4 citations · 14 across the 8 of their papers we have counts for
15 papers
Numerical Methods for Dynamical Low-Rank Approximations of Stochastic Differential Equations -- Part II: Stochastic discretization
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
This paper is the follow up (Part II) of arXiv:2601.21428, which proposed and analyzed time discretization schemes for the Dynamical Low-Rank Approximation (DLRA) of high-dimension…
Existence of Dynamical Low-Rank Approximation for SDEs with Locally Lipschitz Coefficients
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this work, we consider the Dynamical Low Rank Approximation (DLRA) of a high-dimensional system of Stochastic Differential Equations (SDEs); DLRA is an effective reduced order m…
Further Approaches of Dynamical Low-Rank Approximation for SDEs
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this article, we propose two other DLRA-type dynamics for stochastic differential equations (SDEs) than the one studied in arXiv:2308.11581, derived from a minimization of funct…
Dynamical Low-Rank Filters for Data Assimilation
Yoshihito Kazashi, Youssef Marzouk, Fabio Nobile +1
We propose dynamical low-rank (DLRA) filters for data-assimilation problems based on stochastic differential equations (SDEs). We first consider a Kalman filter applied to a Euler-…
Numerical Methods for Dynamical Low-Rank Approximations of Stochastic Differential Equations -- Part I: Time discretization
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this work (Part I), we study three time-discretization schemes for the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Spec…
Dynamical Low-Rank Approximation for Stochastic Differential Equations
Yoshihito Kazashi, Fabio Nobile, Fabio Zoccolan
In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating th…
Density estimation in RKHS with application to Korobov spaces in high dimensions
Yoshihito Kazashi, Fabio Nobile
A kernel method for estimating a probability density function (pdf) from an i.i.d. sample drawn from such density is presented. Our estimator is a linear combination of kernel func…
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…
Stability properties of a projector-splitting scheme for dynamical low rank approximation of random parabolic equations
Yoshihito Kazashi, Fabio Nobile, Eva Vidličková
We consider the Dynamical Low Rank (DLR) approximation of random parabolic equations and propose a class of fully discrete numerical schemes. Similarly to the continuous DLR approx…
Existence of dynamical low rank approximations for random semi-linear evolutionary equations on the maximal interval
Yoshihito Kazashi, Fabio Nobile
An existence result is presented for the dynamical low rank (DLR) approximation for random semi-linear evolutionary equations. The DLR solution approximates the true solution at ea…
Derandomised lattice rules for high dimensional integration
Yoshihito Kazashi, Frances Y. Kuo, Ian H. Sloan
We seek shifted lattice rules that are good for high dimensional integration over the unit cube in the setting of an unanchored weighted Sobolev space of functions with square-inte…
Worst-case error for unshifted lattice rules without randomisation
Yoshihito Kazashi, Frances Y. Kuo, Ian H. Sloan
An existence result is presented for the worst-case error of lattice rules for high dimensional integration over the unit cube, in an unanchored weighted space of functions with sq…
A non-uniform discretization of stochastic heat equations with multiplicative noise on the unit sphere
Yoshihito Kazashi, Quoc T. Le Gia
We investigate a discretization of a class of stochastic heat equations on the unit sphere with multiplicative noises. A spectral method is used for the spatial discretization and…
Quasi-Monte Carlo integration with product weights for elliptic PDEs with log-normal coefficients
Yoshihito Kazashi
Quasi-Monte Carlo (QMC) integration of output functionals of solutions of the diffusion problem with a log-normal random coefficient is considered. The random coefficient is assume…
A fully discretised filtered polynomial approximation on spherical shells
Yoshihito Kazashi
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation.…