WIAS Preprint List: Eigel, Martin

• 3124: Eigel, Martin; Schütte, Janina
  Multilevel CNNs for parametric PDEs based on adaptive finite elements
  
• 3112: Bachmayr, Markus; Eigel, Martin; Eisenmann, Henrik; Voulis, Igor
  A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields
  
• 3079: Eigel, Martin; Miranda, Charles
  Functional SDE approximation inspired by a deep operator network architecture
  
• 3078: Sommer, David; Gruhlke, Robert; Kirstein, Max; Eigel, Martin; Schillings, Claudia
  Generative modelling with tensor train approximations of Hamilton--Jacobi--Bellman equations
  
• 3077: Eigel, Martin; Miranda, Charles; Schütte, Janina; Sommer, David
  Approximating Langevin Monte Carlo with ResNet-like neural network architectures
  
• 3049: Trunschke, Philipp; Eigel, Martin; Nouy, Anthony
  Weighted sparsity and sparse tensor networks for least squares approximation
  
• 3036: Eigel, Martin; Hegemann, Nando
  Guaranteed quasi-error reduction of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients
  
• 3035: Heiß, Cosmas; Gühring, Ingo; Eigel, Martin
  Multilevel CNNs for parametric PDEs
  Appeared in: J. Mach. Learn. Res., 24 (2023), pp. 373/1--373/42.
• 2987: Eigel, Martin; Gruhlke, Robert; Sommer, David
  Less interaction with forward models in Langevin dynamics
  Appeared in: SIAM J. Appl. Dyn. Syst., 23 (2024), pp. 870--1908, DOI 10.1137/23M1546841 with the new title “Less interaction with forward models in Langevin dynamics: Enrichment and homotopy”.
• 2982: Eigel, Martin; Haase, Marvin; Neumann, Johannes
  Topology optimisation under uncertainties with neural networks
  Appeared in: Algorithms, 15 (2022), pp. 241/1--241/34, DOI https://doi.org/10.3390/a15070241 .
• 2981: Kirstein, Max; Eigel, Martin; Sommer, David
  Tensor-train kernel learning for Gaussian processes
  Appeared in: Proceedings of the Eleventh Symposium on Conformal and Probabilistic Prediction with Applications, U. Johansson, H. Boström, K.A. Nguyen, Z. Luo, L. Carlsson, eds., vol. 179 of Proceedings of Machine Learning Research, 2022, pp. 253--272.
• 2928: Drieschner, Martin; Gruhlke, Robert; Petryna, Yuri; Eigel, Martin; Hömberg, Dietmar
  Local surrogate responses in the Schwarz alternating method for elastic problems on random voided domains
  Appeared in: Comput. Methods Appl. Mech. Engrg., 405 (2023), pp. 115858/1--115858/18, DOI 10.1016/j.cma.2022.115858 .
• 2927: Gruhlke, Robert; Eigel, Martin
  Low-rank Wasserstein polynomial chaos expansions in the framework of optimal transport
  
• 2907: Eigel, Martin; Gruhlke, Robert; Moser, Dieter
  Numerical upscaling of parametric microstructures in a possibilistic uncertainty framework with tensor trains
  Appeared in: Comput. Mech., 71 (2023), pp. 615--636 (published online on 27.12.2022), DOI 10.1007/s00466-022-02261-z .
• 2897: Eigel, Martin; Farchmin, Nando; Heidenreich, Sebastian; Trunschke, Philipp
  Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs
  Appeared in: SIAM J. Sci. Comput., (2023), pp. A457--A479, DOI 10.1137/21M1461988 .
• 2896: Eigel, Martin; Schneider, Reinhold; Sommer, David
  Dynamical low-rank approximations of solutions to the Hamilton--Jacobi--Bellman equation
  Appeared in: Numer. Linear Algebra Appl., 30 (2023), pp. e2463/1--e2463/20 (published online on 03.08.2022), DOI 10.1002/nla.2463 .
• 2844: Eigel, Martin; Farchmin, Nando; Heidenreich, Sebastian; Trunschke, Philipp
  Efficient approximation of high-dimensional exponentials by tensor networks
  Appeared in: Int. J. Uncertain. Quantif., 13 (2023), pp. 25--51, DOI 10.1615/Int.J.Uncertainty.Quantification.2022039164 .
• 2821: Bayer, Christian; Eigel, Martin; Sallandt, Leon; Trunschke, Philipp
  Pricing high-dimensional Bermudan options with hierarchical tensor formats
  Appeared in: SIAM J. Financial Math., 14 (2023), pp. 383--406, DOI 10.1137/21M1402170 .
• 2753: Eigel, Martin; Ernst, Oliver; Sprungk, Björn; Tamellini, Lorenzo
  On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
  Appeared in: SIAM J. Numer. Anal., 60 (2022), pp. 659--687, DOI 10.1137/20M1364722 .
• 2714: Eigel, Martin; Trunschke, Philipp; Schneider, Reinhold
  Convergence bounds for empirical nonlinear least-squares
  Appeared in: ESAIM Math. Model. Numer. Anal., 56 (2022), pp. 79--104 , DOI 10.1051/m2an/2021070 .
• 2672: Eigel, Martin; Gruhlke, Robert; Marschall, Manuel
  Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion
  Appeared in: Statist. Comput., 32 (2022), pp. 27/1--27/27, DOI 10.1007/s11222-022-10087-1 .
• 2580: Eigel, Martin; Grasedyck, Lars; Gruhlke, Robert; Moser, Dieter
  Low rank surrogates for polymorphic fields with application to fuzzy-stochastic partial differential equations
  
• 2579: Drieschner, Martin; Eigel, Martin; Gruhlke, Robert; Hömberg, Dietmar; Petryna, Yuri
  Comparison of monomorphic and polymorphic approaches for uncertainty quantification with experimental investigations
  Appeared in: Reliab. Eng. Syst. Safety, 203 (2020), pp. 107106/1--107106/12, DOI 10.1016/j.ress.2020.107106 with the new title "Comparison of various uncertainty models with experimental investigations regarding the failure of plates with holes".
• 2566: Eigel, Martin; Marschall, Manuel; Multerer, Michael
  An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains
  Appeared in: SIAM/ASA J. Uncertain. Quantif., 8 (2020), pp. 1189--1214, DOI 10.1137/19M1246080 .
• 2565: Eigel, Martin; Gruhlke, Robert
  A hybrid FETI-DP method for non-smooth random partial differential equations
  Appeared in: Internat. J. Numer. Methods Engrg., 122 (2021), pp. 1001--1030, DOI 10.1002/nme.6571 with the new title “A local hybrid surrogate-based finite element tearing interconnecting dual-primal method for nonsmooth random partial differential equations”.
• 2544: Eigel, Martin; Trunschke, Philipp; Schneider, Reinhold; Wolf, Sebastian
  Variational Monte Carlo -- Bridging concepts of machine learning and high dimensional partial differential equations
  Appeared in: Adv. Comput. Math., 45 (2019), pp. 2503--2532, DOI 10.1007/s10444-019-09723-8 .
• 2515: Eigel, Martin; Marschall, Manuel; Pfeffer, Max; Schneider, Reinhold
  Adaptive stochastic Galerkin FEM for log-normal coefficients in hierarchical tensor representations
  Appeared in: Numer. Math., 145 (2020), pp. 655--692 (published online on 24.06.2020).
• 2444: Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian
  Non-intrusive tensor reconstruction for high dimensional random PDEs
  Appeared in: Comput. Methods Appl. Math., 19 (2019), pp. 39--53 (published online on 25.07.2018), DOI 10.1515/cmam-2018-0028 .
• 2363: Eigel, Martin; Marschall, Manuel; Schneider, Reinhold
  Bayesian inversion with a hierarchical tensor representation
  Appeared in: Inverse Problems, 34 (2018) pp. 035010/1--035010/29, DOI 10.1088/1361-6420/aaa998; changed title: Sampling-free Bayesian inversion with adaptive hierarchical tensor representations.
• 2362: Eigel, Martin; Neumann, Johannes; Schneider, Reinhold; Wolf, Sebastian
  Stochastic topology optimisation with hierarchical tensor reconstruction
  Appeared in: Computer Methods Appl. Math. Engrg., 334 (2018), pp. 470--482, DOI 10.1016/j.cma.2018.02.003; changed title: Risk averse stochastic structural topology optimization.
• 2251: Carstensen, Carsten; Eigel, Martin
  Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on red-refined meshes
  Appeared in: Comput. Methods Appl. Math., 16 (2016) pp. 213--230.
• 2244: Eigel, Martin; Sturm, Kevin
  Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation
  Appeared in: Optim. Methods Softw., 33 (2018), pp. 268--296 (published online on 03.05.2017), DOI 10.1080/10556788.2017.1314471 .
• 2200: Anker, Felix; Bayer, Christian; Eigel, Martin; Neumann, Johannes; Schoenmakers, John G. M.
  Adaptive SDE based interpolation for random PDEs
  Appeared in: Int. J. Uncertain. Quantif., 7 (2017), pp. 189--205; changed title: A fully adaptive interpolated stochastic sampling method for linear random PDEs
• 2196: Eigel, Martin; Müller, Rüdiger
  A posteriori error control for stationary coupled bulk-surface equations
  Appeared in: IMA J. Numer. Anal., 38 (2018), pp. 271--298, DOI 10.1093/imanum/drw080 .
• 2192: Anker, Felix; Bayer, Christian; Eigel, Martin; Ladkau, Marcel; Neumann, Johannes; Schoenmakers, John G. M.
  SDE based regression for random PDEs
  Appeared in: SIAM J. Sci. Comput., 39 (2017) pp. A1168--A1200.
• 2153: Eigel, Martin; Pfeffer, Max; Schneider, Reinhold
  Adaptive stochastic Galerkin FEM with hierarchical tensor representations
  Appeared in: Numer. Math., 136 (2017) pp. 765--803.
• 2060: Eigel, Martin; Merdon, Christian; Neumann, Johannes
  An adaptive multi level Monte--Carlo method with stochastic bounds for quantities of interest in groundwater flow with uncertain data
  Appeared in: SIAM ASA J. Uncertain. Quantif., 4 (2016) pp. 1219--1245.
• 1997: Eigel, Martin; Merdon, Christian
  Local equilibration error estimators for guaranteed error control in adaptive stochastic higher-order Galerkin FEM
  Appeared in: SIAM ASA J. Uncertain. Quantif., 4 (2016) pp. 1372--1397.
• 1959: Giese, Wolfgang; Eigel, Martin; Westerheide, Sebastian; Engwer, Christian; Klipp, Edda
  Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models
  Appeared in: Phys. Biol., 12 (2015) pp. 066014/1--18.
• 1936: Eigel, Martin; Samrowski, Tatiana
  Functional a posteriori error estimation for stationary reaction-convection-diffusion problems
  Appeared in: Comput. Methods Appl. Math., 14 (2014) pp. 135--150.
• 1911: Eigel, Martin; Gittelson, Claude Jeffrey; Schwab, Christoph; Zander, Elmar
  A convergent adaptive stochastic Galerkin finite element method with quasi-optimal spatial meshes
  Appeared in: ESAIM Math. Model. Numer. Anal., 49 (2015) pp. 1367--1398.
• 1833: Eigel, Martin; Peterseim, Daniel
  Simulation of composite materials by a Network FEM with error control
  Appeared in: Comput. Methods Appl. Math., 15 (2015) pp. 21--37.
• 1822: Eigel, Martin; Merdon, Christian
  Robust equilibration a posteriori error estimation for convection-diffusion-reaction problems
  Appeared in: J. Sci. Comput., 67 (2016) pp. 747--768 under the title “Equilibration a posteriori error estimation for convection-diffusion-reaction problems”