Siam-Asa Journal on Uncertainty Quantification最新文献_第4页

Perron–Frobenius Operator Filter for Stochastic Dynamical Systems 随机动态系统的佩伦-弗罗贝尼斯算子滤波器

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-03-15 DOI: 10.1137/23m1547391

Ningxin Liu, Lijian Jiang

{"title":"Perron–Frobenius Operator Filter for Stochastic Dynamical Systems","authors":"Ningxin Liu, Lijian Jiang","doi":"10.1137/23m1547391","DOIUrl":"https://doi.org/10.1137/23m1547391","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 182-211, March 2024. Abstract.Filtering problems are derived from a sequential minimization of a quadratic function representing a compromise between the model and data. In this paper, we use the Perron–Frobenius operator in a stochastic process to develop a Perron–Frobenius operator filter. The proposed method belongs to Bayesian filtering and works for non-Gaussian distributions for nonlinear stochastic dynamical systems. The recursion of the filtering can be characterized by the composition of the Perron–Frobenius operator and likelihood operator. This gives a significant connection between the Perron–Frobenius operator and Bayesian filtering. We numerically fulfill the recursion by approximating the Perron–Frobenius operator by Ulam’s method. In this way, the posterior measure is represented by a convex combination of the indicator functions in Ulam’s method. To get a low-rank approximation for the Perron–Frobenius operator filter, we take a spectral decomposition for the posterior measure by using the eigenfunctions of the discretized Perron–Frobenius operator. The Perron–Frobenius operator filter employs data instead of flow equations to model the evolution of underlying stochastic dynamical systems. In contrast, standard particle filters require explicit equations or transition probability density for sampling. A few numerical examples are presented to illustrate the advantage of the Perron–Frobenius operator filter over the particle filter and extended Kalman filter.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152281","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

Stacking Designs: Designing Multifidelity Computer Experiments with Target Predictive Accuracy 堆叠设计：设计具有目标预测精度的多保真计算机实验

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-03-11 DOI: 10.1137/22m1532007

Chih-Li Sung, Yi (Irene) Ji, Simon Mak, Wenjia Wang, Tao Tang

{"title":"Stacking Designs: Designing Multifidelity Computer Experiments with Target Predictive Accuracy","authors":"Chih-Li Sung, Yi (Irene) Ji, Simon Mak, Wenjia Wang, Tao Tang","doi":"10.1137/22m1532007","DOIUrl":"https://doi.org/10.1137/22m1532007","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 157-181, March 2024. Abstract. In an era where scientific experiments can be very costly, multifidelity emulators provide a useful tool for cost-efficient predictive scientific computing. For scientific applications, the experimenter is often limited by a tight computational budget, and thus wishes to (i) maximize predictive power of the multifidelity emulator via a careful design of experiments, and (ii) ensure this model achieves a desired error tolerance with some notion of confidence. Existing design methods, however, do not jointly tackle objectives (i) and (ii). We propose a novel stacking design approach that addresses both goals. A multilevel reproducing kernel Hilbert space (RKHS) interpolator is first introduced to build the emulator, under which our stacking design provides a sequential approach for designing multifidelity runs such that a desired prediction error of [math] is met under regularity assumptions. We then prove a novel cost complexity theorem that, under this multilevel interpolator, establishes a bound on the computation cost (for training data simulation) needed to achieve a prediction bound of [math]. This result provides novel insights on conditions under which the proposed multifidelity approach improves upon a conventional RKHS interpolator which relies on a single fidelity level. Finally, we demonstrate the effectiveness of stacking designs in a suite of simulation experiments and an application to finite element analysis.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140107583","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

Adaptive Importance Sampling Based on Fault Tree Analysis for Piecewise Deterministic Markov Process 基于故障树分析的片断确定性马尔可夫过程的自适应重要性采样

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-03-07 DOI: 10.1137/22m1522838

Guillaume Chennetier, Hassane Chraibi, Anne Dutfoy, Josselin Garnier

引用次数: 0

Multifidelity Bayesian Experimental Design to Quantify Rare-Event Statistics 量化罕见事件统计的多保真度贝叶斯实验设计

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-02-29 DOI: 10.1137/22m1503956

Xianliang Gong, Yulin Pan

{"title":"Multifidelity Bayesian Experimental Design to Quantify Rare-Event Statistics","authors":"Xianliang Gong, Yulin Pan","doi":"10.1137/22m1503956","DOIUrl":"https://doi.org/10.1137/22m1503956","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 101-127, March 2024. Abstract. In this work, we develop a multifidelity Bayesian experimental design framework to efficiently quantify the rare-event statistics of an input-to-response (ItR) system with given input probability and expensive function evaluations. The key idea here is to leverage low-fidelity samples whose responses can be computed with a cost of a certain fraction of that for high-fidelity samples, in an optimized configuration to reduce the total computational cost. To accomplish this goal, we employ a multifidelity Gaussian process as the surrogate model of the ItR function and develop a new acquisition based on which the optimized next sample can be selected in terms of its location in the sample space and the fidelity level. In addition, we develop an inexpensive analytical evaluation of the acquisition and its derivative, avoiding numerical integrations that are prohibitive for high-dimensional problems. The new method is mainly tested in a bifidelity context for a series of synthetic problems with varying dimensions, low-fidelity model accuracy, and computational costs. Compared with the single-fidelity method and the bifidelity method with a predefined fidelity hierarchy, our method consistently shows the best (or among the best) performance for all the test cases. Finally, we demonstrate the superiority of our method in solving an engineering problem of estimating rare-event statistics of ship motion in irregular waves, using computational fluid dynamics with two different grid resolutions as the high- and low-fidelity models.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140002037","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

Projective Integral Updates for High-Dimensional Variational Inference 高维变量推理的投影积分更新

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-02-08 DOI: 10.1137/22m1529919

Jed A. Duersch

{"title":"Projective Integral Updates for High-Dimensional Variational Inference","authors":"Jed A. Duersch","doi":"10.1137/22m1529919","DOIUrl":"https://doi.org/10.1137/22m1529919","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 1, Page 69-100, March 2024. Abstract. Variational inference is an approximation framework for Bayesian inference that seeks to improve quantified uncertainty in predictions by optimizing a simplified distribution over parameters to stand in for the full posterior. Capturing model variations that remain consistent with training data enables more robust predictions by reducing parameter sensitivity. This work introduces a fixed-point optimization for variational inference that is applicable when every feasible log density can be expressed as a linear combination of functions from a given basis. In such cases, the optimizer becomes a fixed-point of projective integral updates. When the basis spans univariate quadratics in each parameter, the feasible distributions are Gaussian mean-fields and the projective integral updates yield quasi-Newton variational Bayes (QNVB). Other bases and updates are also possible. Since these updates require high-dimensional integration, this work begins by proposing an efficient quasirandom sequence of quadratures for mean-field distributions. Each iterate of the sequence contains two evaluation points that combine to correctly integrate all univariate quadratic functions and, if the mean-field factors are symmetric, all univariate cubics. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. The corresponding variational updates require four loss evaluations with standard (not second-order) backpropagation to eliminate error terms from over half of all multivariate quadratic basis functions. This integration technique is motivated by first proposing stochastic blocked mean-field quadratures, which may be useful in other contexts. A PyTorch implementation of QNVB allows for better control over model uncertainty during training than competing methods. Experiments demonstrate superior generalizability for multiple learning problems and architectures.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139766388","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

Analysis of a Computational Framework for Bayesian Inverse Problems: Ensemble Kalman Updates and MAP Estimators under Mesh Refinement 贝叶斯逆问题计算框架分析：网格细化下的集合卡尔曼更新和 MAP 估计器

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-02-02 DOI: 10.1137/23m1567035

Daniel Sanz-Alonso, Nathan Waniorek

引用次数: 0

Error Estimate of a Quasi-Monte Carlo Time-Splitting Pseudospectral Method for Nonlinear Schrödinger Equation with Random Potentials 带随机势能的非线性薛定谔方程准蒙特卡洛时间分割伪谱法的误差估计

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-01-30 DOI: 10.1137/22m1525181

Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao

引用次数: 0

Fully Bayesian Inference for Latent Variable Gaussian Process Models 潜变量高斯过程模型的完全贝叶斯推理

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-12-11 DOI: 10.1137/22m1525600

Suraj Yerramilli, Akshay Iyer, Wei Chen, Daniel W. Apley

{"title":"Fully Bayesian Inference for Latent Variable Gaussian Process Models","authors":"Suraj Yerramilli, Akshay Iyer, Wei Chen, Daniel W. Apley","doi":"10.1137/22m1525600","DOIUrl":"https://doi.org/10.1137/22m1525600","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1357-1381, December 2023. Abstract. Real engineering and scientific applications often involve one or more qualitative inputs. Standard Gaussian processes (GPs), however, cannot directly accommodate qualitative inputs. The recently introduced latent variable Gaussian process (LVGP) overcomes this issue by first mapping each qualitative factor to underlying latent variables (LVs) and then uses any standard GP covariance function over these LVs. The LVs are estimated similarly to the other GP hyperparameters through maximum likelihood estimation and then plugged into the prediction expressions. However, this plug-in approach will not account for uncertainty in estimation of the LVs, which can be significant especially with limited training data. In this work, we develop a fully Bayesian approach for the LVGP model and for visualizing the effects of the qualitative inputs via their LVs. We also develop approximations for scaling up LVGPs and fully Bayesian inference for the LVGP hyperparameters. We conduct numerical studies comparing plug-in inference against fully Bayesian inference over a few engineering models and material design applications. In contrast to previous studies on standard GP modeling that have largely concluded that a fully Bayesian treatment offers limited improvements, our results show that for LVGP modeling it offers significant improvements in prediction accuracy and uncertainty quantification over the plug-in approach.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138567754","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

Space-time Multilevel Quadrature Methods and their Application for Cardiac Electrophysiology 时空多层正交方法及其在心脏电生理研究中的应用

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-12-05 DOI: 10.1137/21m1418320

Seif Ben Bader, Helmut Harbrecht, Rolf Krause, Michael D. Multerer, Alessio Quaglino, Marc Schmidlin

{"title":"Space-time Multilevel Quadrature Methods and their Application for Cardiac Electrophysiology","authors":"Seif Ben Bader, Helmut Harbrecht, Rolf Krause, Michael D. Multerer, Alessio Quaglino, Marc Schmidlin","doi":"10.1137/21m1418320","DOIUrl":"https://doi.org/10.1137/21m1418320","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1329-1356, December 2023. Abstract. We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the transmembrane potential inside the cardiac cells, we evaluate the effect of spatially correlated perturbations of the heart fibers on the statistics of the resulting quantities of interest. Our methodology relies on a close integration of multilevel quadrature methods, parallel iterative solvers, and space-time finite element discretizations, allowing for a fully parallelized framework in space, time, and stochastics. Extensive numerical studies are presented to evaluate convergence rates and to compare the performance of classical Monte Carlo methods such as standard Monte Carlo (MC) and quasi-Monte Carlo (QMC), as well as multilevel strategies, i.e., multilevel Monte Carlo (MLMC) and multilevel quasi-Monte Carlo (MLQMC) on hierarchies of nested meshes. We especially also employ a recently suggested variant of the multilevel approach for nonnested meshes to deal with a realistic heart geometry.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512777","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

Parameter Selection in Gaussian Process Interpolation: An Empirical Study of Selection Criteria 高斯过程插值参数选择:选择标准的实证研究

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2023-12-04 DOI: 10.1137/21m1444710

Sébastien J. Petit, Julien Bect, Paul Feliot, Emmanuel Vazquez

{"title":"Parameter Selection in Gaussian Process Interpolation: An Empirical Study of Selection Criteria","authors":"Sébastien J. Petit, Julien Bect, Paul Feliot, Emmanuel Vazquez","doi":"10.1137/21m1444710","DOIUrl":"https://doi.org/10.1137/21m1444710","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 11, Issue 4, Page 1308-1328, December 2023. Abstract. This article revisits the fundamental problem of parameter selection for Gaussian process interpolation. By choosing the mean and the covariance functions of a Gaussian process within parametric families, the user obtains a family of Bayesian procedures to perform predictions about the unknown function and must choose a member of the family that will hopefully provide good predictive performances. We base our study on the general concept of scoring rules, which provides an effective framework for building leave-one-out selection and validation criteria and a notion of extended likelihood criteria based on an idea proposed by Fasshauer et al. [“Optimal” scaling and stable computation of meshfree kernel methods, 2009], which makes it possible to recover standard selection criteria, such as the generalized cross-validation criterion. Under this setting, we empirically show on several test problems of the literature that the choice of an appropriate family of models is often more important than the choice of a particular selection criterion (e.g., the likelihood versus a leave-one-out selection criterion). Moreover, our numerical results show that the regularity parameter of a Matérn covariance can be selected effectively by most selection criteria.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512773","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