23 citations · 51 across the 17 of their papers we have counts for
17 papers
A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data
Max Winkler, Hamdullah Yücel
The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with…
Physics-Informed DeepONets for drift-diffusion on metric graphs: simulation and parameter identification
Jan Blechschmidt, Tom-Christian Riemer, Max Winkler +2
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a…
A Bregman-Kaczmarz method for nonlinear systems of equations
Robert Gower, Dirk A. Lorenz, Maximilian Winkler
We propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes…
A free boundary model for transport induced neurite growth
Greta Marino, Jan-Frederik Pietschmann, Max Winkler
We introduce a free boundary model to example the effect of vesicle transport onto neurite growth. It consists of systems of drift-diffusion equations describing the evolution of t…
Numerical investigation of agent controlled pedestrian dynamics using a structure preserving finite volume scheme
Jan-Frederik Pietschmann, Ailyn Stötzner, Max Winkler
We provide a numerical realisation of an optimal control problem for pedestrian motion with agents that was analysed in Herzog, Pietschmann, Winkler: "Optimal Control of Hughes' Mo…
A comparison of PINN approaches for drift-diffusion equations on metric graphs
Jan Blechschmidt, Jan-Frederik Pietschman, Tom-Christian Riemer +2
In this paper we focus on comparing machine learning approaches for quantum graphs, which are metric graphs, i.e., graphs with dedicated edge lengths, and an associated differentia…
Extended Randomized Kaczmarz Method for Sparse Least Squares and Impulsive Noise Problems
Frank Schöpfer, Dirk A Lorenz, Lionel Tondji +1
The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires onl…
Optimal Control of Hughes' Model for Pedestrian Flow via Local Attraction
Roland Herzog, Jan-Frederik Pietschmann, Max Winkler
We discuss the control of a human crowd whose dynamics is governed by a regularized version of Hughes' model, cf. Hughes: A continuum theory for the flow of pedestrians. Transporta…
Habitability of the early Earth: Liquid water under a faint young Sun facilitated by strong tidal heating due to a closer Moon
René Heller, Jan-Peter Duda, Max Winkler +2
Geological evidence suggests liquid water near the Earth's surface as early as 4.4 billion years ago when the faint young Sun only radiated about 70% of its modern power output. At…
A New Constrained Optimization Model for Solving the Nonsymmetric Stochastic Inverse Eigenvalue Problem
Gabriele Steidl, Maximilian Winkler
The stochastic inverse eigenvalue problem aims to reconstruct a stochastic matrix from its spectrum. While there exists a large literature on the existence of solutions for special…
Error estimation for second-order PDEs in non-variational form
Jan Blechschmidt, Roland Herzog, Max Winkler
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman…
Optimization of a partial differential equation on a complex network
Martin Stoll, Max Winkler
Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is…
Error estimates for the finite element approximation of bilinear boundary control problems
Max Winkler
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in t…
Error estimates for variational normal derivatives and Dirichlet control problems with energy regularization
Max Winkler
This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approxi…
-error estimates for Neumann boundary value problems on graded meshes
Thomas Apel, Johannes Pfefferer, Sergejs Rogovs +1
This paper deals with a priori pointwise error estimates for the finite element solution of boundary value problems with Neumann boundary conditions in polygonal domains. Due to th…
Finite element error estimates for normal derivatives on boundary concentrated meshes
J. Pfefferer, M. Winkler
This paper is concerned with approximations and related discretization error estimates for the normal derivatives of solutions of linear elliptic partial differential equations. In…
Anisotropic mesh refinement in polyhedral domains: error estimates with data in L^2(Ω)
Thomas Apel, Ariel L. Lombardi, Max Winkler
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded mes…