Machine Learning Quantum Phase Transitions via Topology- and Symmetry-aware AI

This PhD project focuses on using topological data analysis (TDA) in machine learning (ML) to study (exotic) quantum matter systems defined on a lattice. TDA is a technique that extracts key, persistent features from large datasets by analyzing their "shape." Instead of examining all data points in a point-cloud simulation (such as the one obtained from a simulation of a quantum system, a neuronal model of the brain, or evolution of a complex biological system), TDA focuses on identifying critical features like "holes" and "voids" in the data's structure, which can reveal hidden patterns.

The project aims to apply and adapt TDA techniques from various fields—such as physics, mathematics, bioinformatics, and neuroscience—to uncover new insights and improve ML models. By exploring how methods used in one discipline can be beneficial in another, the research seeks to foster interdisciplinary collaboration and advance the use of TDA in cutting-edge scientific research. The primary application of these cross-fertilized techniques will be the study of phase transitions of quantum matter systems on a lattice, which are inaccessible with traditional data analysis techniques.

Additionally, the project will explore potential applications of TDA in artificial intelligence, emphasizing the significance of integrating these techniques in broader AI contexts, which is increasingly important in today's technological landscape.