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 drastic reduction in the sample size (number of sampled state points) needed to establish the phase boundary up to a given precision. Although advanced sampling techniques such as Gibbs Ensemble and Gibbs-Duhem integration can sample phase equilibria efficiently, they may fail to generalize to many nonequilbrium systems. This forces researchers to resort to grid search simulations when studying many important active matter systems. Grid search suffers from low efficiency by sampling predetermined state points that provide no information about the phase boundaries. We propose an active learning framework to overcome this deficiency by adaptively choosing the next most informative state point(s) every round. This is done by interpolating the sampled state points' phases by Gaussian Process regression. An acquisition function quantifies the informativeness of possible next stat...