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Matrix completion for cost reduction in finite element simulations under hybrid uncertainties

机译：混合不确定性下有限元模拟中成本降低的矩阵完成

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摘要

In recent years, uncertainty appears in different aspects of physical simulations including probabilistic boundary, stochastic loading, and multiscale modeling. Stretching across engineering domains and applied mathematics, uncertainty quantification is a multi-disciplinary field which is an inseparable part of risk analysis. However, many real-world problems deal with large number of simulations or experiments. Considering the limited budget and time to perform all these efforts (specially for practitioners), an essential task is to reduce the computational cost in an uncertain environment.This paper proposes to use a matrix completion technique for reducing the overall computational cost of engineering systems when they are subjected to the simultaneous effects of aleatory and epistemic uncertainties with high dimensions. The proposed method is further improved using hidden information in the uncertain variables based on clustering techniques. Several parametric and Monte Carlo simulations were performed to demonstrate the accuracy of our method with different compression ratios. Experimental results show a decent overall performance of our technique for high-dimensional hybrid uncertain systems. (C) 2018 Elsevier Inc. All rights reserved.
机译：近年来，不确定性出现在物理模拟的不同方面，包括概率边界，随机负载和多尺度建模。不确定性量化遍及工程领域和应用数学，是一个多学科领域，是风险分析不可分割的一部分。但是，许多实际问题都涉及大量的仿真或实验。考虑到执行所有这些工作的预算和时间有限（特别是针对从业人员），一项基本任务是降低不确定环境中的计算成本。本文提出使用矩阵完成技术来降低工程系统的总体计算成本。它们同时受到高维度偶然和认知不确定性的影响。基于聚类技术，利用不确定变量中的隐藏信息对提出的方法进行了进一步的改进。进行了几次参数和蒙特卡洛模拟，以证明我们的方法在不同压缩比下的准确性。实验结果表明，我们的技术在高维混合不确定系统中具有良好的整体性能。 （C）2018 Elsevier Inc.保留所有权利。

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