibbs free energy is a fundamental physical property for understanding the stability and synthesizability of materials under various thermodynamic conditions, but its accessibility and availability are still limited. In this study, we used 9880 phonon databases to construct a machine learning model to predict approximately 40 000 Inorganic Crystalline Solid Database (ICSD) materials, whose free energy information has not been fully explored. To improve the prediction accuracy, a sampling strategy was implemented by including structures with low accuracy metrics, leading to R² and mean absolute error values of 0.99 and 18.7 kJ/mol, respectively, in the testing set. Uncertainty analysis was followed for unexplored ICSD materials by obtaining the standard deviation in predictions from 10 surrogate models with different samplings in the training set. Based on this, an optimization process was conducted: density functional calculations were performed for 50 structures with high uncertainty and the training database was updated; this loop was repeated 15 times. This demonstrates the reduction and saturation in the uncertainty, confirming that the constructed model can provide a comprehensive map of the Gibbs free energy for inorganic solid materials. This can accelerate the material screening process by providing information on thermodynamic stability.