17 citations · 33 across the 17 of their papers we have counts for
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A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields
Markus Bachmayr, Martin Eigel, Henrik Eisenmann +1
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product p…
Weighted sparsity and sparse tensor networks for least squares approximation
Philipp Trunschke, Anthony Nouy, Martin Eigel
Approximation of high-dimensional functions is a problem in many scientific fields that is only feasible if advantageous structural properties, such as sparsity in a given basis, c…
On the convergence of adaptive Galerkin FEM for parametric PDEs with lognormal coefficients
Martin Eigel, Nando Hegemann
Numerically solving high-dimensional random parametric PDEs poses a challenging computational problem. It is well-known that numerical methods can greatly benefit from adaptive ref…
Less interaction with forward models in Langevin dynamics
Martin Eigel, Robert Gruhlke, David Sommer
Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invari…
Generative modeling with low-rank Wasserstein polynomial chaos expansions
Robert Gruhlke, Martin Eigel
A new Wasserstein multi-element polynomial chaos expansion (WPCE) is proposed, which is inspired by recent advances in computational optimal transport for estimating Wasserstein di…
Adaptive non-intrusive reconstruction of solutions to high-dimensional parametric PDEs
Martin Eigel, Nando Farchmin, Sebastian Heidenreich +1
Numerical methods for random parametric PDEs can greatly benefit from adaptive refinement schemes, in particular when functional approximations are computed as in stochastic Galerk…