Snake net and balloon force with a neural network for detecting multiple phases

TL;DR

This paper introduces an advanced unsupervised neural network method using a snake net with multiple contours and balloon forces to accurately detect multiple phase boundaries in phase diagrams from experimental data.

Contribution

It extends previous snake model approaches by implementing a multi-contour snake net with balloon forces, enabling the detection of multiple phases in complex phase diagrams.

Findings

Successfully mapped phase diagrams with three and four phases.

Enhanced phase boundary detection with balloon forces accelerating convergence.

Applicable to experimental data without prior phase knowledge.

Abstract

Unsupervised machine learning applied to the study of phase transitions is an ongoing and interesting research direction. The active contour model, also called the snake model, was initially proposed for target contour extraction in two-dimensional images. In order to obtain a physical phase diagram, the snake model with an artificial neural network is applied in an unsupervised learning way by the authors of [Phys.Rev.Lett. 120, 176401(2018)]. It guesses the phase boundary as an initial snake and then drives the snake to convergence with forces estimated by the artificial neural network. In this paper, we extend this unsupervised learning method with one contour to a snake net with multiple contours for the purpose of obtaining several phase boundaries in a phase diagram. For the classical Blume-Capel model, the phase diagram containing three and four phases is obtained. Moreover, to overcome the limitations of the initial position and speed up the movement of the snake, the balloon force decaying with the iteration steps is introduced and applied to the snake net structure. Our method is helpful in determining the phase diagram with multiple phases, using just snapshots of configurations from cold atoms or other experiments without knowledge of the phases.