Snake net with a neural network for detecting multiple phases in the phase diagram

Area of Science:

• Physics
• Computational Science
• Machine Learning

Background:

• Unsupervised machine learning is increasingly applied to study phase transitions.
• The active contour model (snake model) is traditionally used for image analysis.
• Previous work combined snake models with artificial neural networks for unsupervised phase diagram determination.

Purpose of the Study:

• To extend unsupervised learning methods for phase diagram determination to handle multiple phase boundaries.
• To develop a more robust and flexible snake-based approach for analyzing experimental data.
• To accurately map complex phase diagrams without prior knowledge of the phases.

Main Methods:

• Extension of the single-contour snake model to a multi-contour snake net for identifying multiple phase boundaries.
• Application of artificial neural networks to estimate forces guiding snake convergence.
• Introduction of a balloon force to improve snake initialization and escape local minima.

Main Results:

• Successfully obtained phase diagrams with three and four phases for the Blume-Capel model.
• Demonstrated the ability to determine multiple phase boundaries using the snake net approach.
• Validated the effectiveness of the balloon force in enhancing snake initialization flexibility.

Conclusions:

• The developed multi-contour snake net offers a powerful unsupervised method for determining complex phase diagrams.
• This approach can analyze experimental snapshots (e.g., from cold atom experiments) without pre-existing phase information.
• The method advances the application of machine learning in condensed matter physics and materials science.