PDE-Based Models in Semi-Supervised Learning

Explore the mathematical foundations and applications of partial differential equation (PDE) based models in semi-supervised learning through this 57-minute conference talk presented at ICBS2025 by Zuoqiang Shi from BIMSA. Delve into the theoretical framework that connects PDEs with machine learning paradigms, examining how differential equations can be leveraged to address challenges in semi-supervised learning scenarios where labeled data is limited. Discover the mathematical principles underlying PDE-based approaches, their computational implementation, and their effectiveness in handling datasets with both labeled and unlabeled examples. Learn about the convergence properties, stability analysis, and practical considerations when applying these models to real-world problems. Gain insights into the intersection of mathematical analysis and modern machine learning techniques, understanding how classical PDE theory can inform and enhance contemporary learning algorithms in situations where traditional supervised methods may be insufficient due to data constraints.