Leon Bungert

Leon Bungert is a Professor of Mathematics of Machine Learning at the University of Würzburg, working in applied analysis and numerics with a particular focus on data science and machine learning. His research investigates PDEs and variational models on graphs, adversarial robustness of machine learning, variational regularization, and nonlinear optimization.

Dr. Bungert serves as a guest editor for the European Journal of Applied Mathematics, an associate editor for Advances in Continuous and Discrete Models: Theory and Applications, and is a member of the program committee at SSVM 2025. He is also an ELLIS member and actively organizes conferences and workshops, including "MIA'25" at IHP in Paris (January 13-15, 2025), "Synergies of Machine Learning and Numerics" in Osaka (March 11-13, 2025), and "Mathematical Analysis of Adversarial Machine Learning" in Oaxaca (August 17-22, 2025).

Research Interests

Dr. Bungert's primary research areas include:

• PDEs on graphs
• Adversarial robustness in machine learning
• Inverse problems
• Optimization
• Variational problems in L-infinity
• Nonlinear eigenvalue problems
• Image reconstruction with structural priors

His work bridges theoretical mathematics with practical applications in machine learning, particularly focusing on the mathematical foundations of deep learning and developing robust algorithms that can withstand adversarial attacks. He has made significant contributions to understanding the connections between partial differential equations and machine learning algorithms.

Research Trends

Analysis of Dr. Bungert's recent publications reveals a strong focus on the intersection of machine learning and mathematical analysis. A key theme is the application of variational methods and partial differential equations to machine learning problems, particularly in understanding and improving the robustness of neural networks against adversarial examples. His work on Lipschitz learning on graphs has established important theoretical foundations for graph-based semi-supervised learning. Additionally, his research on the infinity Laplacian and p-Laplacian equations provides deep insights into the mathematical structure of machine learning algorithms. The development of Bregman learning frameworks for sparse neural networks represents a significant contribution to efficient deep learning model training.

Professional Activities

Dr. Bungert is actively involved in the academic community through editorial roles and conference organization. His current professional activities include:

• Guest editor for the European Journal of Applied Mathematics
• Associate editor for Advances in Continuous and Discrete Models: Theory and Applications
• Member of the program committee at SSVM 2025
• ELLIS member
• Co-organizer of multiple international conferences and workshops

Technical Contributions

Dr. Bungert has developed several open-source software packages that implement his theoretical contributions, including:

• Code for convergence rates of Lipschitz learning on graphs
• A Bregman training framework for sparse neural networks
• CLIP: Cheap Lipschitz Training of Neural Networks
• Nonlinear Power Method for Proximal Operators and Neural Networks
• Robust Image Reconstruction with Misaligned Structural Information

These implementations are primarily in Python and MATLAB, demonstrating his commitment to making theoretical advances accessible for practical applications.