3 citations · 6 across the 17 of their papers we have counts for
22 papers
On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data
Michael Griebel, Guanglian Li, Christian Rieger
In many applications, random fields reflect uncertain parameters, and often their moments are part of the modeling process and thus well known. However, there are practical situati…
A Dimension-adaptive Combination Technique for Uncertainty Quantification
Uta Seidler, Michael Griebel
We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized b…
Low-rank approximation of continuous functions in Sobolev spaces with dominating mixed smoothness
Michael Griebel, Helmut Harbrecht, Reinhold Schneider
Let , , be given domains. In this article, we study the low-rank approximation with respect to of functions…
On the Numerical Approximation of the Karhunen-Loève Expansion for Random Fields with Random Discrete Data
Michael Griebel, Guanglian Li, Christian Rieger
Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--different…
A dimension-oblivious domain decomposition method based on space-filling curves
Michael Griebel, Marc Alexander Schweitzer, Lukas Troska
In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed paralle…
Deep Neural Networks and PIDE discretizations
Bastian Bohn, Michael Griebel, Dinesh Kannan
In this paper, we propose neural networks that tackle the problems of stability and field-of-view of a Convolutional Neural Network (CNN). As an alternative to increasing the netwo…
A fault-tolerant domain decomposition method based on space-filling curves
Michael Griebel, Marc-Alexander Schweitzer, Lukas Troska
We propose a simple domain decomposition method for -dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse prob…
Sparse tensor product approximation for a class of generalized method of moments estimators
Alexandros Gilch, Michael Griebel, Jens Oettershagen
Generalized Method of Moments (GMM) estimators in their various forms, including the popular Maximum Likelihood (ML) estimator, are frequently applied for the evaluation of complex…
Maximum Approximated Likelihood Estimation
Michael Griebel, Florian Heiss, Jens Oettershagen +1
Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature…
On the Numerical Approximation of the Karhunen-Loève Expansion for Lognormal Random Fields
Michael Griebel, Guanglian Li
The Karhunen-Loève (KL) expansion is a popular method for approximating random fields by transforming an infinite-dimensional stochastic domain into a finite-dimensional parameter…
Analysis of tensor approximation schemes for continuous functions
Michael Griebel, Helmut Harbrecht
In this article, we analyze tensor approximation schemes for continuous functions. We assume that the function to be approximated lies in an isotropic Sobolev space and discuss the…
Kernel-based stochastic collocation for the random two-phase Navier-Stokes equations
Michael Griebel, Christian Rieger, Peter Zaspel
In this work, we apply stochastic collocation methods with radial kernel basis functions for an uncertainty quantification of the random incompressible two-phase Navier-Stokes equa…
Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
Bastian Bohn, Michael Griebel, Jens Oettershagen
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved…
Stochastic subspace correction methods and fault tolerance
Michael Griebel, Peter Oswald
We present convergence results in expectation for stochastic subspace correction schemes and their accelerated versions to solve symmetric positive-definite variational problems, a…
Stochastic subspace correction in Hilbert space
Michael Griebel, Peter Oswald
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected su…
A representer theorem for deep kernel learning
Bastian Bohn, Michael Griebel, Christian Rieger
In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert…
On the expected uniform error of Brownian motion approximated by the Lévy-Ciesielski construction
Bruce Brown, Michael Griebel, Frances Y. Kuo +1
It is known that the Brownian bridge or Lévy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus…
An Adaptive Multiscale Approach for Electronic Structure Methods
Sambasiva Rao Chinnamsetty, Michael Griebel, Jan Hamaekers
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schrödinger equation for molecules. It is based on the combination of a many-body e…
Hilbert function space splittings on domains with infinitely many variables
Michael Griebel, Peter Oswald
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based o…
Multilevel quadrature for elliptic parametric partial differential equations in case of polygonal approximations of curved domains
Michael Griebel, Helmut Harbrecht, Michael D. Multerer
Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation be…
Hyperbolic cross approximation in infinite dimensions
Dinh Dũng, Michael Griebel
We give tight upper and lower bounds of the cardinality of the index sets of certain hyperbolic crosses which reflect mixed Sobolev-Korobov-type smoothness and mixed Sobolev-analyt…
Schwarz Iterative Methods: Infinite Space Splittings
Michael Griebel, Peter Oswald
We prove the convergence of greedy and randomized versions of Schwarz iterative methods for solving linear elliptic variational problems based on infinite space splittings of a Hil…