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Martin Eigel
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2020 – today
- 2024
- [j21]Martin Eigel, Robert Gruhlke
, David Sommer
:
Less Interaction with Forward Models in Langevin Dynamics: Enrichment and Homotopy. SIAM J. Appl. Dyn. Syst. 23(3): 1870-1908 (2024) - [i16]Martin Eigel, Charles Miranda:
Functional SDE approximation inspired by a deep operator network architecture. CoRR abs/2402.03028 (2024) - [i15]David Sommer, Robert Gruhlke, Max Kirstein, Martin Eigel, Claudia Schillings:
Generative Modelling with Tensor Train approximations of Hamilton-Jacobi-Bellman equations. CoRR abs/2402.15285 (2024) - [i14]Janina E. Schütte, Martin Eigel:
Adaptive Multilevel Neural Networks for Parametric PDEs with Error Estimation. CoRR abs/2403.12650 (2024) - [i13]Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis:
A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields. CoRR abs/2403.13770 (2024) - 2023
- [j20]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) - [j19]Christian Bayer
, Martin Eigel, Leon Sallandt
, Philipp Trunschke
:
Pricing High-Dimensional Bermudan Options with Hierarchical Tensor Formats. SIAM J. Financial Math. 14(2): 383-406 (2023) - [j18]Martin Eigel, Nando Farchmin, Sebastian Heidenreich, Philipp Trunschke:
Adaptive Nonintrusive Reconstruction of Solutions to High-Dimensional Parametric PDEs. SIAM J. Sci. Comput. 45(2): 457- (2023) - [i12]Martin Eigel, Nando Farchmin:
Convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients. CoRR abs/2302.02839 (2023) - [i11]Cosmas Heiß, Ingo Gühring, Martin Eigel:
Multilevel CNNs for Parametric PDEs. CoRR abs/2304.00388 (2023) - [i10]Philipp Trunschke, Anthony Nouy, Martin Eigel:
Weighted sparsity and sparse tensor networks for least squares approximation. CoRR abs/2310.08942 (2023) - [i9]Martin Eigel, Charles Miranda, Janina Schütte, David Sommer:
Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures. CoRR abs/2311.03242 (2023) - 2022
- [j17]Martin Eigel, Marvin Haase, Johannes Neumann:
Topology Optimisation under Uncertainties with Neural Networks. Algorithms 15(7): 241 (2022) - [j16]Martin Eigel, Robert Gruhlke
, Manuel Marschall
:
Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. Stat. Comput. 32(2): 27 (2022) - [j15]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): 659-687 (2022) - [c4]Gregor Thiele
, Theresa Johanni
, David Sommer
, Martin Eigel
, Jörg Krüger
:
OptTopo: Automated set-point optimization for coupled systems using topology information. CoDIT 2022: 224-229 - [c3]Max Kirstein, David Sommer, Martin Eigel:
Tensor-Train Kernel Learning for Gaussian Processes. COPA 2022: 253-272 - [i8]Robert Gruhlke, Martin Eigel:
Low-rank Wasserstein polynomial chaos expansions in the framework of optimal transport. CoRR abs/2203.09358 (2022) - [i7]Martin Eigel, Robert Gruhlke, David Sommer:
Less interaction with forward models in Langevin dynamics. CoRR abs/2212.11528 (2022) - 2021
- [i6]Christian Bayer, Martin Eigel, Leon Sallandt, Philipp Trunschke:
Pricing high-dimensional Bermudan options with hierarchical tensor formats. CoRR abs/2103.01934 (2021) - [i5]Martin Eigel, Nando Farchmin, Sebastian Heidenreich, Philipp Trunschke:
Efficient approximation of high-dimensional exponentials by tensornetworks. CoRR abs/2105.09064 (2021) - [i4]Martin Eigel, Nando Farchmin, Sebastian Heidenreich, Philipp Trunschke:
Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs. CoRR abs/2112.01285 (2021) - 2020
- [j14]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): 1189-1214 (2020) - [j13]Martin Eigel, Manuel Marschall, Max Pfeffer
, Reinhold Schneider:
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations. Numerische Mathematik 145(3): 655-692 (2020) - [j12]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: 107106 (2020) - [i3]Martin Eigel, Reinhold Schneider, Philipp Trunschke:
Convergence bounds for empirical nonlinear least-squares. CoRR abs/2001.00639 (2020) - [i2]Martin Eigel, Robert Gruhlke, Manuel Marschall:
Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion. CoRR abs/2008.04264 (2020) - [i1]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 abs/2008.07186 (2020)
2010 – 2019
- 2019
- [j11]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): 2503-2532 (2019) - [j10]Martin Eigel, Johannes Neumann
, Reinhold Schneider, Sebastian Wolf:
Non-intrusive Tensor Reconstruction for High-Dimensional Random PDEs. Comput. Methods Appl. Math. 19(1): 39-53 (2019) - 2018
- [j9]Martin Eigel, Kevin Sturm
:
Reproducing kernel Hilbert spaces and variable metric algorithms in PDE-constrained shape optimization. Optim. Methods Softw. 33(2): 268-296 (2018) - 2017
- [j8]Martin Eigel, Max Pfeffer
, Reinhold Schneider:
Adaptive stochastic Galerkin FEM with hierarchical tensor representations. Numerische Mathematik 136(3): 765-803 (2017) - [j7]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) - 2016
- [j6]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): 213-230 (2016) - [j5]Martin Eigel, Christian Merdon:
Equilibration a Posteriori Error Estimation for Convection-Diffusion-Reaction Problems. J. Sci. Comput. 67(2): 747-768 (2016) - [j4]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): 1219-1245 (2016) - [j3]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): 1372-1397 (2016) - 2015
- [j2]Martin Eigel, Daniel Peterseim
:
Simulation of Composite Materials by a Network FEM with Error Control. Comput. Methods Appl. Math. 15(1): 21-37 (2015) - 2014
- [j1]Martin Eigel, Tatiana Samrowski:
Functional A Posteriori Error Estimation for Stationary Reaction-Convection-Diffusion Problems. Comput. Methods Appl. Math. 14(2): 135-150 (2014)
2000 – 2009
- 2008
- [c2]Markus Kirkilionis, Mirela Domijan, Martin Eigel, Erwin George
, Mike Li, Luca Sbano:
A Definition of Cellular Interface Problems. Workshop on Membrane Computing 2008: 36-62 - 2004
- [c1]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: 161-171
Coauthor Index
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