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Results for “multi-dimensional multi-resolution analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

An Adaptive Wavelet Stochastic Collocation Method for Irregular Solutions of Stochastic Partial Differential Equations

Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.

adaptive sparse grids↗
DOE OSTI2016

Statistical Projections for Multi-resolution, Multi-dimensional Visual Data Exploration and Analysis

An ongoing challenge in visual exploration and analysis of large, multi-dimensional datasets is how to present useful, concise information to a user for some specific visualization tasks. Typical approaches to this problem have proposed either reduced-resolution versions of data, or projections of data, or both. These approaches still have some limitations such as consuming high computation or suffering from errors. In this work, we explore the use of a statistical metric as the basis for both projections and reduced-resolution versions of data, with a particular focus on preserving one key trait in data, namely variation. We use two different case studies to explore this idea, one that uses a synthetic dataset, and another that uses a large ensemble collection produced by an atmospheric modeling code to study long-term changes in global precipitation. The primary findings of our work are that in terms of preserving the variation signal inherent in data, that using a statistical measure more faithfully preserves this key characteristic across both multi-dimensional projections and multi-resolution representations than a methodology based upon averaging.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Fast Detection of Material Deformation through Structural Dissimilarity

Designing materials that are resistant to extreme temperatures and brittleness relies on assessing structural dynamics of samples. Algorithms are critically important to characterize material deformation under stress conditions. Here, we report on our design of coarse-grain parallel algorithms for image quality assessment based on structural information and on crack detection of gigabyte-scale experimental datasets. We show how key steps can be decomposed into distinct processing flows, one based on structural similarity (SSIM) quality measure, and another on spectral content. These algorithms act upon image blocks that fit into memory, and can execute independently. We discuss the scientific relevance of the problem, key developments, and decomposition of complementary tasks into separate executions. We show how to apply SSIM to detect material degradation, and illustrate how this metric can be allied to spectral analysis for structure probing, while using tiled multi-resolution pyramids stored in HDF5 chunked multi-dimensional arrays. Results show that the proposed experimental data representation supports an average compression rate of 10X, and data compression scales linearly with the data size. We also illustrate how to correlate SSIM to crack formation, and how to use our numerical schemes to enable fast detection of deformation from 3D datasets evolving in time.

Ushizima, Daniela↗