Pub Date : 2021-01-01DOI: 10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021034623
E. Camporeale, A. Carè
{"title":"ACCRUE: ACCURATE AND RELIABLE UNCERTAINTY ESTIMATE IN DETERMINISTIC MODELS","authors":"E. Camporeale, A. Carè","doi":"10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021034623","DOIUrl":"https://doi.org/10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021034623","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531017","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 : 2021-01-01DOI: 10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021035691
Saja Almohammadi, O. Maître, O. Knio
This work focuses on constructing functional representations of quantities of interest (QoIs) of an uncertain system in high dimension. Attention is focused on the ignition delay time of an iso-octane air mixture, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log-uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parametrizing the uncertain rates. We explored two avenues, namely sparse regression (SR) using LASSO, and a coordinate transform (CT) approach. Preconditioned variants of both approaches were also considered, namely using the logarithm of the ignition delay time as QoI. Both approaches resulted in representations of the ignition delay with similar representation errors. However, the CT approach was able to reproduce better the empirical distribution of the underlying LHS ensemble, and also preserved the positivity of the ignition delay time. When preconditioned representations were considered, however, similar performances were obtained using CT and SR representations. The results also revealed that both the CT and SR representations yield consistent global sensitivity estimates. The results were finally used to test a reduced dimension representation, and to outline potential extensions of the work.
{"title":"Computational Challenges in Sampling and Representation of Uncertain Reaction Kinetics in Large Dimensions","authors":"Saja Almohammadi, O. Maître, O. Knio","doi":"10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021035691","DOIUrl":"https://doi.org/10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021035691","url":null,"abstract":"This work focuses on constructing functional representations of quantities of interest (QoIs) of an uncertain system in high dimension. Attention is focused on the ignition delay time of an iso-octane air mixture, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log-uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parametrizing the uncertain rates. We explored two avenues, namely sparse regression (SR) using LASSO, and a coordinate transform (CT) approach. Preconditioned variants of both approaches were also considered, namely using the logarithm of the ignition delay time as QoI. Both approaches resulted in representations of the ignition delay with similar representation errors. However, the CT approach was able to reproduce better the empirical distribution of the underlying LHS ensemble, and also preserved the positivity of the ignition delay time. When preconditioned representations were considered, however, similar performances were obtained using CT and SR representations. The results also revealed that both the CT and SR representations yield consistent global sensitivity estimates. The results were finally used to test a reduced dimension representation, and to outline potential extensions of the work.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531167","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 : 2021-01-01DOI: 10.1615/int.j.uncertaintyquantification.2021035851
Kai Cheng, Zhenzhou Lu, Sinan Xiao, S. Oladyshkin, W. Nowak
{"title":"Sparse Gaussian process model with mixed covariance function for uncertainty quantification","authors":"Kai Cheng, Zhenzhou Lu, Sinan Xiao, S. Oladyshkin, W. Nowak","doi":"10.1615/int.j.uncertaintyquantification.2021035851","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2021035851","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531216","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 : 2021-01-01DOI: 10.1615/int.j.uncertaintyquantification.2020032807
R. Maraia, Sebastian Springer, H. Haario, J. Hakkarainen, E. Saksman
{"title":"PARAMETER ESTIMATION OF STOCHASTIC CHAOTIC SYSTEMS","authors":"R. Maraia, Sebastian Springer, H. Haario, J. Hakkarainen, E. Saksman","doi":"10.1615/int.j.uncertaintyquantification.2020032807","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2020032807","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67530507","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 : 2021-01-01DOI: 10.1615/int.j.uncertaintyquantification.2021038512
G. Ajith, D. Ghosh
{"title":"A FETI-DP based parallel algorithm for solving high dimensional stochastic PDEs using collocation","authors":"G. Ajith, D. Ghosh","doi":"10.1615/int.j.uncertaintyquantification.2021038512","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2021038512","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531351","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 : 2021-01-01DOI: 10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021033499
Kyle Neal, Benjamin Schroeder, Joshua Mullins, Abhinav Subramanian, S. Mahadevan
{"title":"ROBUST IMPORTANCE SAMPLING FOR BAYESIAN MODEL CALIBRATION WITH SPATIOTEMPORAL DATA","authors":"Kyle Neal, Benjamin Schroeder, Joshua Mullins, Abhinav Subramanian, S. Mahadevan","doi":"10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021033499","DOIUrl":"https://doi.org/10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021033499","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67530575","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 : 2021-01-01DOI: 10.1615/int.j.uncertaintyquantification.2020032982
M. Sacher, O. Maître, R. Duvigneau, F. Hauville, M. Durand, Corentin Lothodé
Efficient Global Optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multi-fidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multi-fidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multi-fidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multi-fidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements.
{"title":"A NON-NESTED INFILLING STRATEGY FOR MULTIFIDELITY BASED EFFICIENT GLOBAL OPTIMIZATION","authors":"M. Sacher, O. Maître, R. Duvigneau, F. Hauville, M. Durand, Corentin Lothodé","doi":"10.1615/int.j.uncertaintyquantification.2020032982","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2020032982","url":null,"abstract":"Efficient Global Optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multi-fidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multi-fidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multi-fidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multi-fidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67530613","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 : 2021-01-01DOI: 10.1615/int.j.uncertaintyquantification.2020032674
M. Arnst, Christian Soize, K. Bulthuis
Global sensitivity analysis provides insight into how sources of uncertainty contribute to uncertainty in predictions of computational models. Global sensitivity indices, also called variance-based sensitivity indices and Sobol indices, are most often computed with Monte Carlo methods. However, when the computational model is computationally expensive and only a small number of samples can be generated, that is, in so-called small-data settings, usual Monte Carlo estimates may lack sufficient accuracy. As a means of improving accuracy in such small-data settings, we explore the use of probabilistic learning. The objective of the probabilistic learning is to learn from the available samples a probabilistic model that can be used to generate additional samples, from which Monte Carlo estimates of the global sensitivity indices are then deduced. We demonstrate the interest of such a probabilistic learning method by applying it in an illustration concerned with forecasting the contribution of the Antarctic ice sheet to sea-level rise.
{"title":"COMPUTATION OF SOBOL INDICES IN GLOBAL SENSITIVITY ANALYSIS FROM SMALL DATA SETS BY PROBABILISTIC LEARNING ON MANIFOLDS","authors":"M. Arnst, Christian Soize, K. Bulthuis","doi":"10.1615/int.j.uncertaintyquantification.2020032674","DOIUrl":"https://doi.org/10.1615/int.j.uncertaintyquantification.2020032674","url":null,"abstract":"Global sensitivity analysis provides insight into how sources of uncertainty contribute to uncertainty in predictions of computational models. Global sensitivity indices, also called variance-based sensitivity indices and Sobol indices, are most often computed with Monte Carlo methods. However, when the computational model is computationally expensive and only a small number of samples can be generated, that is, in so-called small-data settings, usual Monte Carlo estimates may lack sufficient accuracy. As a means of improving accuracy in such small-data settings, we explore the use of probabilistic learning. The objective of the probabilistic learning is to learn from the available samples a probabilistic model that can be used to generate additional samples, from which Monte Carlo estimates of the global sensitivity indices are then deduced. We demonstrate the interest of such a probabilistic learning method by applying it in an illustration concerned with forecasting the contribution of the Antarctic ice sheet to sea-level rise.","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67530892","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 : 2021-01-01DOI: 10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021033774
G. Geraci, J. Crussell, L. Swiler, B. Debusschere
{"title":"EXPLORATION OF MULTIFIDELITY UQ SAMPLING STRATEGIES FOR COMPUTER NETWORK APPLICATIONS","authors":"G. Geraci, J. Crussell, L. Swiler, B. Debusschere","doi":"10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021033774","DOIUrl":"https://doi.org/10.1615/INT.J.UNCERTAINTYQUANTIFICATION.2021033774","url":null,"abstract":"","PeriodicalId":48814,"journal":{"name":"International Journal for Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67531403","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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