Active learning to overcome exponential-wall problem for effective structure prediction of chemical-disordered materials

Chemical-disordered materials have a wide range of applications whereas the determination of their structures or configurations is one of the most important and challenging problems. Traditional methods are extremely inefficient or intractable for large systems due to the notorious exponential-wall issue that the number of possible structures increase exponentially for N-body systems. Herein, we introduce an efficient approach to predict the thermodynamically stable structures of chemical-disordered materials via active-learning accompanied by first-principles calculations. Our method, named LAsou, can efficiently compress the sampling space and dramatically reduce the computational cost. Three distinct and typical finite-size systems are investigated, including the anion-disordered BaSc(O x F 1−x ) 3 (x = 0.667), the cation-disordered Ca 1−x Mn x CO 3 (x = 0.25) with larger size and the defect-disordered ε-FeC x (x = 0.5) with larger space. The commonly used enumeration method requires to explicitly calculate 2664, 1033, and 10496 configurations, respectively, while the LAsou method just needs to explicitly calculate about 15, 20, and 10 configurations, respectively. Besides the finite-size system, our LAsou method is ready for quasi-infinite size systems empowering materials design.