Robust identification of topological phase transition by self-supervised machine learning approach

We propose a systematic methodology to identify the topological phase transition through a self-supervised machine learning model, which is trained to correlate system parameters to the non-local observables in time-of-flight experiments of ultracold atoms. Different from the conventional supervised learning approach, where the predicted phase transition point is very sensitive to the training region and data labeling, our self-supervised learning approach identifies the phase transition point by the largest deviation of the predicted results from the known system parameters and by the highest confidence through a systematic shift of the training regions. We demonstrate the robust application of this approach results in various 1D and 2D exactly solvable models, using different input features (time-of-flight images, spatial correlation function or density-density correlation function). As a result, our self-supervised approach should be a very general and reliable method for many condensed matter or solid state systems to observe new states of matters solely based on experimental measurements, even without a priori knowledge of the phase transition models.