Multifidelity Uncertainty Quantification Using Spectral Stochastic Discrepancy Models.
Multifidelity Uncertainty Quantification Using Spectral Stochastic Discrepancy Models.
复制标题
使用谱随机差异模型进行多保真度不确定性量化。
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
S. Domino
中科院分区：
文献类型：
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作者：
M. Eldred;L. W. Ng;M. Barone;S. Domino
当面临当今高保真仿真模型典型的限制性评估预算时，在不确定性量化 (UQ) 过程中有效利用低保真度替代方案变得至关重要。在此，我们探索了昆士兰大学内多保真度建模的使用，为此，我们在保真度层次结构中严格组合来自多个基于模拟的模型的信息，以较低的计算成本寻求准确的高保真统计数据。在校正函数的推动下，校正函数能够将多重保真度优化方法可证明地收敛到最优的高保真点解，我们将这些想法扩展到随机域内的差异建模，并寻求多重保真度不确定性量化过程向全局集成的高保真统计数据的收敛。为了构建低保真模型和模型差异的随机模型，我们采用通过结构化稀疏网格上的积分/插值或非结构化网格上的正则化回归计算的随机扩展方法（非侵入式多项式混沌和随机搭配）。我们寻求采用粗略解析的网格来解决差异，并结合更精细解析的网格来解决低保真度模型。这些网格的分辨率可以静态定义或通过统一和自适应细化过程确定。自适应细化特别有吸引力，因为它能够优先定位模型差异变得更加复杂的随机区域，即低保真模型的预测能力开始崩溃并且需要更多地依赖高保真模型（通过差异）的区域。这些自适应细化过程可以针对不同网格单独执行，也可以在协调的多保真度算法内执行。特别是，我们提出了一种自适应贪婪多保真方法，其中我们扩展了广义稀疏网格概念，以考虑从多个稀疏网格中提取的候选索引集细化，由感兴趣的统计量的诱发变化控制并通过相对计算成本进行归一化。通过使用静态定义的稀疏网格、自适应多保真稀疏网格和多保真压缩感知的一系列数值实验，我们证明了在差异方差相对于高保真模型方差减小（导致初始随机误差减小）的情况下，多保真UQ过程比单保真UQ过程收敛得更快，其中模型差异的扩展系数的频谱比高保真模型差异的扩展系数的频谱衰减得更快。高保真模型（导致收敛速度加快），和/或差异比高保真模型更稀疏（需要恢复较少的重要项）。使用谱随机的多保真度不确定性量化。 。 。 3
When faced with a restrictive evaluation budget that is typical of today’s highfidelity simulation models, the effective exploitation of lower-fidelity alternatives within the uncertainty quantification (UQ) process becomes critically important. Herein, we explore the use of multifidelity modeling within UQ, for which we rigorously combine information from multiple simulation-based models within a hierarchy of fidelity, in seeking accurate high-fidelity statistics at lower computational cost. Motivated by correction functions that enable the provable convergence of a multifidelity optimization approach to an optimal high-fidelity point solution, we extend these ideas to discrepancy modeling within a stochastic domain and seek convergence of a multifidelity uncertainty quantification process to globally integrated high-fidelity statistics. For constructing stochastic models of both the low-fidelity model and the model discrepancy, we employ stochastic expansion methods (non-intrusive polynomial chaos and stochastic collocation) computed by integration/interpolation on structured sparse grids or regularized regression on unstructured grids. We seek to employ a coarsely resolved grid for the discrepancy in combination with a more finely resolved grid for the low-fidelity model. The resolutions of these grids may be defined statically or determined through uniform and adaptive refinement processes. Adaptive refinement is particularly attractive, as it has the ability to preferentially target stochastic regions where the model discrepancy becomes more complex, i.e., where the predictive capabilities of the low-fidelity model start to break down and greater reliance on the high-fidelity model (via the discrepancy) is necessary. These adaptive refinement processes can either be performed separately for the different grids or within a coordinated multifidelity algorithm. In particular, we present an adaptive greedy multifidelity approach in which we extend the generalized sparse grid concept to consider candidate index set refinements drawn from multiple sparse grids, as governed by induced changes in the statistical quantities of interest and normalized by relative computational cost. Through a series of numerical experiments using statically defined sparse grids, adaptive multifidelity sparse grids, and multifidelity compressed sensing, we demonstrate that the multifidelity UQ process converges more rapidly than a single-fidelity UQ in cases where the variance of the discrepancy is reduced relative to the variance of the high-fidelity model (resulting in reductions in initial stochastic error), where the spectrum of the expansion coefficients of the model discrepancy decays more rapidly than that of the high-fidelity model (resulting in accelerated convergence rates), and/or where the discrepancy is more sparse than the high-fidelity model (requiring the recovery of fewer significant terms). Multifidelity Uncertainty Quantification Using Spectral Stochastic. . . 3
影响因子：
2.7
作者：
Giles, Michael B.
通讯作者：
Giles, Michael B.
影响因子：
2.1
作者：
Barth, Andrea;Schwab, Christoph;Zollinger, Nathaniel
通讯作者：
Zollinger, Nathaniel