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

Understand

We develop the neural network based "learning from regression uncertainty" approach for automated detection of phases of matter in nonequilibrium active systems.

• Taking the flocking phase transition of self-propelled active particles described by the Vicsek model for example, we find that after training a neural network for solving the inverse statistical problem, i.e., for performing the regression task of reconstructing the noise level from given samples of such a nonequilibrium many-body complex system's steady state configurations, the uncertainty of regression results obtained by the well-trained network can actually be utilized to reveal possible phase transitions in the system under study.
• The noise level dependence of regression uncertainty assumes a non-trivial M-shape, and its valley appears at the critical point of the flocking phase transition.
• By directly comparing this regression-based approach with the widely-used classification-based "learning by confusion" and "learning with blanking" approaches, we show that our approach has practical effectiveness, efficiency, good generality for various physical systems across interdisciplinary fields, and a greater possibility of being interpretable via conventional notions of physics.