Deep learning stochastic processes with QCD phase transition

TL;DR

This paper demonstrates how deep learning, specifically CNNs, can classify phase transitions and predict damping coefficients in stochastic systems modeled by Langevin equations, with applications to QCD matter near criticality.

Contribution

It introduces a deep learning framework to classify phase transitions and estimate damping coefficients from stochastic field configurations in QCD-like systems.

Findings

CNNs accurately classify phase transition types despite noise.

The method reliably predicts damping coefficients across a broad parameter range.

Deep learning effectively extracts dynamical information from fluctuating fields.

Abstract

It is non-trivial to recognize phase transitions and track dynamics inside a stochastic process because of its intrinsic stochasticity. In this paper, we employ the deep learning method to classify the phase orders and predict the damping coefficient of fluctuating systems under Langevin's description. As a concrete set-up, we demonstrate this paradigm for the scalar condensation in QCD matter near the critical point, in which the order parameter of chiral phase transition can be characterized in a $1+1$-dimensional Langevin equation for $\sigma$ field. In a supervised learning manner, the Convolutional Neural Networks(CNNs) accurately classify the first-order phase transition and crossover based on $\sigma$ field configurations with fluctuations. Noise in the stochastic process does not significantly hinder the performance of the well-trained neural network for phase order recognition. For mixed dynamics with diverse dynamical parameters, we further devise and train the machine to predict the damping coefficients $\eta$ in a broad range. The results show that it is robust to extract the dynamics from the bumpy field configurations.