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

TL;DR

This paper introduces a neural network regression uncertainty method to detect phase transitions in nonequilibrium active systems, exemplified by flocking in self-propelled particles, offering a new, effective data-driven approach.

Contribution

It presents a novel regression uncertainty approach using neural networks to identify phase transitions, especially in complex nonequilibrium systems, complementing existing classification methods.

Findings

Regression uncertainty exhibits a non-trivial M-shape with a valley at the critical point.

The approach effectively detects flocking phase transition in the Vicsek model.

It demonstrates practical effectiveness and generality across physical systems.

Abstract

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. These approaches can complement each other to serve as a promising generic toolbox for investigating rich critical phenomena and providing data-driven evidence on the existence of various phase transitions, especially for those complex scenarios associated with first-order phase transitions or nonequilibrium active systems where traditional research methods in physics could face difficulties.