Pub Date : 2023-01-01DOI: 10.1615/int.j.uncertaintyquantification.2023042817
J. Blanchard
{"title":"Sensitivity analysis with correlated inputs: focus on the linear case.","authors":"J. Blanchard","doi":"10.1615/int.j.uncertaintyquantification.2023042817","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023042817","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531336","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}
Pub Date : 2023-01-01DOI: 10.1615/int.j.uncertaintyquantification.2023046331
Nicolas Leoni, O. Le Maître, M. G. Rodio, P. Congedo
{"title":"BAYESIAN CALIBRATION WITH ADAPTIVE MODEL DISCREPANCY","authors":"Nicolas Leoni, O. Le Maître, M. G. Rodio, P. Congedo","doi":"10.1615/int.j.uncertaintyquantification.2023046331","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023046331","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531938","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}
Pub Date : 2023-01-01DOI: 10.1615/int.j.uncertaintyquantification.2023046666
Amandine Marrel, Heloise Velardo, Antoine Bouloré
Within the framework of Best-Estimate-Plus-Uncertainty approaches, the assessment of model parameter uncertainties, associated with numerical simulators, is a key element in safety analysis. The results (or outputs) of the simulation must be compared and validated against experimental values, when such data is available. This validation step, as part of the broader Verification, Validation and Uncertainty Quantification process, is required to ensure a reliable use of the simulator for modeling and prediction. This work aims to define quantitative criteria to support this validation for multivariate outputs, while taking into account modeling uncertainties (uncertain input parameters) and experimental uncertainties (measurement uncertainties). For this purpose, different statistical indicators, based on likelihood or statistical depths, are investigated and extended to the multidimensional case. First, the properties of the criteria are studied, either analytically or by simulation, for some specific cases (Gaussian distribution for experimental uncertainties, identical distributions of experiments and simulations, particular discrepancies). Then, some natural extensions to multivariate outputs are proposed, with guidelines for practical use depending on the objectives of the validation (strict/hard or average validation). From this, transformed criteria are proposed to make them more comparable and less sensitive to the dimension of the output. It is shown that these transformations allow for a fairer and more relevant comparison and interpretation of the different criteria. Finally, these criteria are applied to a code dedicated to nuclear material behavior simulation.
{"title":"Likelihood and depth-based criteria for comparing simulation results with experimental data, in support to validation of numerical simulators","authors":"Amandine Marrel, Heloise Velardo, Antoine Bouloré","doi":"10.1615/int.j.uncertaintyquantification.2023046666","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023046666","url":null,"abstract":"Within the framework of Best-Estimate-Plus-Uncertainty approaches, the assessment of model parameter uncertainties, associated with numerical simulators, is a key element in safety analysis. The results (or outputs) of the simulation must be compared and validated against experimental values, when such data is available. This validation step, as part of the broader Verification, Validation and Uncertainty Quantification process, is required to ensure a reliable use of the simulator for modeling and prediction. This work aims to define quantitative criteria to support this validation for multivariate outputs, while taking into account modeling uncertainties (uncertain input parameters) and experimental uncertainties (measurement uncertainties). For this purpose, different statistical indicators, based on likelihood or statistical depths, are investigated and extended to the multidimensional case. First, the properties of the criteria are studied, either analytically or by simulation, for some specific cases (Gaussian distribution for experimental uncertainties, identical distributions of experiments and simulations, particular discrepancies). Then, some natural extensions to multivariate outputs are proposed, with guidelines for practical use depending on the objectives of the validation (strict/hard or average validation). From this, transformed criteria are proposed to make them more comparable and less sensitive to the dimension of the output. It is shown that these transformations allow for a fairer and more relevant comparison and interpretation of the different criteria. Finally, these criteria are applied to a code dedicated to nuclear material behavior simulation.","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":"135838179","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}
Pub Date : 2023-01-01DOI: 10.1615/int.j.uncertaintyquantification.2023046204
M. Taghizadeh, D. Xiu, Negin Alemazkoor
{"title":"Improving Accuracy and Computational Efficiency of Optimal Design of Experiment via Greedy Backward Approach","authors":"M. Taghizadeh, D. Xiu, Negin Alemazkoor","doi":"10.1615/int.j.uncertaintyquantification.2023046204","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2023046204","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531881","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}
Pub Date : 2022-04-01DOI: 10.1615/int.j.uncertaintyquantification.2022038553
Juan Restrepo
We explore a homotopy sampling procedure and its generalization, loosely based on importance sampling, known as annealed importance sampling. The procedure makes use of a known probability distribution to find, via homotopy, the unknown normalization of a target distribution, as well as samples of the target distribution. In the context of stationary distributions that are associated with physical systems the method is an alternative way to estimate an unknown microcanonical ensemble. We make the connection between the homotopy and a dynamics problem explicit. Further, we propose a reformulation of the method that leads to a rejection sampling alternative. We derive the error incurred in computing the target distribution normalization, when sample inversion is not possible. The error in the procedure depends on the errors incurred in sample averaging and the number of stages used in the computational implementation of the process. However, we show that it is possible to exchange the number of homotopy stages and the total number of samples needed at each stage in order to enhance the computational efficiency of the implemented algorithm. Estimates of the error as a function of stages and sample averages are derived. These could guide computational efficiency decisions on how the calculation would be mapped to a given computer architecture. Consideration is given to how the procedure can be adapted to Bayesian estimation problems, both stationary and non-stationary. The connection between homotopy sampling and thermodynamic integration is made. Emphasis is placed on the non-stationary problems, and in particular, on a sequential estimation technique know
{"title":"CALCULATING PROBABILITY DENSITIES WITH HOMOTOPY, AND APPLICATIONS TO PARTICLE FILTERS","authors":"Juan Restrepo","doi":"10.1615/int.j.uncertaintyquantification.2022038553","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2022038553","url":null,"abstract":"We explore a homotopy sampling procedure and its generalization, loosely based on importance sampling, known as annealed importance sampling. The procedure makes use of a known probability distribution to\u0000find, via homotopy, the unknown normalization of a target distribution, as well as samples of the target distribution.\u0000In the context of stationary distributions that are associated with physical systems the method is an alternative way to estimate an unknown microcanonical ensemble.\u0000We make the connection between the homotopy and a dynamics problem explicit. Further, we propose a reformulation of the method that leads to a rejection sampling alternative. We derive the error incurred in computing the target distribution normalization, when sample inversion is not possible.\u0000The error in the procedure depends on the errors incurred in sample averaging and the number of stages used in the\u0000computational implementation of the process. However, we show that it is possible to exchange the number of homotopy stages and the total number of samples needed at each stage in order to enhance the computational efficiency of the implemented algorithm. Estimates of the error as a function of stages and sample averages are derived. These could guide computational efficiency decisions on how the calculation would be mapped to a given computer architecture.\u0000Consideration is given to how the procedure can be adapted to Bayesian estimation problems, both stationary and non-stationary. The connection between homotopy sampling and thermodynamic integration is made. Emphasis is placed on the non-stationary problems, and in particular, on a sequential estimation technique know","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138536970","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}
Pub Date : 2022-02-25DOI: 10.1615/int.j.uncertaintyquantification.2022043692
Julien Demange-Chryst, F. Bachoc, J. Morio
Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N-sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.
{"title":"Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling","authors":"Julien Demange-Chryst, F. Bachoc, J. Morio","doi":"10.1615/int.j.uncertaintyquantification.2022043692","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2022043692","url":null,"abstract":"Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N-sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41376851","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}
Pub Date : 2022-02-07DOI: 10.1615/Int.J.UncertaintyQuantification.2022042912
X. Zhu, B. Sudret
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the output of which is a random variable for a given set of input parameters. To alleviate the computational burden, surrogate models are usually constructed and evaluated instead. However, due to the random nature of the model response, classical surrogate models cannot be applied directly to the emulation of stochastic simulators. To efficiently represent the probability distribution of the model output for any given input values, we develop a new stochastic surrogate model called stochastic polynomial chaos expansions. To this aim, we introduce a latent variable and an additional noise variable, on top of the well-defined input variables, to reproduce the stochasticity. As a result, for a given set of input parameters, the model output is given by a function of the latent variable with an additive noise, thus a random variable. In this paper, we propose an adaptive algorithm which does not require repeated runs of the simulator for the same input parameters. The performance of the proposed method is compared with the generalized lambda model and a state-of-the-art kernel estimator on two case studies in mathematical finance and epidemiology and on an analytical example whose response distribution is bimodal. The results show that the proposed method is able to accurately represent general response distributions, i.e., not only normal or unimodal ones. In terms of accuracy, it generally outperforms both the generalized lambda model and the kernel density estimator.
{"title":"Stochastic polynomial chaos expansions to emulate stochastic simulators","authors":"X. Zhu, B. Sudret","doi":"10.1615/Int.J.UncertaintyQuantification.2022042912","DOIUrl":"https://doi.org/10.1615/Int.J.UncertaintyQuantification.2022042912","url":null,"abstract":"In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the output of which is a random variable for a given set of input parameters. To alleviate the computational burden, surrogate models are usually constructed and evaluated instead. However, due to the random nature of the model response, classical surrogate models cannot be applied directly to the emulation of stochastic simulators. To efficiently represent the probability distribution of the model output for any given input values, we develop a new stochastic surrogate model called stochastic polynomial chaos expansions. To this aim, we introduce a latent variable and an additional noise variable, on top of the well-defined input variables, to reproduce the stochasticity. As a result, for a given set of input parameters, the model output is given by a function of the latent variable with an additive noise, thus a random variable. In this paper, we propose an adaptive algorithm which does not require repeated runs of the simulator for the same input parameters. The performance of the proposed method is compared with the generalized lambda model and a state-of-the-art kernel estimator on two case studies in mathematical finance and epidemiology and on an analytical example whose response distribution is bimodal. The results show that the proposed method is able to accurately represent general response distributions, i.e., not only normal or unimodal ones. In terms of accuracy, it generally outperforms both the generalized lambda model and the kernel density estimator.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43994104","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}
Pub Date : 2022-01-26DOI: 10.1615/int.j.uncertaintyquantification.2022043638
Hang Yang, Y. Fujii, K. W. Wang, A. Gorodetsky
We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems such as automotive propulsion systems. Our approach is to build upon ideas from multifidelity uncertainty quantification to leverage the benefits of both sampling and surrogate modeling, while mitigating their downsides. In particular, the surrogate model is selected to exploit problem structure, such as smoothness, and offers a highly correlated information source to the original nonlinear dynamical system. We utilize an intrusive generalized Polynomial Chaos surrogate because it avoids any statistical errors in its construction and provides analytic estimates of output statistics. We then leverage a Monte Carlo-based Control Variate technique to correct the bias caused by the surrogate approximation error. The primary theoretical contribution of this work is the analysis and solution of an estimator design strategy that optimally balances the computational effort needed to adapt a surrogate compared with sampling the original expensive nonlinear system. While previous works have similarly combined surrogates and sampling, to our best knowledge this work is the first to provide rigorous analysis of estimator design. We deploy our approach on multiple examples stemming from the simulation of mechanical automotive propulsion system models. We show that the estimator is able to achieve orders of magnitude reduction in mean squared error of statistics estimation in some cases under comparable costs of purely sampling or purely surrogate approaches.
{"title":"Control Variate Polynomial Chaos: Optimal Fusion of Sampling and Surrogates for Multifidelity Uncertainty Quantification","authors":"Hang Yang, Y. Fujii, K. W. Wang, A. Gorodetsky","doi":"10.1615/int.j.uncertaintyquantification.2022043638","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2022043638","url":null,"abstract":"We present a hybrid sampling-surrogate approach for reducing the computational expense of uncertainty quantification in nonlinear dynamical systems. Our motivation is to enable rapid uncertainty quantification in complex mechanical systems such as automotive propulsion systems. Our approach is to build upon ideas from multifidelity uncertainty quantification to leverage the benefits of both sampling and surrogate modeling, while mitigating their downsides. In particular, the surrogate model is selected to exploit problem structure, such as smoothness, and offers a highly correlated information source to the original nonlinear dynamical system. We utilize an intrusive generalized Polynomial Chaos surrogate because it avoids any statistical errors in its construction and provides analytic estimates of output statistics. We then leverage a Monte Carlo-based Control Variate technique to correct the bias caused by the surrogate approximation error. The primary theoretical contribution of this work is the analysis and solution of an estimator design strategy that optimally balances the computational effort needed to adapt a surrogate compared with sampling the original expensive nonlinear system. While previous works have similarly combined surrogates and sampling, to our best knowledge this work is the first to provide rigorous analysis of estimator design. We deploy our approach on multiple examples stemming from the simulation of mechanical automotive propulsion system models. We show that the estimator is able to achieve orders of magnitude reduction in mean squared error of statistics estimation in some cases under comparable costs of purely sampling or purely surrogate approaches.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48144960","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}
{"title":"CONTROL VARIATES WITH A DIMENSION REDUCED BAYESIAN MONTE CARLO SAMPLER","authors":"Xin Cai, Junda Xiong, Hongqiao Wang, Jinglai Jinglai","doi":"10.1615/int.j.uncertaintyquantification.2022035744","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2022035744","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531028","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}
Pub Date : 2022-01-01DOI: 10.1615/int.j.uncertaintyquantification.2022038966
O. Chatrabgoun, M. Esmaeilbeigi, M. Cheraghi, A. Daneshkhah
{"title":"Stable Likelihood Computation for Machine Learning of Linear Differential Operators with Gaussian Processes","authors":"O. Chatrabgoun, M. Esmaeilbeigi, M. Cheraghi, A. Daneshkhah","doi":"10.1615/int.j.uncertaintyquantification.2022038966","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2022038966","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531128","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}
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