Efficient Phase Diagram Sampling by Active Learning

We address the problem of efficient phase diagram sampling by adopting active learning techniques from machine learning, and achieve an 80% reduction in the sample size (number of sampled statepoints) needed to establish the phase boundary up to a given precision in example application. Traditionally, data is collected on a uniform grid of predetermined statepoints. This approach, also known as grid search in the machine learning community, suffers from low efficiency by sampling statepoints that provide no information about the phase boundaries. We propose an active learning approach to overcome this deficiency by adaptively choosing the next most informative statepoint(s) every round. This is done by interpolating the sampled statepoints' phases by Gaussian Process regression. An acquisition function quantifies the informativeness of possible next statepoints, maximizing the information content in each subsequently sampled statepoint. We also generalize our approach with state-of-the-art batch sampling techniques to better utilize parallel computing resources. We demonstrate the usefulness of our approach in a few example simulations relevant to soft matter physics, although our algorithms are general. Our active learning enhanced phase diagram sampling method greatly accelerates research and opens up opportunities for extra-large scale exploration of a wide range of phase diagrams by simulations or experiments.