Spatial Modeling and Simulation of Diffusion in Nuclei of Living Cells. - Dietmar Volz; Martin Eigel; Chaitanya A. Athale; Peter Bastian; Harald Hermann; Constantin Kappel; Roland Eils (CMSB, 2004)

A Definition of Cellular Interface Problems. - Markus Kirkilionis; Mirela Domijan; Martin Eigel; Erwin George; Mike Li; Luca Sbano (Workshop on Membrane Computing, 2008)

Functional A Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems. - Martin Eigel; Tatiana Samrowski (Comput. Methods Appl. Math., 2014)

Simulation of Composite Materials by a Network FEM with Error Control. - Martin Eigel; Daniel Peterseim (Comput. Methods Appl. Math., 2015)

Reliable Averaging for the Primal Variable in the Courant FEM and Hierarchical Error Estimators on Red-Refined Meshes. - Carsten Carstensen; Martin Eigel (Comput. Methods Appl. Math., 2016)

Equilibration a Posteriori Error Estimation for Convection-Diffusion-Reaction Problems. - Martin Eigel; Christian Merdon (J. Sci. Comput., 2016)

Local Equilibration Error Estimators for Guaranteed Error Control in Adaptive Stochastic Higher-Order Galerkin Finite Element Methods. - Martin Eigel; Christian Merdon (SIAM/ASA J. Uncertain. Quantification, 2016)

An Adaptive Multilevel Monte Carlo Method with Stochastic Bounds for Quantities of Interest with Uncertain Data. - Martin Eigel; Christian Merdon; Johannes Neumann (SIAM/ASA J. Uncertain. Quantification, 2016)

Adaptive stochastic Galerkin FEM with hierarchical tensor representations. - Martin Eigel; Max Pfeffer; Reinhold Schneider (Numerische Mathematik, 2017)

SDE Based Regression for Linear Random PDEs. - Felix Anker; Christian Bayer 001; Martin Eigel; Marcel Ladkau; Johannes Neumann; John Schoenmakers (SIAM J. Sci. Comput., 2017)

Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization. - Martin Eigel; Kevin Sturm (Optim. Methods Softw., 2018)

Variational Monte Carlo - bridging concepts of machine learning and high-dimensional partial differential equations. - Martin Eigel; Reinhold Schneider; Philipp Trunschke; Sebastian Wolf (Adv. Comput. Math., 2019)

Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs. - Martin Eigel; Johannes Neumann; Reinhold Schneider; Sebastian Wolf (Comput. Methods Appl. Math., 2019)

Convergence bounds for empirical nonlinear least-squares. - Martin Eigel; Reinhold Schneider; Philipp Trunschke (CoRR, 2020)

An Adaptive Stochastic Galerkin Tensor Train Discretization for Randomly Perturbed Domains. - Martin Eigel; Manuel Marschall; Michael D. Multerer (SIAM/ASA J. Uncertain. Quantification, 2020)

Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations. - Martin Eigel; Manuel Marschall; Max Pfeffer; Reinhold Schneider (Numerische Mathematik, 2020)

Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes. - Martin Drieschner; Yuri Petryna; Robert Gruhlke; Martin Eigel; Dietmar Hömberg (Reliab. Eng. Syst. Saf., 2020)

Efficient approximation of high-dimensional exponentials by tensornetworks. - Martin Eigel; Nando Farchmin; Sebastian Heidenreich; Philipp Trunschke (CoRR, 2021)

Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs. - Martin Eigel; Nando Farchmin; Sebastian Heidenreich; Philipp Trunschke (CoRR, 2021)

OptTopo: Automated set-point optimization for coupled systems using topology information. - Gregor Thiele 001; Theresa Johanni; David Sommer; Martin Eigel; Jörg Krüger (CoDIT, 2022)

Tensor-Train Kernel Learning for Gaussian Processes. - Max Kirstein; David Sommer; Martin Eigel (COPA, 2022)

Topology Optimisation under Uncertainties with Neural Networks. - Martin Eigel; Marvin Haase; Johannes Neumann (Algorithms, 2022)

Low-rank Wasserstein polynomial chaos expansions in the framework of optimal transport. - Robert Gruhlke; Martin Eigel (CoRR, 2022)

Less interaction with forward models in Langevin dynamics. - Martin Eigel; Robert Gruhlke; David Sommer (CoRR, 2022)

Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. - Martin Eigel; Robert Gruhlke; Manuel Marschall (Stat. Comput., 2022)

On the Convergence of Adaptive Stochastic Collocation for Elliptic Partial Differential Equations with Affine Diffusion. - Martin Eigel; Oliver G. Ernst; Björn Sprungk; Lorenzo Tamellini (SIAM J. Numer. Anal., 2022)

Convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients. - Martin Eigel; Nando Farchmin (CoRR, 2023)

Weighted sparsity and sparse tensor networks for least squares approximation. - Philipp Trunschke; Anthony Nouy; Martin Eigel (CoRR, 2023)

Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures. - Martin Eigel; Charles Miranda; Janina Schütte; David Sommer (CoRR, 2023)

Multilevel CNNs for Parametric PDEs. - Cosmas Heiß; Ingo Gühring; Martin Eigel (J. Mach. Learn. Res., 2023)

Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs. - Martin Eigel; Nando Farchmin; Sebastian Heidenreich; Philipp Trunschke (SIAM J. Sci. Comput., 2023)

Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation. - Martin Eigel; Reinhold Schneider; David Sommer (Numer. Linear Algebra Appl., 2023)

Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats. - Christian Bayer 001; Martin Eigel; Leon Sallandt; Philipp Trunschke (SIAM J. Financial Math., 2023)

Functional SDE approximation inspired by a deep operator network architecture. - Martin Eigel; Charles Miranda (CoRR, 2024)

Generative Modelling with Tensor Train approximations of Hamilton-Jacobi-Bellman equations. - David Sommer; Robert Gruhlke; Max Kirstein; Martin Eigel; Claudia Schillings (CoRR, 2024)

Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation. - Janina E. Schütte; Martin Eigel (CoRR, 2024)

A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields. - Markus Bachmayr; Martin Eigel; Henrik Eisenmann; Igor Voulis (CoRR, 2024)

Multilevel CNNs for Parametric PDEs based on Adaptive Finite Elements. - Janina E. Schütte; Martin Eigel (CoRR, 2024)

An Eulerian approach to regularized JKO scheme with low-rank tensor decompositions for Bayesian inversion. - Vitalii Aksenov; Martin Eigel (CoRR, 2024)

Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy. - Martin Eigel; Robert Gruhlke; David Sommer (SIAM J. Appl. Dyn. Syst., 2024)

Sampling from Boltzmann Densities with Physics Informed Low-Rank Formats. - Paul Hagemann; Janina Schütte; David Sommer; Martin Eigel; Gabriele Steidl (SSVM (1), 2025)

Multi-level Neural Networks for high-dimensional parametric obstacle problems. - Martin Eigel; Cosmas Heiß; Janina E. Schütte (CoRR, 2025)