Siam-Asa Journal on Uncertainty Quantification最新文献_第10页

Finite Sample Approximations of Exact and Entropic Wasserstein Distances Between Covariance Operators and Gaussian Processes 协方差算子与高斯过程之间精确和熵Wasserstein距离的有限样本逼近

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-01-01 DOI: 10.1137/21m1410488

H. Q. Minh

{"title":"Finite Sample Approximations of Exact and Entropic Wasserstein Distances Between Covariance Operators and Gaussian Processes","authors":"H. Q. Minh","doi":"10.1137/21m1410488","DOIUrl":"https://doi.org/10.1137/21m1410488","url":null,"abstract":"This work studies finite sample approximations of the exact and entropic regularized Wasserstein distances between centered Gaussian processes and, more generally, covariance operators of functional random processes. We first show that these distances/divergences are fully represented by reproducing kernel Hilbert space (RKHS) covariance and cross-covariance operators associated with the corresponding covariance functions. Using this representation, we show that the Sinkhorn divergence between two centered Gaussian processes can be consistently and efficiently estimated from the divergence between their corresponding normalized finite-dimensional covariance matrices, or alternatively, their sample covariance operators. Consequently, this leads to a consistent and efficient algorithm for estimating the Sinkhorn divergence from finite samples generated by the two processes. For a fixed regularization parameter, the convergence rates are {it dimension-independent} and of the same order as those for the Hilbert-Schmidt distance. If at least one of the RKHS is finite-dimensional, we obtain a {it dimension-dependent} sample complexity for the exact Wasserstein distance between the Gaussian processes.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82721824","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: 2

Landmark-Warped Emulators for Models with Misaligned Functional Response 具有失调功能响应的模型的地标弯曲仿真器

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-01-01 DOI: 10.1137/20m135279x

Devin Francom, B. Sansó, A. Kupresanin

引用次数: 2

A Generalized Kernel Method for Global Sensitivity Analysis 全局灵敏度分析的广义核方法

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2022-01-01 DOI: 10.1137/20m1354829

John Barr, H. Rabitz

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

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 : 2021-09-28 DOI: 10.26226/morressier.612f6736bc98103724100846

Ö. D. Akyildiz, Connor Duffin, S. Sabanis, M. Girolami

{"title":"Statistical Finite Elements via Langevin Dynamics","authors":"Ö. D. Akyildiz, Connor Duffin, S. Sabanis, M. Girolami","doi":"10.26226/morressier.612f6736bc98103724100846","DOIUrl":"https://doi.org/10.26226/morressier.612f6736bc98103724100846","url":null,"abstract":"The recent statistical finite element method (statFEM) provides a coherent statistical framework to synthesise 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 characterisation 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, for both the prior and posterior, 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":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72921826","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: 6

Multifidelity Surrogate Modeling for Time-Series Outputs 时间序列输出的多保真代理建模

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2021-09-23 DOI: 10.1137/20m1386694

Baptiste Kerleguer

引用次数: 1

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

Finite Element Representations of Gaussian Processes: Balancing Numerical and Statistical Accuracy 高斯过程的有限元表示:平衡数值和统计精度

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2021-09-06 DOI: 10.1137/21m144788x

D. Sanz-Alonso, Ruiyi Yang

引用次数: 11

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems 连续统协方差传播法在平流系统中理解方差损失

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2021-09-06 DOI: 10.1137/21m1442449

Shay Gilpin, T. Matsuo, S. Cohn

{"title":"Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems","authors":"Shay Gilpin, T. Matsuo, S. Cohn","doi":"10.1137/21m1442449","DOIUrl":"https://doi.org/10.1137/21m1442449","url":null,"abstract":"Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance is often attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results demonstrate in the context of mass conservation that this leads to significant, spurious variance loss in regions of mass convergence and gain in regions of mass divergence. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2021-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78940583","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: 4