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Mathematics of Machine Learning

Leon Bungert, Prof. Dr.

Prof. Dr. Leon Bungert

W2 Professor with Tenure Track to W3
Professorship for Mathematics III (Mathematics of Machine Learning)
Emil-Fischer-Straße 40
97074 Würzburg
Building: Mathematik Ost (40)
Room: 01.008
Phone: +49 931 31-82849
Fax: +49 931 31-81492

Personal Website

SuSe 2026 Research sabbatical, therefore no courses

Portrait Leon Bungert

The following links provide information on

Professor (Tenure Track) at the University of Würzburg since 2023

Previous Positions:

  • Junior Research Group Leader at the Technical University of Berlin (2023)
  • Postdoctoral Researcher at the Hausdorff Center for Mathematics, University of Bonn (2021 - 2023)
  • Postdoctoral Researcher at the University of Erlangen-Nürnberg (2020 - 2021)

Education:

  • Ph.D. (summa cum laude) from the University of Erlangen-Nürnberg (2020), title of the thesis: "Nonlinear spectral theory with variational methods"
  • M.Sc. in Mathematics from the University of Erlangen-Nürnberg (2017)
  • B.Sc. in Mathematics from the University of Erlangen-Nürnberg (2016)

Publications

  • 1.
    Meshless Shape Optimization using Neural Networks and Partial Differential Equations on Graphs
    Martinet, E., Bungert, L.
    https://arxiv.org/abs/2502.14821 (2025)
  • 1.
    MirrorCBO: A consensus-based optimization method in the spirit of mirror descent
    Bungert, L., Hoffmann, F., Kim, D. Y., Roith, T.
    https://arxiv.org/abs/2501.12189 (2025)
  • 1.
    Convergence rates for Poisson learning to a Poisson equation with measure data
    Bungert, L., Calder, J., Mihailescu, M., Houssou, K., Yuan, A.
    https://arxiv.org/abs/2407.06783 (2024)
  • 1.
    Convergence rates of the fractional to the local Dirichlet problem
    Bungert, L., del Teso, F.
    https://arxiv.org/abs/2408.03299 (2024)
  • 1.
    It begins with a boundary: A geometric view on probabilistically robust learning
    Bungert, L., Trillos, N. G., Jacobs, M., McKenzie, D., Nikolić, Đorđe, Wang, Q.
    https://arxiv.org/abs/2305.18779 (2023)
  • 1.
    Neural Architecture Search via Bregman Iterations
    Bungert, L., Roith, T., Tenbrinck, D., Burger, M.
    https://arxiv.org/abs/2106.02479 (2021)
  • 1.
    The lion in the attic -- A resolution of the Borel--Kolmogorov paradox
    Bungert, L., Wacker, P.
    (2020)

  • 1.
    A mean curvature flow arising in adversarial training
    Bungert, L., Laux, T., Stinson, K.
    Journal de Mathématiques Pures et Appliquées 192, 103625 (2024)
  • 1.
    Polarized consensus-based dynamics for optimization and sampling
    Bungert, L., Roith, T., Wacker, P.
    Mathematical Programming (2024)
  • 1.
    The infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
    Bozorgnia, F., Bungert, L., Tenbrinck, D.
    Journal of Scientific Computing 98, 40 (2024)
  • 1.
    Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian
    Bungert, L., Calder, J., Roith, T.
    Annals of Applied Probability 34, 3870-3910 (2024)
  • 1.
    Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning
    Bungert, L., Stinson, K.
    Calculus of Variations and Partial Differential Equations 63, 114 (2024)
  • 1.
    The convergence rate of $p$-harmonic to infinity-harmonic functions
    Bungert, L.
    Communications in Partial Differential Equations 48, 1323-1339 (2024)
  • 1.
    The geometry of adversarial training in binary classification
    Bungert, L., García Trillos, N., Murray, R.
    Information and Inference: A Journal of the IMA 12, 921-968 (2023)
  • 1.
    Uniform convergence rates for Lipschitz learning on graphs
    Bungert, L., Calder, J., Roith, T.
    IMA Journal of Numerical Analysis 43, 2445-2495 (2023)
  • 1.
    The inhomogeneous $p$-Laplacian equation with Neumann boundary conditions in the limit $ ptoinfty$
    Bungert, L.
    Advances in Continuous and Discrete Models 2023, 1-17 (2023)
  • 1.
    Complete Deterministic Dynamics and Spectral Decomposition of the Linear Ensemble Kalman Inversion
    Bungert, L., Wacker, P.
    SIAM/ASA Journal on Uncertainty Quantification (2023)
  • 1.
    Eigenvalue problems in $mathrmL^infty$: optimality conditions, duality, and relations with optimal transport
    Bungert, L., Korolev, Y.
    Communications of the American Mathematical Society 2, 345–373 (2022)
  • 1.
    Continuum Limit of Lipschitz Learning on Graphs
    Roith, T., Bungert, L.
    Foundations of Computational Mathematics (2022)
  • 1.
    A Bregman Learning Framework for Sparse Neural Networks
    Bungert, L., Roith, T., Tenbrinck, D., Burger, M.
    Journal of Machine Learning Research 23, 1-43 (2022)
  • 1.
    Nonlinear power method for computing eigenvectors of proximal operators and neural networks
    Bungert, L., Hait-Fraenkel, E., Papadakis, N., Gilboa, G.
    SIAM Journal on Imaging Sciences 14, 1114-1148 (2021)
  • 1.
    Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals
    Bungert, L., Burger, M., Chambolle, A., Novaga, M.
    Analysis & PDE 14, 823-860 (2021)
  • 1.
    Structural analysis of an $L$-infinity variational problem and relations to distance functions
    Bungert, L., Korolev, Y., Burger, M.
    Pure and Applied Analysis 2, 703–738 (2020)
  • 1.
    Localization of Passive 3-D Coils as an Inverse Problem: Theoretical Analysis and a Numerical Method
    Doß, M., Bungert, L., Cichon, D., Brauer, H., Psiuk, R.
    IEEE Transactions on Magnetics 56, 1-10 (2020)
  • 1.
    Asymptotic profiles of nonlinear homogeneous evolution equations of gradient flow type
    Bungert, L., Burger, M.
    Journal of Evolution Equations 20, 1061-1092 (2020)
  • 1.
    Variational regularisation for inverse problems with imperfect forward operators and general noise models
    Bungert, L., Burger, M., Korolev, Y., Schönlieb, C.-B.
    Inverse Problems 36, 125014 (2020)
  • 1.
    Robust Image Reconstruction with Misaligned Structural Information
    Bungert, L., Ehrhardt, M. J.
    IEEE Access 8, 222944-222955 (2020)
  • 1.
    Solution paths of variational regularization methods for inverse problems
    Bungert, L., Burger, M.
    Inverse Problems 35, 105012 (2019)
  • 1.
    Blind image fusion for hyperspectral imaging with the directional total variation
    Bungert, L., Coomes, D. A., Ehrhardt, M. J., Rasch, J., Reisenhofer, R., Schönlieb, C.-B.
    Inverse Problems 34, 044003 (2018)
  • 1.
    Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data
    Bungert, L., Ehrhardt, M. J., Reisenhofer, R.
    PAMM 18, e201800033 (2018)
  • 1.
    Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem
    Aizinger, V., Bungert, L., Fried, M.
    Computing and Visualization in Science 18, 193-202 (2018)
  • 1.
    A discontinuous Galerkin method for the subjective surfaces problem
    Bungert, L., Aizinger, V., Fried, M.
    Journal of Mathematical Imaging and Vision 58, 147-161 (2017)

  • 1.
    Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification
    Schwinn, L., Bungert, L., Nguyen, A., Raab, R., Pulsmeyer, F., Precup, D., Eskofier, B., Zanca, D.
    In: Chaudhuri, K., Jegelka, S., Song, L., Szepesvari, C., Niu, G., and Sabato, S. (eds.) Proceedings of the 39th International Conference on Machine Learning. pp. 19434-19449. PMLR (2022)
  • 1.
    Chapter 13 - Gradient flows and nonlinear power methods for the computation of nonlinear eigenfunctions
    Bungert, L., Burger, M.
    In: Trélat, E. and Zuazua, E. (eds.) Numerical Control: Part A. pp. 427-465. Elsevier (2022)
  • 1.
    Identifying untrustworthy predictions in neural networks by geometric gradient analysis
    Schwinn, L., Nguyen, A., Raab, R., Bungert, L., Tenbrinck, D., Zanca, D., Burger, M., Eskofier, B.
    In: de Campos, C. and Maathuis, M. H. (eds.) Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence. pp. 854-864. PMLR (2021)
  • 1.
    CLIP: Cheap Lipschitz Training of Neural Networks
    Bungert, L., Raab, R., Roith, T., Schwinn, L., Tenbrinck, D.
    In: Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., and Simon, L. (eds.) Scale Space and Variational Methods in Computer Vision. pp. 307-319. Springer International Publishing, Cham (2021)
  • 1.
    Computing nonlinear eigenfunctions via gradient flow extinction
    Bungert, L., Burger, M., Tenbrinck, D.
    In: International Conference on Scale Space and Variational Methods in Computer Vision. pp. 291-302. Springer (2019)