Bayesian Active Learning to Accelerate High Throughput Phase Diagram Exploration

Abstract

Phase diagrams are fundamental for understanding phase stability and guiding the synthesis of new materials. However, constructing high-dimensional phase diagrams through exhaustive CALPHAD (CALculation of PHAse Diagrams) computations remains costly. We introduce a Bayesian Active Learning for Phase Diagram Discovery (BALPI) framework that efficiently identifies phase stability regions by adaptively sampling the thermodynamic space using uncertainty-aware acquisition strategies. BALPI integrates Gaussian Process Classifiers and Regressors within two complementary formulations-classification and level-set estimation-and introduces non-myopic Bayesian acquisition functions, including the Soft Mean Objective Cost of Uncertainty (SMOCU) and an extended straddle (estraddle) criterion. Using CALPHAD-based phase stability predictions as the ground-truth oracle, BALPI achieves accurate reconstruction of phase boundaries with significantly fewer queries than conventional label propagation and label spreading baselines. Results on SiO2-Al2O3-MgO and Ni-Ti-Hf-Cu systems demonstrate that BALPI captures disconnected phase regions and achieves consistent reductions in Bayesian error and computational cost. More importantly, this work establishes BALPI as a general framework for uncertainty-guided phase diagram discovery and highlights the potential of Bayesian active learning to accelerate computational thermodynamics and materials design, through the efficient exploration of the phase stability landscape at much lower costs relative to competing strategies.