Topic
Sparse grid
About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.
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01 Dec 2013
TL;DR: A novel adaptive sparse grid method for unsupervised image segmentation based on spectral clustering that is able to segment larger images by solving an eigenvalue system of dimensions 500 × 500 instead of 150,000 × 150, 000.
Abstract: We present a novel adaptive sparse grid method for unsupervised image segmentation. The method is based on spectral clustering. The use of adaptive sparse grids achieves that the dimensions of the involved eigensystem do not depend on the number of pixels. In contrast to classical spectral clustering, our sparse-grid variant is therefore able to segment larger images. We evaluate the method on real-world images from the Berkeley Segmentation Dataset. The results indicate that images with 150,000 pixels can be segmented by solving an eigenvalue system of dimensions 500 × 500 instead of 150, 000 × 150, 000.
2 citations
TL;DR: Some algorithms to solve the system of linear equations arising from the finite difference discretization on sparse grids using the multilevel structure of the sparse grid space or its full grid subspaces are proposed.
Abstract: We propose some algorithms to solve the system of linear equations arising from the finite difference discretization on sparse grids. For this, we will use the multilevel structure of the sparse grid space or its full grid subspaces, respectively.
2 citations
01 Jan 2014
TL;DR: Numerical evidence is given that adaptive sparse grids are applicable in the case of reinforcement learning for model-based online reinforcement learning.
Abstract: We propose a model-based online reinforcement learning approach for continuous domains with deterministic transitions using a spatially adaptive sparse grid in the planning stage. The model learning employs Gaussian processes regression and allows a low sample complexity. The adaptive sparse grid is introduced to allow the representation of the value function in the planning stage in higher dimensional state spaces. This work gives numerical evidence that adaptive sparse grids are applicable in the case of reinforcement learning.
2 citations
TL;DR: An adaptive method is proposed, steered by dual error indicators, which combines rational Arnoldi model order reduction and sparse grid interpolation with hierarchical Leja nodes to achieve a prescribed accuracy in statistical moments in discrete linear systems in the frequency domain.
2 citations
TL;DR: In this article, a sparse grid-based interval and random polynomial expansion method, called Sparse Grids' Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, was proposed to obtain the response of a vibro-acoustic system with random uncertainties.
Abstract: For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the simplicity of the traditional arbitrary polynomial chaos method, while avoiding its inefficiency. In the SGS-IRAPC, the response is approximated by the moment-based arbitrary polynomial chaos expansion and the expansion coefficient is determined by the least squares approximation method. A new sparse sampling scheme combined the sparse grids’ scheme with the sequential sampling scheme which is employed to generate the sampling points used to calculate the expansion coefficient to decrease the computational cost. The efficiency of the proposed surrogate method is demonstrated using a typical mathematical problem and an engineering application.
2 citations