15 citations · 34 across the 19 of their papers we have counts for
26 papers
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…
On the optimality of dimension truncation error rates for a class of parametric partial differential equations
Philipp A. Guth, Vesa Kaarnioja
In uncertainty quantification for parametric partial differential equations (PDEs), it is common to model uncertain random field inputs using countably infinite sequences of indepe…
New upper and lower bounds on the smallest singular values of nonsingular lower triangular -matrices
Vesa Kaarnioja, André-Alexander Zepernick
Let denote the set of all nonsingular lower triangular -matrices. Hong and Loewy (2004) introduced the number sequence $$ c_n=\min\{λ\midλ~\text{is an eige…
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…
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…
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 electrical impedance tomography using quasi-Monte Carlo methods
Laura Bazahica, Vesa Kaarnioja, Lassi Roininen
The theoretical development of quasi-Monte Carlo (QMC) methods for uncertainty quantification of partial differential equations (PDEs) is typically centered around simplified model…
Quasi-Monte Carlo for partial differential equations with generalized Gaussian input uncertainty
Philipp A. Guth, Vesa Kaarnioja
There has been a surge of interest in uncertainty quantification for parametric partial differential equations (PDEs) with Gevrey regular inputs. The Gevrey class contains function…
Quasi-Monte Carlo for Bayesian design of experiment problems governed by parametric PDEs
Vesa Kaarnioja, Claudia Schillings
This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the para…
Doubling the rate -- improved error bounds for orthogonal projection with application to interpolation
Ian H. Sloan, Vesa Kaarnioja
Convergence rates for approximation in a Hilbert space are a central theme in numerical analysis. The present work is inspired by Schaback (Math. Comp., 1999), who showed…
Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions
Vesa Kaarnioja, Frances Y. Kuo, Ian H. Sloan
We describe a fast method for solving elliptic partial differential equations (PDEs) with uncertain coefficients using kernel interpolation at a lattice point set. By representing…
Application of dimension truncation error analysis to high-dimensional function approximation in uncertainty quantification
Philipp A. Guth, Vesa Kaarnioja
Parametric mathematical models such as parameterizations of partial differential equations with random coefficients have received a lot of attention within the field of uncertainty…
Uncertainty quantification for random domains using periodic random variables
Harri Hakula, Helmut Harbrecht, Vesa Kaarnioja +2
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random domain, we use the model recently in…
Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond
Philipp A. Guth, Vesa Kaarnioja
Partial differential equations (PDEs) with uncertain or random inputs have been considered in many studies of uncertainty quantification. In forward uncertainty quantification, one…
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo +2
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints un…
Quasi-Monte Carlo and discontinuous Galerkin
Vesa Kaarnioja, Andreas Rupp
In this study, we consider the development of tailored quasi-Monte Carlo (QMC) cubatures for non-conforming discontinuous Galerkin (DG) approximations of elliptic partial different…
Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification
Vesa Kaarnioja, Yoshihito Kazashi, Frances Y. Kuo +2
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out…
Bounds on the spectrum of nonsingular triangular -matrices
Vesa Kaarnioja
Let be the set of all nonsingular lower triangular -matrices. Hong and Loewy (2004) introduced the numbers $$ c_n={\rm min}\{λ\mid λ~\text{is an eigenvalue…
A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty
Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo +2
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a…
Uncertainty quantification using periodic random variables
Vesa Kaarnioja, Frances Y. Kuo, Ian H. Sloan
Many studies in uncertainty quantification have been carried out under the assumption of an input random field in which a countable number of independent random variables are each…
Positive definite functions on semilattices
Vesa Kaarnioja, Pentti Haukkanen, Pauliina Ilmonen +1
We introduce a notion of positive definiteness for functions defined on meet semilattices and prove several properties for these functions…
Generalized eigenvalue problems for meet and join matrices on semilattices
Pauliina Ilmonen, Vesa Kaarnioja
We study generalized eigenvalue problems for meet and join matrices with respect to incidence functions on semilattices. We provide new bounds for generalized eigenvalues of meet m…
On the structure of join tensors with applications to tensor eigenvalue problems
Vesa Kaarnioja
We investigate the structure of join tensors, which may be regarded as the multivariable extension of lattice-theoretic join matrices. Explicit formulae for a polyadic decompositio…
Computation of extremal eigenvalues of high-dimensional lattice-theoretic tensors via tensor-train decompositions
Harri Hakula, Pauliina Ilmonen, Vesa Kaarnioja
This paper lies in the intersection of several fields: number theory, lattice theory, multilinear algebra, and scientific computing. We adapt existing solution algorithms for tenso…