Topological data analysis refers to approaches for systematically and reliably computing
abstract 'shapes' of complex data sets. There are various applications of topological data …

We use persistent homology and persistence images as an observable of three variants of
the two-dimensional XY model to identify and study their phase transitions. We examine …

We apply modern methods in computational topology to the task of discovering and
characterizing phase transitions. As illustrations, we apply our method to four two …

The identification of universal properties from minimally processed data sets is one goal of
machine learning techniques applied to statistical physics. Here, we study how the minimum …

We propose two machine-learning methods based on neural networks, which we
respectively call the phase-classification method and the temperature-identification method …

Persistent homology (PH) is a relatively new field in applied mathematics that studies the
components and shapes of discrete data. In this paper, we demonstrate that PH can be used …

We investigate the use of persistent homology, a tool from topological data analysis, as a
means to detect and quantitatively describe center vortices in SU (2) lattice gauge theory in …

We implement a computational pipeline based on a recent machine learning technique,
namely, topological data analysis (TDA), that has the capability of extracting powerful …

Network science provides very powerful tools for extracting information from interacting data.
Although recently the unsupervised detection of phases of matter using machine learning …

We investigate the structure of confining and deconfining phases in SU (2) lattice gauge
theory via persistent homology, which gives us access to the topology of a hierarchy of …