From the 2 of 11 linked papers with an AI index.
11 papers
On the optimality of dimension truncation error rates for a class of parametric partial differential equations
Philipp A. Guth, Vesa Kaarnioja
The paper analyzes the error introduced when infinite-dimensional random field inputs in parametric PDEs are truncated to finite dimensions, and proves that the known dimension‑tru…
Quasi-Monte Carlo for Bayesian design of experiment problems governed by parametric PDEs
Vesa Kaarnioja, Claudia Schillings
The paper studies Bayesian optimal experimental design for PDE-governed inverse problems, deriving regularity estimates and analyzing quasi‑Monte Carlo integration using full and s…
Quasi-Monte Carlo for Bayesian shape inversion governed by the Poisson problem subject to Gevrey regular domain deformations
Ana Djurdjevac, Vesa Kaarnioja, Max Orteu +1
We consider the application of a quasi-Monte Carlo cubature rule to Bayesian shape inversion subject to the Poisson equation under Gevrey regular parameterizations of domain uncert…
Lattice Rules Meet Kernel Cubature
Vesa Kaarnioja, Ilja Klebanov, Claudia Schillings +1
Rank-1 lattice rules are a class of equally weighted quasi-Monte Carlo methods that achieve essentially linear convergence rates for functions in a reproducing kernel Hilbert space…
Uncertainty quantification for stationary and time-dependent PDEs subject to Gevrey regular random domain deformations
Ana Djurdjevac, Vesa Kaarnioja, Claudia Schillings +1
We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chern…
Sufficient conditions for QMC analysis of finite elements for parametric differential equations
Vesa Kaarnioja, Andreas Rupp, Jay Gopalakrishnan
Parametric regularity of discretizations of flux vector fields satisfying a balance law is studied under some assumptions on a random parameter that links the flux with an unknown…