From the 1 of 5 linked papers with an AI index.
5 papers
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…
Mixture-Weighted Ensemble Kalman Filter with Quasi-Monte Carlo Transport
Ilja Klebanov, Claudia Schillings, Dana Wrischnig
The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suf…
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…