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We develop the neural network based "learning from regression uncertainty"approach for automated detection of phases of matter in nonequilibrium activesystems. Taking the flocking phase transition of self-propelled activeparticles described by the Vicsek model for example, we find that aftertraining a neural network for solving the inverse statistical problem, i.e.,for performing the regression task of reconstructing the noise level from givensamples of such a nonequilibrium many-body complex system's steady stateconfigurations, the uncertainty of regression results obtained by thewell-trained network can actually be utilized to reveal possible phasetransitions in the system under study. The noise level dependence of regressionuncertainty assumes a non-trivial M-shape, and its valley appears at thecritical point of the flocking phase transition. By directly comparing thisregression-based approach with the widely-used classification-based "learningby confusion" and "learning with blanking" approaches, we show that ourapproach has practical effectiveness, efficiency, good generality for variousphysical systems across interdisciplinary fields, and a greater possibility ofbeing interpretable via conventional notions of physics. These approaches cancomplement each other to serve as a promising generic toolbox for investigatingrich critical phenomena and providing data-driven evidence on the existence ofvarious phase transitions, especially for those complex scenarios associatedwith first-order phase transitions or nonequilibrium active systems wheretraditional research methods in physics could face difficulties.

Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty