Martin Eigel

Publication Activity (10 Years)

Years Active: 2004-2024
Publications (10 Years): 38

Top Topics

Error Estimation

Ambrosio Tortorelli

Finite Element Methods

Top Venues

Comput. Methods Appl. Math.

SIAM/ASA J. Uncertain. Quantification

Numerische Mathematik

Publications

Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis
A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields. CoRR (2024)
David Sommer, Robert Gruhlke, Max Kirstein, Martin Eigel, Claudia Schillings
Generative Modelling with Tensor Train approximations of Hamilton-Jacobi-Bellman equations. CoRR (2024)
Martin Eigel, Robert Gruhlke, David Sommer
Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy. SIAM J. Appl. Dyn. Syst. 23 (3) (2024)
Martin Eigel, Charles Miranda
Functional SDE approximation inspired by a deep operator network architecture. CoRR (2024)
Janina E. Schütte, Martin Eigel
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation. CoRR (2024)
Martin Eigel, Nando Farchmin
Convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients. CoRR (2023)
Christian Bayer, Martin Eigel, Leon Sallandt, Philipp Trunschke
Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats. SIAM J. Financial Math. 14 (2) (2023)
Philipp Trunschke, Anthony Nouy, Martin Eigel
Weighted sparsity and sparse tensor networks for least squares approximation. CoRR (2023)
Martin Eigel, Charles Miranda, Janina Schütte, David Sommer
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures. CoRR (2023)
Martin Eigel, Reinhold Schneider, David Sommer
Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation. Numer. Linear Algebra Appl. 30 (3) (2023)
Cosmas Heiß, Ingo Gühring, Martin Eigel
Multilevel CNNs for Parametric PDEs. CoRR (2023)
Martin Eigel, Nando Farchmin, Sebastian Heidenreich, Philipp Trunschke
Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs. SIAM J. Sci. Comput. 45 (2) (2023)
Robert Gruhlke, Martin Eigel
Low-rank Wasserstein polynomial chaos expansions in the framework of optimal transport. CoRR (2022)
Max Kirstein, David Sommer, Martin Eigel
Tensor-Train Kernel Learning for Gaussian Processes. COPA (2022)
Martin Eigel, Marvin Haase, Johannes Neumann
Topology Optimisation under Uncertainties with Neural Networks. Algorithms 15 (7) (2022)
Martin Eigel, Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini
On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion. SIAM J. Numer. Anal. 60 (2) (2022)
Martin Eigel, Robert Gruhlke, David Sommer
Less interaction with forward models in Langevin dynamics. CoRR (2022)
Martin Eigel, Robert Gruhlke, Manuel Marschall
Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. Stat. Comput. 32 (2) (2022)
Gregor Thiele, Theresa Johanni, David Sommer, Martin Eigel, Jörg Krüger
OptTopo: Automated set-point optimization for coupled systems using topology information. CoDIT (2022)
Martin Eigel, Nando Farchmin, Sebastian Heidenreich, Philipp Trunschke
Efficient approximation of high-dimensional exponentials by tensornetworks. CoRR (2021)
Christian Bayer, Martin Eigel, Leon Sallandt, Philipp Trunschke
Pricing high-dimensional Bermudan options with hierarchical tensor formats. CoRR (2021)
Martin Eigel, Nando Farchmin, Sebastian Heidenreich, Philipp Trunschke
Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs. CoRR (2021)
Martin Eigel, Manuel Marschall, Michael D. Multerer
An Adaptive Stochastic Galerkin Tensor Train Discretization for Randomly Perturbed Domains. SIAM/ASA J. Uncertain. Quantification 8 (3) (2020)
Martin Eigel, Manuel Marschall, Max Pfeffer, Reinhold Schneider
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations. Numerische Mathematik 145 (3) (2020)
Martin Eigel, Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion. CoRR (2020)
Martin Eigel, Reinhold Schneider, Philipp Trunschke
Convergence bounds for empirical nonlinear least-squares. CoRR (2020)
Martin Eigel, Robert Gruhlke, Manuel Marschall
Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. CoRR (2020)
Martin Drieschner, Yuri Petryna, Robert Gruhlke, Martin Eigel, Dietmar Hömberg
Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes. Reliab. Eng. Syst. Saf. 203 (2020)
Martin Eigel, Johannes Neumann, Reinhold Schneider, Sebastian Wolf
Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs. Comput. Methods Appl. Math. 19 (1) (2019)
Martin Eigel, Reinhold Schneider, Philipp Trunschke, Sebastian Wolf
Variational Monte Carlo - bridging concepts of machine learning and high-dimensional partial differential equations. Adv. Comput. Math. 45 (5) (2019)
Martin Eigel, Kevin Sturm
Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization. Optim. Methods Softw. 33 (2) (2018)
Felix Anker, Christian Bayer, Martin Eigel, Marcel Ladkau, Johannes Neumann, John Schoenmakers
SDE Based Regression for Linear Random PDEs. SIAM J. Sci. Comput. 39 (3) (2017)
Martin Eigel, Max Pfeffer, Reinhold Schneider
Adaptive stochastic Galerkin FEM with hierarchical tensor representations. Numerische Mathematik 136 (3) (2017)
Martin Eigel, Christian Merdon, Johannes Neumann
An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data. SIAM/ASA J. Uncertain. Quantification 4 (1) (2016)
Carsten Carstensen, Martin Eigel
Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes. Comput. Methods Appl. Math. 16 (2) (2016)
Martin Eigel, Christian Merdon
Equilibration a Posteriori Error Estimation for Convection-Diffusion-Reaction Problems. J. Sci. Comput. 67 (2) (2016)
Martin Eigel, Christian Merdon
Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods. SIAM/ASA J. Uncertain. Quantification 4 (1) (2016)
Martin Eigel, Daniel Peterseim
Simulation of Composite Materials by a Network FEM with Error Control. Comput. Methods Appl. Math. 15 (1) (2015)
Martin Eigel, Tatiana Samrowski
Functional A Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems. Comput. Methods Appl. Math. 14 (2) (2014)
Markus Kirkilionis, Mirela Domijan, Martin Eigel, Erwin George, Mike Li, Luca Sbano
A Definition of Cellular Interface Problems. Workshop on Membrane Computing (2008)
Dietmar Volz, Martin Eigel, Chaitanya A. Athale, Peter Bastian, Harald Hermann, Constantin Kappel, Roland Eils
Spatial Modeling and Simulation of Diffusion in Nuclei of Living Cells. CMSB (2004)