Topological Persistence Machine of Phase Transitions

Understand

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available.

• Topological data analysis is an emerging framework for characterizing the shape of data and has recently achieved success in detecting structural transitions in material science, such as the glass--liquid transition.
• However, data obtained from physical states may not have explicit shapes as structural materials.
• We thus propose a general framework, termed "topological persistence machine," to construct the shape of data from correlations in states, so that we can subsequently decipher phase transitions via qualitative changes in the shape.