Guangyu Meng

PhD Candidate in Computer Science | University of Notre Dame

About Me

I am a PhD candidate in Computer Science at the University of Notre Dame, working under the supervision of Prof. Erin W. Chambers and Prof. Danny Z. Chen. My research brings geometric and topological structure to machine learning, creating methods that are both more interpretable and more effective.

Rather than treating data as raw pixels or vectors, I develop approaches that extract and leverage underlying shape and structural properties. Using persistent homology and optimal transport, I build representations that capture connectivity, anatomical relationships, and geometric invariants. This perspective has enabled unsupervised medical image clustering that rivals supervised methods, topology-enhanced contrastive learning with consistent improvements across architectures, and efficient algorithms with theoretical guarantees for large-scale applications.

Research Interests

• Medical Image Analysis with Topological Data Analysis
• Self-Supervised Learning and Contrastive Learning
• Computational Geometry and Optimal Transport
• Curriculum Learning for Large Language Models
• Persistent Homology and Shape Analysis