International Journal for Uncertainty Quantification最新文献_第4页

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023045369

Miguel Angel Alvarez Ballesteros, Neil K. Chada, Ajay Jasra

{"title":"UNBIASED ESTIMATION OF THE VANILLA AND DETERMINISTIC ENSEMBLE KALMAN-BUCY FILTERS","authors":"Miguel Angel Alvarez Ballesteros, Neil K. Chada, Ajay Jasra","doi":"10.1615/int.j.uncertaintyquantification.2023045369","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023045369","url":null,"abstract":"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 &#8594; &#8734;, 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.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135636630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023045300

Isaac Sunseri, Alen Alexanderian, Joseph Hart, Bart Van Bloemen Waanders

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023047256

Niklas Miska, S. Freitag, D. Balzani

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023045687

M. Ganesh, S. Hawkins, A. Tartakovsky, R. Tipireddy

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023041042

Jeferson Osmar de Almeida, F. Rochinha

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023044543

Andrew White, S. Mahadevan

引用次数: 0

HIGH-DIMENSIONAL STOCHASTIC DESIGN OPTIMIZATION UNDER DEPENDENT RANDOM VARIABLES BY A DIMENSIONALLY DECOMPOSED GENERALIZED POLYNOMIAL CHAOS EXPANSION 基于维数分解的广义多项式混沌展开的因变量下高维随机设计优化

IF 1.7 4区工程技术

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023043457

Dongjin Lee, S. Rahman

引用次数: 3

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2022039993

Jigar Parekh, Roel Verstappen

{"title":"QUANTIFICATION AND PROPAGATION OF MODEL-FORM UNCERTAINTIES IN RANS TURBULENCE MODELING VIA INTRUSIVE POLYNOMIAL CHAOS","authors":"Jigar Parekh, Roel Verstappen","doi":"10.1615/int.j.uncertaintyquantification.2022039993","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2022039993","url":null,"abstract":"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.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135235913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

International Journal for Uncertainty Quantification Pub Date : 2023-01-01 DOI: 10.1615/int.j.uncertaintyquantification.2023046861

Michael Griebel, Uta Seidler

{"title":"A Dimension-adaptive Combination Technique for Uncertainty Quantification","authors":"Michael Griebel, Uta Seidler","doi":"10.1615/int.j.uncertaintyquantification.2023046861","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023046861","url":null,"abstract":"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.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135445089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

International Journal for Uncertainty Quantification 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

{"title":"Hyper-differential sensitivity analysis in the context of Bayesian inference applied to ice-sheet problems","authors":"William Reese, Joseph Hart, Bart van Bloemen Waanders, Mauro Perego, John Jakeman, Arvind Saibaba","doi":"10.1615/int.j.uncertaintyquantification.2023047605","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023047605","url":null,"abstract":"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.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135211134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1