55 citations · 598 across the 84 of their papers we have counts for
13 papers · 1 filter
Variational Regularization in Inverse Problems and Machine Learning
Martin Burger
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties n…
Learning convex regularizers satisfying the variational source condition for inverse problems
Subhadip Mukherjee, Carola-Bibiane Schönlieb, Martin Burger
Variational regularization has remained one of the most successful approaches for reconstruction in imaging inverse problems for several decades. With the emergence and astonishing…
Phase Separation in Systems of Interacting Active Brownian Particles
M. Bruna, M. Burger, A. Esposito +1
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present f…
On multi-species diffusion with size exclusion
Katharina Hopf, Martin Burger
We revisit a classical continuum model for the diffusion of multiple species with size-exclusion constraint, which leads to a degenerate nonlinear cross-diffusion system. The purpo…
A Diffuse Interface Model for Cell Blebbing Including Membrane-Cortex Coupling with Linker Dynamics
Philipp Werner, Martin Burger, Florian Frank +1
The aim of this paper is to develop suitable models for the phenomenon of cell blebbing, which allow for computational predictions of mechanical effects including the crucial inter…
Region-of-Interest Prioritised Sampling for Constrained Autonomous Exploration Systems
Protim Bhattacharjee, Martin Burger, Anko Boerner +1
Goal oriented autonomous operation of space rovers has been known to increase scientific output of a mission. In this work we present an algorithm, called the RoI Prioritised Sampl…
Active Crowds
Maria Bruna, Martin Burger, Jan-Frederik Pietschmann +1
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the deriva…
Gradient Flows and Nonlinear Power Methods for the Computation of Nonlinear Eigenfunctions
Leon Bungert, Martin Burger
This chapter describes how gradient flows and nonlinear power methods in Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how convergence…
A Bregman Learning Framework for Sparse Neural Networks
Leon Bungert, Tim Roith, Daniel Tenbrinck +1
We propose a learning framework based on stochastic Bregman iterations, also known as mirror descent, to train sparse neural networks with an inverse scale space approach. We deriv…
Kinetic Equations for Processes on Co-evolving Networks
Martin Burger
The aim of this paper is to derive macroscopic equations for processes on large co-evolving networks, examples being opinion polarization with the emergence of filter bubbles or ot…
Identifying Untrustworthy Predictions in Neural Networks by Geometric Gradient Analysis
Leo Schwinn, An Nguyen, René Raab +5
The susceptibility of deep neural networks to untrustworthy predictions, including out-of-distribution (OOD) data and adversarial examples, still prevent their widespread use in sa…
Convex regularization in statistical inverse learning problems
Tatiana A. Bubba, Martin Burger, Tapio Helin +1
We consider a statistical inverse learning problem, where the task is to estimate a function based on noisy point evaluations of , where is a linear operator. The funct…
Dynamic optimal transport on networks
Martin Burger, Ina Humpert, Jan-Frederik Pietschmann
We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter , has to be paid for inter…