Siam-Asa Journal on Uncertainty Quantification最新文献_第2页

Choosing Observation Operators to Mitigate Model Error in Bayesian Inverse Problems 在贝叶斯逆问题中选择观测操作符以减少模型误差

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-07-10 DOI: 10.1137/23m1602140

Nada Cvetković, Han Cheng Lie, Harshit Bansal, Karen Veroy

{"title":"Choosing Observation Operators to Mitigate Model Error in Bayesian Inverse Problems","authors":"Nada Cvetković, Han Cheng Lie, Harshit Bansal, Karen Veroy","doi":"10.1137/23m1602140","DOIUrl":"https://doi.org/10.1137/23m1602140","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 723-758, September 2024. Abstract.In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to misspecified likelihoods and thus to incorrect estimates. In many inverse problems, the parameter-to-observable map is the composition of a linear state-to-observable map called an “observation operator” and a possibly nonlinear parameter-to-state map called the “model.” We consider such Bayesian inverse problems where the discrepancy in the parameter-to-observable map is due to the use of an approximate model that differs from the best model, i.e., to nonzero “model error.” Multiple approaches have been proposed to address such discrepancies, each leading to a specific posterior. We show how to use local Lipschitz stability estimates of posteriors with respect to likelihood perturbations to bound the Kullback–Leibler divergence of the posterior of each approach with respect to the posterior associated to the best model. Our bounds lead to criteria for choosing observation operators that mitigate the effect of model error for Bayesian inverse problems of this type. We illustrate the feasibility of one such criterion on an advection-diffusion-reaction PDE inverse problem and use this example to discuss the importance and challenges of model error-aware inference.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141585368","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

Proportional Marginal Effects for Global Sensitivity Analysis 全球敏感性分析的比例边际效应

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-26 DOI: 10.1137/22m153032x

Margot Herin, Marouane Il Idrissi, Vincent Chabridon, Bertrand Iooss

{"title":"Proportional Marginal Effects for Global Sensitivity Analysis","authors":"Margot Herin, Marouane Il Idrissi, Vincent Chabridon, Bertrand Iooss","doi":"10.1137/22m153032x","DOIUrl":"https://doi.org/10.1137/22m153032x","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 667-692, June 2024. Abstract.Performing (variance-based) global sensitivity analysis (GSA) with dependent inputs has recently benefited from cooperative game theory concepts, leading to meaningful sensitivity indices suitable with dependent inputs. The “Shapley effects,” i.e., the Shapley values transposed to variance-based GSA problems, are an example of such indices. However, these indices exhibit a particular behavior that can be undesirable: an exogenous input (i.e., which is not explicitly included in the structural equations of the model) can be associated with a strictly positive index when it is correlated to endogenous inputs. This paper investigates using a different allocation, called the “proportional values” for GSA purposes. First, an extension of this allocation is proposed to make it suitable for variance-based GSA. A novel GSA index is then defined: the proportional marginal effect (PME). The notion of exogeneity is formally defined in the context of variance-based GSA. It is shown that the PMEs are more discriminant than the Shapley values and allow the distinction of exogenous variables, even when they are correlated to endogenous inputs. Moreover, their behavior is compared to the Shapley effects on analytical toy cases and more realistic use cases.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508626","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 Combination Technique for Optimal Control Problems Constrained by Random PDEs 受随机 PDE 约束的最优控制问题的组合技术

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-26 DOI: 10.1137/22m1532263

Fabio Nobile, Tommaso Vanzan

{"title":"A Combination Technique for Optimal Control Problems Constrained by Random PDEs","authors":"Fabio Nobile, Tommaso Vanzan","doi":"10.1137/22m1532263","DOIUrl":"https://doi.org/10.1137/22m1532263","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 693-721, June 2024. Abstract.We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equations. The method requires to solve the OCP for several low-fidelity spatial grids and quadrature formulae for the objective functional. All the computed solutions are then linearly combined to get a final approximation which, under suitable regularity assumptions, preserves the same accuracy of fine tensor product approximations, while drastically reducing the computational cost. The combination technique involves only tensor product quadrature formulae, and thus the discretized OCPs preserve the (possible) convexity of the continuous OCP. Hence, the combination technique avoids the inconveniences of multilevel Monte Carlo and/or sparse grids approaches but remains suitable for high-dimensional problems. The manuscript presents an a priori procedure to choose the most important mixed differences and an analysis stating that the asymptotic complexity is exclusively determined by the spatial solver. Numerical experiments validate the results.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529781","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

Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation 广义贝叶斯 MARS：随机计算机模型仿真工具

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-20 DOI: 10.1137/23m1577122

Kellin N. Rumsey, Devin Francom, Andy Shen

{"title":"Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation","authors":"Kellin N. Rumsey, Devin Francom, Andy Shen","doi":"10.1137/23m1577122","DOIUrl":"https://doi.org/10.1137/23m1577122","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 646-666, June 2024. Abstract. The multivariate adaptive regression spline (MARS) approach of Friedman [J. H. Friedman, Ann. Statist., 19 (1991), pp. 1–67] and its Bayesian counterpart [D. Francom et al., Statist. Sinica, 28 (2018), pp. 791–816] are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. We propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508625","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

One-Shot Learning of Surrogates in PDE-Constrained Optimization under Uncertainty 不确定性条件下 PDE 受限优化中代用物的一次性学习

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-12 DOI: 10.1137/23m1553170

Philipp A. Guth, Claudia Schillings, Simon Weissmann

引用次数: 0

Differential Equation–Constrained Optimization with Stochasticity 带随机性的微分方程约束优化

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-07 DOI: 10.1137/23m1571162

Qin Li, Li Wang, Yunan Yang

{"title":"Differential Equation–Constrained Optimization with Stochasticity","authors":"Qin Li, Li Wang, Yunan Yang","doi":"10.1137/23m1571162","DOIUrl":"https://doi.org/10.1137/23m1571162","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 549-578, June 2024. Abstract.Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured data. The formulation is powerful and widely used in many science and engineering fields. However, one crucial assumption is that the unknown parameter must be deterministic. In reality, however, many problems are stochastic in nature, and the unknown parameter is random. The challenge then becomes recovering the full distribution of this unknown random parameter. It is a much more complex task. In this paper, we examine this problem in a general setting. In particular, we conceptualize the PDE solver as a push-forward map that pushes the parameter distribution to the generated data distribution. In this way, the SDE-constrained optimization translates to minimizing the distance between the generated distribution and the measurement distribution. We then formulate a gradient flow equation to seek the ground-truth parameter probability distribution. This opens up a new paradigm for extending many techniques in PDE-constrained optimization to optimization for systems with stochasticity.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508628","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

Quantifying the Effect of Random Dispersion for Logarithmic Schrödinger Equation 量化随机分散对对数薛定谔方程的影响

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-07 DOI: 10.1137/23m1578619

Jianbo Cui, Liying Sun

引用次数: 0

Computationally Efficient Sampling Methods for Sparsity Promoting Hierarchical Bayesian Models 促进稀疏性的层次贝叶斯模型的计算高效采样方法

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-06-07 DOI: 10.1137/23m1564043

D. Calvetti, E. Somersalo

{"title":"Computationally Efficient Sampling Methods for Sparsity Promoting Hierarchical Bayesian Models","authors":"D. Calvetti, E. Somersalo","doi":"10.1137/23m1564043","DOIUrl":"https://doi.org/10.1137/23m1564043","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 524-548, June 2024. Abstract.Bayesian hierarchical models have been demonstrated to provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models comprise typically a conditionally Gaussian prior model for the unknown, augmented by a hyperprior model for the variances. A widely used choice for the hyperprior is a member of the family of generalized gamma distributions. Most of the work in the literature has concentrated on numerical approximation of the maximum a posteriori estimates, and less attention has been paid on sampling methods or other means for uncertainty quantification. Sampling from the hierarchical models is challenging mainly for two reasons: The hierarchical models are typically high dimensional, thus suffering from the curse of dimensionality, and the strong correlation between the unknown of interest and its variance can make sampling rather inefficient. This work addresses mainly the first one of these obstacles. By using a novel reparametrization, it is shown how the posterior distribution can be transformed into one dominated by a Gaussian white noise, allowing sampling by using the preconditioned Crank–Nicholson (pCN) scheme that has been shown to be efficient for sampling from distributions dominated by a Gaussian component. Furthermore, a novel idea for speeding up the pCN in a special case is developed, and the question of how strongly the hierarchical models are concentrated on sparse solutions is addressed in light of a computed example.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508630","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

Quantifying Domain Uncertainty in Linear Elasticity 量化线性弹性中的领域不确定性

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-05-30 DOI: 10.1137/23m1578589

Helmut Harbrecht, Viacheslav Karnaev, Marc Schmidlin

引用次数: 0

Conglomerate Multi-fidelity Gaussian Process Modeling, with Application to Heavy-Ion Collisions 集合体多保真高斯过程建模，应用于重离子碰撞

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-05-30 DOI: 10.1137/22m1525004

Yi Ji, Henry Shaowu Yuchi, Derek Soeder, J.-F. Paquet, Steffen A. Bass, V. Roshan Joseph, C. F. Jeff Wu, Simon Mak

{"title":"Conglomerate Multi-fidelity Gaussian Process Modeling, with Application to Heavy-Ion Collisions","authors":"Yi Ji, Henry Shaowu Yuchi, Derek Soeder, J.-F. Paquet, Steffen A. Bass, V. Roshan Joseph, C. F. Jeff Wu, Simon Mak","doi":"10.1137/22m1525004","DOIUrl":"https://doi.org/10.1137/22m1525004","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 2, Page 473-502, June 2024. Abstract.In an era where scientific experimentation is often costly, multi-fidelity emulation provides a powerful tool for predictive scientific computing. While there has been notable work on multi-fidelity modeling, existing models do not incorporate an important “conglomerate” property of multi-fidelity simulators, where the accuracies of different simulator components are controlled by different fidelity parameters. Such conglomerate simulators are widely encountered in complex nuclear physics and astrophysics applications. We thus propose a new CONglomerate multi-FIdelity Gaussian process (CONFIG) model, which embeds this conglomerate structure within a novel non-stationary covariance function. We show that the proposed CONFIG model can capture prior knowledge on the numerical convergence of conglomerate simulators, which allows for cost-efficient emulation of multi-fidelity systems. We demonstrate the improved predictive performance of CONFIG over state-of-the-art models in a suite of numerical experiments and two applications, the first for emulation of cantilever beam deflection and the second for emulating the evolution of the quark-gluon plasma, which was theorized to have filled the universe shortly after the Big Bang.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141166728","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