Articles by Leon Bungert

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Meshless Shape Optimization using Neural Networks and Partial Differential Equations on Graphs

20 February 2025 by Eloi Martinet and Leon Bungert

Numerical Analysis, Machine Learning

MirrorCBO: A consensus-based optimization method in the spirit of mirror descent

21 January 2025 by Leon Bungert and others

Optimization and Control, Machine Learning

MirrorCBO: A consensus-based optimization method in the spirit of mirror descent

21 January 2025 by Leon Bungert and others

Optimization and Control, Machine Learning

MirrorCBO: A consensus-based optimization method in the spirit of mirror descent

21 January 2025 by Leon Bungert and others

Optimization and Control, Machine Learning

It begins with a boundary: A geometric view on probabilistically robust learning

30 September 2024 by Leon Bungert and others

Machine Learning, Analysis of PDEs

Convergence rates of the fractional to the local Dirichlet problem

6 August 2024 by Leon Bungert and Félix Del Teso

Analysis of PDEs

Convergence rates for Poisson learning to a Poisson equation with measure data

9 July 2024 by Leon Bungert and others

Analysis of PDEs, Machine Learning

A mean curvature flow arising in adversarial training

22 April 2024 by Leon Bungert and others

Analysis of PDEs, Machine Learning

Ratio convergence rates for Euclidean first-passage percolation: Applications to the graph infinity Laplacian

22 February 2024 by Leon Bungert and others

Probability, Numerical Analysis

Gamma-convergence of a nonlocal perimeter arising in adversarial machine learning

29 January 2024 by Leon Bungert and Kerrek Stinson

Analysis of PDEs, Machine Learning

The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme

28 November 2023 by Farid Bozorgnia and others

Numerical Analysis, Analysis of PDEs

The convergence rate of p-harmonic to infinity-harmonic functions

10 October 2023 by Leon Bungert

Analysis of PDEs

Polarized consensus-based dynamics for optimization and sampling

9 October 2023 by Leon Bungert and others

Optimization and Control, Numerical Analysis

The inhomogeneous p-Laplacian equation with Neumann boundary conditions in the limit p\to\infty

13 December 2022 by Leon Bungert

Analysis of PDEs

CLIP: Cheap Lipschitz Training of Neural Networks

31 October 2022 by Leon Bungert and others

Machine Learning, Optimization and Control

The Geometry of Adversarial Training in Binary Classification

1 August 2022 by Leon Bungert and others

Machine Learning, Analysis of PDEs

Uniform Convergence Rates for Lipschitz Learning on Graphs

29 June 2022 by Leon Bungert and others

Numerical Analysis, Machine Learning

Eigenvalue Problems in \mathrm{L}^\infty: Optimality Conditions, Duality, and Relations with Optimal Transport

28 June 2022 by Leon Bungert and Yury Korolev

Analysis of PDEs, Optimization and Control

Improving Robustness against Real-World and Worst-Case Distribution Shifts through Decision Region Quantification

19 May 2022 by Leo Schwinn and others

Machine Learning

The lion in the attic -- A resolution of the Borel--Kolmogorov paradox

1 April 2022 by Leon Bungert and Philipp Wacker

Probability

Gradient Flows and Nonlinear Power Methods for the Computation of Nonlinear Eigenfunctions

9 October 2021 by Leon Bungert and Martin Burger

Numerical Analysis, Analysis of PDEs

Complete Deterministic Dynamics and Spectral Decomposition of the Ensemble Kalman Inversion

21 June 2021 by Leon Bungert and Philipp Wacker

Numerical Analysis, Optimization and Control

Neural Architecture Search via Bregman Iterations

4 June 2021 by Leon Bungert and others

Machine Learning, Neural and Evolutionary Computing

A Bregman Learning Framework for Sparse Neural Networks

17 May 2021 by Leon Bungert and others

Machine Learning, Numerical Analysis

Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis

24 February 2021 by Leo Schwinn and others

Machine Learning

Continuum Limit of Lipschitz Learning on Graphs

3 February 2021 by Tim Roith and Leon Bungert

Machine Learning, Numerical Analysis

Robust Image Reconstruction with Misaligned Structural Information

15 October 2020 by Leon Bungert and Matthias Ehrhardt

Image and Video Processing, Computer Vision and Pattern Recognition

Variational regularisation for inverse problems with imperfect forward operators and general noise models

12 October 2020 by Leon Bungert and others

Numerical Analysis, Optimization and Control

Structural analysis of an L-infinity variational problem and relations to distance functions

13 July 2020 by Leon Bungert and others

Analysis of PDEs, Spectral Theory

Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks

1 April 2020 by Leon Bungert and others

Spectral Theory, Optimization and Control

Topics

Numerical Analysis Machine Learning Analysis of PDEs Optimization and Control Spectral Theory Computer Vision and Pattern Recognition Probability Statistics Theory Metric Geometry Neural and Evolutionary Computing Image and Video Processing