Active Learning for Discovering Complex Phase Diagrams with Gaussian Processes

Abstract: We introduce a Bayesian active learning algorithm that efficiently elucidates phase diagrams. Using a novel acquisition function that assesses both the impact and likelihood of the next observation, the algorithm iteratively determines the most informative next experiment to conduct and rapidly discerns the phase diagrams with multiple phases. Comparative studies against existing methods highlight the superior efficiency of our approach. We demonstrate the algorithm's practical application through the successful identification of the entire phase diagram of a spin Hamiltonian with antisymmetric interaction on Honeycomb lattice, using significantly fewer sample points than traditional grid search methods and a previous method based on support vector machines. Our algorithm identifies the phase diagram consisting of skyrmion, spiral and polarized phases with error less than 5% using only 8% of the total possible sample points, in both two-dimensional and three-dimensional phase spaces. Additionally, our method proves highly efficient in constructing three-dimensional phase diagrams, significantly reducing computational and experimental costs. Our methodological contributions extend to higher-dimensional phase diagrams with multiple phases, emphasizing the algorithm's effectiveness and versatility in handling complex, multi-phase systems in various dimensions.