Active Learning for Discovering Complex Phase Diagrams with Gaussian Processes

TL;DR

This paper presents a Bayesian active learning algorithm using Gaussian processes that efficiently maps complex phase diagrams with multiple phases, significantly reducing the number of samples needed compared to traditional methods.

Contribution

The paper introduces a novel acquisition function for active learning that improves the efficiency of phase diagram discovery, especially in high-dimensional, multi-phase systems.

Findings

Successfully identified complex phase diagrams with less than 10% of total samples

Achieved less than 5% error in phase boundary detection

Demonstrated superior efficiency over existing methods in 2D and 3D systems

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.