Related papers: Local and Dimension Adaptive Sparse Grid Interpola…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…

Structured kernel interpolation (SKI) accelerates Gaussian process (GP) inference by interpolating the kernel covariance function using a dense grid of inducing points, whose corresponding kernel matrix is highly structured and thus…

We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…

This paper continues to develop a fault tolerant extension of the sparse grid combination technique recently proposed in [B. Harding and M. Hegland, ANZIAM J., 54 (CTAC2012), pp. C394-C411]. The approach is novel for two reasons, first it…

Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…

Sparse grids are popular tools for high-dimensional function approximation. In this work, we study the use of sparse grids for interpolation using separable Mat\'ern kernels…

We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…

We propose a scalable method for computing global solutions of nonlinear, high-dimensional dynamic stochastic economic models. First, within a time iteration framework, we approximate economic policy functions using an adaptive,…

In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…

We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic PDE where the diffusion coefficient is parametrized by means of a Karhunen-Lo\`eve expansion. The approximation…

The simulation of high-dimensional problems with manageable computational resource represents a long-standing challenge. In a series of our recent work [25, 17, 18, 24], a class of sparse grid DG methods has been formulated for solving…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

The \emph{deterministic} sparse grid method, also known as Smolyak's method, is a well-established and widely used tool to tackle multivariate approximation problems, and there is a vast literature on it. Much less is known about…

As we aim at alleviating the curse of high-dimensionality, subspace learning is becoming more popular. Existing approaches use either information about global or local structure of the data, and few studies simultaneously focus on global…

In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…

In this paper, a sparsity-aware adaptive algorithm for distributed learning in diffusion networks is developed. The algorithm follows the set-theoretic estimation rationale. At each time instance and at each node of the network, a closed…

We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the…

Interpolation of sparse pixel information towards a dense target resolution finds its application across multiple disciplines in computer vision. State-of-the-art interpolation of motion fields applies model-based interpolation that makes…

This paper considers a distributed stochastic non-convex optimization problem, where the nodes in a network cooperatively minimize a sum of $L$-smooth local cost functions with sparse gradients. By adaptively adjusting the stepsizes…

In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions…