Accurate predictions of phase transition temperatures have always been a dream of materials physicists. However, calculations using first-principles methods are usually extremely time consuming and challenging, while force fields without extensive and careful tuning tend to provide inaccurate answers. Machine-learned force fields are an obvious solution to this dilemma, but training them can be a time-consuming and tedious process.

In this talk, I show that training on the fly leads to highly accurate machine-learned force fields (MLFF) that meet the challenges of predicting properties at finite temperatures with an accuracy close to the original first-principles methods. Our machine learning approach is based on Bayesian inference and uses a combination of radial and angular features computed locally for each atom. Bayesian regression not only provides predictions for the energies, forces, and stress tensor, but also predicts the uncertainty of these predictions. When the uncertainties exceed a certain threshold, on-the-fly first-principles calculations are performed, the structure is added to the training data set, and the MLFF is refined. Training is simply done by heating (or cooling) all phases of interest. Typically, an accurate force field can be obtained in a few days, and the training requires no special intervention or expertise by the user.