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Topological data analysis and machine learning

ADVANCES IN PHYSICS-X (2023)

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Hidden Topological Structure of Flow Network Functionality

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Topological Metric Detects Hidden Order in Disordered Media

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Summary: This study introduces persistent homology observables inspired by topological data analysis techniques and applies them in a geometric analysis of quantum field theories. Using data from a classical-statistical simulation of a two-dimensional Bose gas, the study discovers a continuous spectrum of dynamical scaling exponents and links the persistent homology scaling exponents to the geometry of the system. The study suggests a new way to analyze quantum many-body dynamics through robust topological structures.

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