74 citations · 142 across the 17 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…
On the Convergence of the Laplace Approximation and Noise-Level-Robustness of Laplace-based Monte Carlo Methods for Bayesian Inverse Problems
Claudia Schillings, Björn Sprungk, Philipp Wacker
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are int…
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…