Siam-Asa Journal on Uncertainty Quantification最新文献_第7页

A Multilevel Stochastic Collocation Method for Schrödinger Equations with a Random Potential 具有随机势的Schrödinger方程的多层随机配置方法

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-12-20 DOI: 10.1137/21m1440517

T. Jahnke, B. Stein

引用次数: 0

Uncertainty Quantification by Multilevel Monte Carlo and Local Time-Stepping for Wave Propagation 波传播的多电平蒙特卡罗和局部时间步进不确定性量化

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-12-05 DOI: 10.1137/21m1429047

M. Grote, Simon Michel, F. Nobile

引用次数: 1

Statistical Finite Elements via Langevin Dynamics 基于朗格万动力学的统计有限元

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-12-05 DOI: 10.1137/21m1463094

Ömer Deniz Akyildiz, Connor Duffin, Sotirios Sabanis, Mark Girolami

{"title":"Statistical Finite Elements via Langevin Dynamics","authors":"Ömer Deniz Akyildiz, Connor Duffin, Sotirios Sabanis, Mark Girolami","doi":"10.1137/21m1463094","DOIUrl":"https://doi.org/10.1137/21m1463094","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 10, Issue 4, Page 1560-1585, December 2022. <br/> Abstract. The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesize finite element models with observed data. Through embedding uncertainty inside of the governing equations, finite element solutions are updated to give a posterior distribution which quantifies all sources of uncertainty associated with the model. However to incorporate all sources of uncertainty, one must integrate over the uncertainty associated with the model parameters, the known forward problem of uncertainty quantification. In this paper, we make use of Langevin dynamics to solve the statFEM forward problem, studying the utility of the unadjusted Langevin algorithm (ULA), a Metropolis-free Markov chain Monte Carlo sampler, to build a sample-based characterization of this otherwise intractable measure. Due to the structure of the statFEM problem, these methods are able to solve the forward problem without explicit full PDE solves, requiring only sparse matrix-vector products. ULA is also gradient-based, and hence provides a scalable approach up to high degrees-of-freedom. Leveraging the theory behind Langevin-based samplers, we provide theoretical guarantees on sampler performance, demonstrating convergence, for both the prior and posterior, in the Kullback–Leibler divergence and in Wasserstein-2, with further results on the effect of preconditioning. Numerical experiments are also provided, to demonstrate the efficacy of the sampler, with a Python package also included.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A Locally Adapted Reduced-Basis Method for Solving Risk-Averse PDE-Constrained Optimization Problems 求解风险规避pde约束优化问题的局部自适应降基方法

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-12-05 DOI: 10.1137/21m1411342

Zilong Zou, Drew P. Kouri, Wilkins Aquino

引用次数: 0

Corrigendum: "Existence and Optimality Conditions for Risk-Averse PDE-Constrained Optimization" 更正:“风险规避pde约束优化的存在性和最优性条件”

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-09-30 DOI: 10.1137/21m143251x

D. Kouri, T. Surowiec

引用次数: 1

Extrapolated Polynomial Lattice Rule Integration in Computational Uncertainty Quantification 计算不确定性量化中的外推多项式格规则积分

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-06-29 DOI: 10.1137/20m1338137

J. Dick, M. Longo, C. Schwab

引用次数: 2

Multilevel Delayed Acceptance MCMC 多层延迟接受MCMC

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-02-08 DOI: 10.1137/22m1476770

Mikkel B. Lykkegaard, T. Dodwell, C. Fox, Grigorios Mingas, Robert Scheichl

引用次数: 5

A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors Gamma超先验反问题的变分推理方法

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2021-11-26 DOI: 10.1137/21m146209x

Shivendra Agrawal, Hwanwoo Kim, D. Sanz-Alonso, A. Strang

引用次数: 6

A Spline Dimensional Decomposition for Uncertainty Quantification in High Dimensions 高维不确定度量化的样条维数分解

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2021-11-25 DOI: 10.1137/20m1364175

S. Rahman, Ramin Jahanbin

{"title":"A Spline Dimensional Decomposition for Uncertainty Quantification in High Dimensions","authors":"S. Rahman, Ramin Jahanbin","doi":"10.1137/20m1364175","DOIUrl":"https://doi.org/10.1137/20m1364175","url":null,"abstract":"This study debuts a new spline dimensional decomposition (SDD) for uncertainty quantification analysis of high-dimensional functions, including those endowed with high nonlinearity and nonsmoothness, if they exist, in a proficient manner. The decomposition creates an hierarchical expansion for an output random variable of interest with respect to measure-consistent orthonormalized basis splines (B-splines) in independent input random variables. A dimensionwise decomposition of a spline space into orthogonal subspaces, each spanned by a reduced set of such orthonormal splines, results in SDD. Exploiting the modulus of smoothness, the SDD approximation is shown to converge in mean-square to the correct limit. The computational complexity of the SDD method is polynomial, as opposed to exponential, thus alleviating the curse of dimensionality to the extent possible. Analytical formulae are proposed to calculate the second-moment properties of a truncated SDD approximation for a general output random variable in terms of the expansion coefficients involved. Numerical results indicate that a low-order SDD approximation of nonsmooth functions calculates the probabilistic characteristics of an output variable with an accuracy matching or surpassing those obtained by high-order approximations from several existing methods. Finally, a 34-dimensional random eigenvalue analysis demonstrates the utility of SDD in solving practical problems.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2021-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90851195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 10

Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint 逆问题的随机归一化流:一个马尔可夫链的观点

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2021-09-23 DOI: 10.1137/21M1450604

Paul Hagemann, J. Hertrich, G. Steidl

引用次数: 24