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Uncertainty Quantification by Gaussian Random Fields for Point-Like Emissions from Satellite Observations 用高斯随机场量化卫星观测点状辐射的不确定性
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023044906
Teemu Härkönen, A. Sundström, J. Tamminen, J. Hakkarainen, E. Vakkilainen, H. Haario
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引用次数: 0
UNBIASED ESTIMATION OF THE VANILLA AND DETERMINISTIC ENSEMBLE KALMAN-BUCY FILTERS 香草和确定性集合卡尔曼-布希滤波器的无偏估计
4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023045369
Miguel Angel Alvarez Ballesteros, Neil K. Chada, Ajay Jasra
In this paper, we consider the development of unbiased estimators for the ensemble Kalman-Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology, which can be viewed as a continuous-time analog of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work (Rhee and Glynn, Oper. Res., 63:1026-1053, 2015) which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of discretization and through the number of samples at each level. Our unbiased estimator will be specific to models that are linear and Gaussian. This is due to the fact that the EnKBF itself is consistent, in the large particle limit N → ∞, with the Kalman-Bucy filter, which allows us one derive theoretical insights. Specifically, we introduce two unbiased EnKBF estimators that will be applied to two particular variants of the EnKBF, which are the deterministic and vanilla EnKBF. Numerical experiments are conducted on a linear Ornstein-Uhlenbeck process, which includes a high-dimensional example. Our unbiased estimators will be compared to the multilevel. We also provide a proof of the multilevel deterministic EnKBF, which provides a guideline for some of the unbiased methods.
本文研究了集成卡尔曼-布西滤波器(EnKBF)无偏估计量的发展。EnKBF是一种连续时间滤波方法,可以看作是著名的离散时间集合卡尔曼滤波的连续时间模拟。我们的无偏估计将从最近的工作中得到激励(Rhee和Glynn, Oper。Res., 63:1026- 1053,2015),其中引入了随机化作为产生无偏和有限方差估计量的手段。随机化通过离散化水平和每个水平上的样本数量进入。我们的无偏估计量将特定于线性和高斯模型。这是因为在大粒子极限N →∞,通过卡尔曼-布西滤波器,我们可以获得理论见解。具体来说,我们引入了两个无偏的EnKBF估计器,它们将应用于EnKBF的两个特定变体,即确定性和香草EnKBF。对一个包含高维算例的线性Ornstein-Uhlenbeck过程进行了数值实验。我们的无偏估计量将与多水平估计量进行比较。我们还提供了多层确定性EnKBF的证明,这为一些无偏方法提供了指导。
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引用次数: 1
Hyper-differential sensitivity analysis for nonlinear Bayesian inverse problems 非线性贝叶斯反问题的超微分灵敏度分析
4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023045300
Isaac Sunseri, Alen Alexanderian, Joseph Hart, Bart Van Bloemen Waanders
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by PDEs with infinite-dimensional parameters. In previous works, HDSA has been used to assess the sensitivity of the solution of deterministic inverse problems to additional model uncertainties and also different types of measurement data. In the present work, we extend HDSA to the class of Bayesian inverse problems governed by PDEs. The focus is on assessing the sensitivity of certain key quantities derived from the posterior distribution. Specifically, we focus on analyzing the sensitivity of the MAP point and the Bayes risk and make full use of the information embedded in the Bayesian inverse problem. After establishing our mathematical framework for HDSA of Bayesian inverse problems, we present a detailed computational approach for computing the proposed HDSA indices. We examine the effectiveness of the proposed approach on a model inverse problem governed by a PDE for heat conduction.
研究了具有无限维参数的偏微分方程控制的非线性贝叶斯反问题的超微分灵敏度分析(HDSA)。在以前的工作中,HDSA已被用于评估确定性逆问题解对附加模型不确定性和不同类型测量数据的敏感性。在本工作中,我们将HDSA推广到一类由偏微分方程控制的贝叶斯逆问题。重点是评估从后验分布得出的某些关键数量的敏感性。具体来说,我们着重分析了MAP点的敏感性和贝叶斯风险,充分利用了贝叶斯反问题所包含的信息。在建立了贝叶斯反问题HDSA的数学框架后,我们给出了计算所提出的HDSA指标的详细计算方法。我们检验了所提出的方法在由PDE控制的热传导模型逆问题上的有效性。
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引用次数: 0
Nested optimal uncertainty quantification for an efficient incorporation of random fields - Application to sheet metal forming 有效结合随机场的嵌套最优不确定度量化。在金属板成形中的应用
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023047256
Niklas Miska, S. Freitag, D. Balzani
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引用次数: 0
A stochastic domain decomposition and post-processing algorithm for epistemic uncertainty quantification 认知不确定性量化的随机域分解及后处理算法
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023045687
M. Ganesh, S. Hawkins, A. Tartakovsky, R. Tipireddy
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引用次数: 0
Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems 应用贝叶斯推理的超微分敏感性分析在冰盖问题中的应用
4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023047605
William Reese, Joseph Hart, Bart van Bloemen Waanders, Mauro Perego, John Jakeman, Arvind Saibaba
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the Bayesian formulation is attractive for such problems, computational cost and high dimensionality frequently prohibit a thorough exploration of the parametric uncertainty. A common approach is to reduce the dimension by fixing some parameters (which we will call auxiliary parameters) to a best estimate and use techniques from PDE-constrained optimization to approximate properties of the Bayesian posterior distribution. For instance, the maximum a posteriori probability (MAP) and the Laplace approximation of the posterior covariance can be computed. In this article, we propose using hyper-differential sensitivity analysis (HDSA) to assess the sensitivity of the MAP point to changes in the auxiliary parameters. We establish an interpretation of HDSA as correlations in the posterior distribution. Our proposed framework is demonstrated on the inversion of bedrock topography for the Greenland ice sheet with uncertainties arising from the basal friction coefficient and climate forcing (ice accumulation rate). %Foundational assumptions for HDSA require satisfaction of the optimality conditions which are not always feasible or appropriate as a result of ill-posedness in the inverse problem. %We introduce novel theoretical and computational approaches to justify and enable HDSA for ill-posed inverse problems by projecting the sensitivities on likelihood informed subspaces and defining a posteriori updates.
偏微分方程约束下的逆问题在模型开发和标定中起着至关重要的作用。在许多应用中,模型中存在多个不确定参数,必须对其进行估计。虽然贝叶斯公式对这类问题很有吸引力,但计算成本和高维数往往阻碍了对参数不确定性的深入探索。一种常见的方法是通过将一些参数(我们称之为辅助参数)固定为最佳估计来降低维数,并使用pde约束优化技术来近似贝叶斯后验分布的性质。例如,可以计算最大后验概率(MAP)和后验协方差的拉普拉斯近似。在本文中,我们建议使用超差灵敏度分析(HDSA)来评估MAP点对辅助参数变化的敏感性。我们将HDSA解释为后验分布中的相关性。我们提出的框架在格陵兰冰盖基岩地形的反演中得到了证明,其中存在由基底摩擦系数和气候强迫(冰积累率)引起的不确定性。HDSA的基本假设要求满足最优性条件,但由于逆问题的病态性,这些最优性条件并不总是可行或适当的。我们引入了新的理论和计算方法,通过在似然通知子空间上投影灵敏度和定义后验更新来证明和启用HDSA来解决不适定逆问题。
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引用次数: 1
QUANTIFICATION AND PROPAGATION OF MODEL-FORM UNCERTAINTIES IN RANS TURBULENCE MODELING VIA INTRUSIVE POLYNOMIAL CHAOS 基于入侵多项式混沌的随机湍流建模中模型形式不确定性的量化与传播
4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2022039993
Jigar Parekh, Roel Verstappen
Undeterred by its inherent limitations, Reynolds-averaged Navier-Stokes (RANS) based modeling is still considered the most recognized approach for several computational fluid dynamics (CFD) applications. Recently, in the turbulence modeling community, quantification of model-form uncertainties in RANS has attracted significant interest. We present a stochastic RANS solver with an efficient implementation of the intrusive polynomial chaos (IPC) method in OpenFOAM. The stochastic solver quantifies and propagates the uncertainties associated with the output of the RANS model (eddy viscosity or Reynolds stress tensor). Two distinct high-dimensional variants of the uncertainties are considered, namely, the random eddy viscosity field (REVF) and the random Reynolds stress tensor field (RRSTF). The randomness is introduced in the approximated eddy viscosity field and the Reynolds stress tensor, while asserting the realizability. The stochastic RANS solver has been tested on various benchmark problems for RANS turbulence modeling. In this study, we discuss two important problems where the stochastic RANS solver shows significantly better performance than the traditional uncertainty quantification (UQ) methods. The first problem analyzed is the flow over periodic hills with a REVF, while the second stochastic problem considered is the flow in a square duct with a RRSTF. Along with the comparison for three different RANS turbulence models, a detailed analysis of the stochastic solver based on various influential model parameters is also presented. The IPC based stochastic solver demonstrated the potential to be used in the UQ analysis of further complex CFD applications, especially when a large number of deterministic simulations is not feasible, e.g., wind farm CFD simulations.
尽管存在固有的局限性,基于reynolds -average Navier-Stokes (RANS)的建模仍然被认为是几种计算流体动力学(CFD)应用中最受认可的方法。最近,在湍流模拟界,RANS中模型形式不确定性的量化引起了极大的兴趣。本文提出了一种随机RANS求解器,并在OpenFOAM中有效地实现了入侵多项式混沌(IPC)方法。随机求解器量化和传播与RANS模型(涡流粘度或雷诺应力张量)输出相关的不确定性。考虑了不确定性的两个不同的高维变量,即随机涡流黏度场(REVF)和随机雷诺应力张量场(RRSTF)。在保证可实现性的同时,引入了涡流黏度近似场和雷诺应力张量的随机性。随机RANS求解器已经在RANS湍流建模的各种基准问题上进行了测试。在本研究中,我们讨论了两个重要的问题,其中随机RANS求解器比传统的不确定性量化(UQ)方法表现出明显更好的性能。分析的第一个问题是带REVF的周期性山丘的流动,而考虑的第二个随机问题是带RRSTF的方形管道中的流动。通过对三种不同的RANS湍流模型的比较,详细分析了基于各种影响模型参数的随机求解方法。基于IPC的随机求解器展示了在进一步复杂CFD应用的UQ分析中使用的潜力,特别是在大量确定性模拟不可行的情况下,例如风电场CFD模拟。
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引用次数: 1
A Dimension-adaptive Combination Technique for Uncertainty Quantification 一种不确定度量化的自适应组合技术
4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023046861
Michael Griebel, Uta Seidler
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 of the equivalent parametric problem requires a restriction of the countably infinite-dimensional parameter space to a finite-dimensional parameter set, a spatial discretization and an approximation in the parametric variables. We consider a sparse grid approach between these approximation directions in order to reduce the computational effort and propose a dimension-adaptive combination technique. In addition, a sparse grid quadrature for the high-dimensional parametric approximation is employed and simultaneously balanced with the spatial and stochastic approximation. Our adaptive algorithm constructs a sparse grid approximation based on the benefit-cost ratio such that the regularity and thus the decay of the Karhunen-Lo`eve coefficients is not required beforehand. The decay is detected and exploited as the algorithm adjusts to the anisotropy in the parametric variables. We include numerical examples for the Darcy problem with a lognormal permeability field, which illustrate a good performance of the algorithm: For sufficiently smooth random fields, we essentially recover the spatial order of convergence as asymptotic convergence rate with respect to the computational cost.
我们提出了一种自适应算法,用于计算涉及随机椭圆PDE解的感兴趣量,其中扩散系数是通过Karhunen-Lo ' eve展开参数化的。等效参数问题的逼近需要将可数无限维参数空间限制为有限维参数集,并进行空间离散化和参数变量的逼近。为了减少计算量,我们考虑在这些近似方向之间采用稀疏网格方法,并提出了一种自适应维数组合技术。此外,采用稀疏网格正交法进行高维参数逼近,并与空间逼近和随机逼近相平衡。我们的自适应算法构建了一个基于收益-成本比的稀疏网格近似,使得Karhunen-Lo ' eve系数的规律性和衰减不需要事先考虑。当算法调整参数变量的各向异性时,可以检测和利用衰减。我们包括具有对数正态渗透率场的Darcy问题的数值示例,这说明了该算法的良好性能:对于足够光滑的随机场,我们基本上恢复收敛的空间顺序作为相对于计算成本的渐近收敛速率。
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引用次数: 0
Uncertainty Quantification of water-flooding in oil reservoirs computational simulations using a probabilistic learning approach 基于概率学习方法的油藏注水计算模拟的不确定性量化
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023041042
Jeferson Osmar de Almeida, F. Rochinha
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引用次数: 2
Discrepancy modeling for model calibration with multivariate output 多变量输出模型校正的差异建模
IF 1.7 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023044543
Andrew White, S. Mahadevan
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引用次数: 0
期刊
International Journal for Uncertainty Quantification
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