Publications
L. Bungert, K. Stinson. Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning. Calculus of Variations and Partial Differential Equations, 63(114) (2024) [print] [preprint]
L. Bungert, J. Calder, T. Roith. Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian. Annals of Applied Probability. In press (2024) [preprint]
F. Bozorgnia, L. Bungert, D. Tenbrinck. The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme. Journal for Scientific Computing, 98, 40 (2024). [print] [preprint]
L. Bungert. The convergence rate of p-harmonic to infinity-harmonic functions. Communications in Partial Differential Equations, 48(10-12), 1323-1393 (2024). [print] [preprint]
L. Bungert, J. Calder, T. Roith. Uniform Convergence Rates for Lipschitz Learning on Graphs. IMA Journal of Numerical Analysis, 43(4), 2445-2495 (2022). [print] [preprint]
T. Roith, L. Bungert. Continuum Limit of Lipschitz Learning on Graphs. Foundations of Computational Mathematics, 23(2), 393-431 (2023). [print] [preprint]
L. Bungert, P. Wacker. Complete Deterministic Dynamics and Spectral Decomposition of the Ensemble Kalman Inversion. SIAM/ASA Journal on Uncertainty Quantification, 11(1), 320-357 (2023). [print] [preprint]
L. Bungert, N. García Trillos, R. Murray. The Geometry of Adversarial Training in Binary Classification. Information and Inference: A Journal of the IMA, 12(2), 921-968 (2023). [print] [preprint]
L. Bungert. The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit p→∞. Advances in Continuous and Discrete Models: Theory and Applications, 8 (2023). [print] [preprint]
L. Bungert, Y. Korolev. Eigenvalue Problems in L∞: Optimality Conditions, Duality, and Relations with Optimal Transport. Communications of the American Mathematical Society, 2(8), 345-373 (2022). [print] [preprint]
L. Bungert, T. Roith, D. Tenbrinck, M. Burger. A Bregman Learning Framework for Sparse Neural Networks. Journal of Machine Learning Research, 23(192), 1-43 (2022) [print] [preprint]
L. Schwinn, L. Bungert, A. Nguyen, R. Raab, F. Pulsmeyer, D. Precup, B. Eskofier, D. Zanca. Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification. Proceedings of the 39th International Conference on Machine Learning, PMLR 162:19434-19449, 2022. [print] [preprint]
L. Bungert, M. Burger. Gradient Flows and Nonlinear Power Methods for the Computation of Nonlinear Eigenfunctions. Handbook of Numerical Analysis, Numerical Control: Part A, Volume 23 (2022). [print] [preprint]
L. Schwinn, A. Nguyen, R. Raab, L. Bungert, D. Tenbrinck, D. Zanca, M. Burger, B. Eskofier. Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis. Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:854-864, 2021. [print] [preprint]
L. Bungert, E. Hait-Fraenkel, N. Papadakis, G. Gilboa. Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks. SIAM Journal of Imaging Sciences, 14(3), 1114-1148 (2021) [print] [preprint]
L. Bungert, M. Burger, A. Chambolle, M. Novaga. Nonlinear spectral decompositions by gradient flows of one-homogeneous functionals. Analysis and PDE, 14(3), 823–860 (2021) [print] [preprint]
L. Bungert, R. Raab, R. Roith, L. Schwinn, D. Tenbrinck. CLIP: Cheap Lipschitz Training of Deep Neural Networks. International Conference on Scale Space and Variational Methods in Computer Vision, pp. 307-319. Springer, Cham, 2021. [print] [preprint]
L. Bungert, M. J. Ehrhardt. Robust Image Reconstruction with Misaligned Structural Information. IEEE Access, 8, 222944-222955 (2020) [print] [preprint]
L. Bungert, M. Burger, Y. Korolev, C.-B. Schönlieb. Variational regularisation for inverse problems with imperfect forward operators and general noise models. Inverse Problems 36, no. 12 (2020): 125014 . [print] [preprint]
L. Bungert, Y. Korolev, M. Burger. Structural analysis of an L-infinity variational problem and relations to distance functions. Pure and Applied Analysis, 2(3), 703–738 (2020) [print] [preprint]
M. Doß, L. Bungert, D. Cichon, H. Brauer, R. Psiuk. Localization of Passive 3-D Coils as an Inverse Problem: Theoretical Analysis and a Numerical Method. IEEE Transactions on Magnetics 56, no. 4 (2020): 1-10. [print]
L. Bungert, M. Burger. Asymptotic profiles of nonlinear homogeneousolution equations of gradient flow type. Journal of Evolution Equations 20, 1061–1092 (2020). [print] [preprint]
L. Bungert, M. Burger, D. Tenbrinck. Computing nonlinear eigenfunctions via gradient flow extinction. International Conference on Scale Space and Variational Methods in Computer Vision, pp. 291-302. Springer, Cham, 2019. [print] [preprint]
L. Bungert, M. Burger. Solution paths of variational regularization methods for inverse problems. Inverse Problems 35, no. 10 (2019): 105012. [print] [preprint]
L. Bungert, M. J. Ehrhardt, R. Reisenhofer. Robust Blind Image Fusion for Misaligned Hyperspectral Imaging Data. PAMM 18, no. 1 (2018): e201800033. [print]
L. Bungert, D. A. Coomes, M. J. Ehrhardt, J. Rasch, R. Reisenhofer, C.-B. Schönlieb. Blind image fusion for hyperspectral imaging with the directional total variation. Inverse Problems 34, no. 4 (2018): 044003. [print] [preprint]
V. Aizinger, L. Bungert, M. Fried. Comparison of two local discontinuous Galerkin formulations for the subjective surfaces problem. Computing and Visualization in Science 18, no. 6 (2018): 193-202. [print]
L. Bungert, V. Aizinger, M. Fried. A discontinuous Galerkin method for the subjective surfaces problem. Journal of Mathematical Imaging and Vision 58, no. 1 (2017): 147-161. [print]
Preprints
L. Bungert, T. Laux, K. Stinson. A mean curvature flow arising in adversarial training. (2023) [preprint]
L. Bungert, N. García Trillos, M. Jacobs, D. McKenzie, Đ. Nikolić, Q. Wang. It begins with a boundary: A geometric view on probabilistically robust learning. (2023) [preprint]
L. Bungert, T. Roith, P. Wacker. Polarized consensus-based dynamics for optimization and sampling. (2022) [preprint]
L. Bungert, T. Roith, D. Tenbrinck, M. Burger. Neural Architecture Search via Bregman Iterations. (2021) [preprint]
L. Bungert, P. Wacker. The lion in the attic – A resolution of the Borel–Kolmogorov paradox. (2020) [preprint]