2 citations · 4 across the 7 of their papers we have counts for
10 papers
Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems
Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke +1
Sampling from the posterior is the central task of computational Bayesian inverse problems. The standard workhorse in Bayesian inference - Markov chain Monte Carlo (MCMC) - is sequ…
Efficient solution of parameter identification problems with regularization
Jan Blechta, Oliver G. Ernst
We consider the identification of spatially distributed parameters under regularization. Solving the associated minimization problem by Gauss-Newton iteration results in line…
Three Ways to Solve Partial Differential Equations with Neural Networks -- A Review
Jan Blechschmidt, Oliver G. Ernst
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three importa…
Integrability and Approximability of Solutions to the Stationary Diffusion Equation with Lévy Coefficient
Oliver G. Ernst, Hanno Gottschalk, Thomas Kalmes +2
We investigate the stationary diffusion equation with a coefficient given by a (transformed) Lévy random field. Lévy random fields are constructed by smoothing Lévy noise fields wi…
Regularization for the inversion of Fibre Bragg Grating spectra
Daniel Gerth, Susann Hannusch, Oliver Ernst +1
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is sim…
On the convergence of adaptive stochastic collocation for elliptic partial differential equations with affine diffusion
Martin Eigel, Oliver Ernst, Björn Sprungk +1
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on…
Wasserstein sensitivity of Risk and Uncertainty Propagation
Oliver G. Ernst, Alois Pichler, Björn Sprungk
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a se…
On Expansions and Nodes for Sparse Grid Collocation of Lognormal Elliptic PDEs
Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini
This work is a follow-up to our previous contribution ("Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PD…
Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs)
Oliver G. Ernst, Björn Sprungk, Lorenzo Tamellini
We give a convergence proof for the approximation by sparse collocation of Hilbert-space-valued functions depending on countably many Gaussian random variables. Such functions appe…
Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems
Oliver G. Ernst, Björn Sprungk, Hans-Jörg Starkloff
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary pro…