Efficient Computation of Sobol' Indices for Stochastic Models

Hart, Joseph; Alexanderian, Alen; Gremaud, Pierre A.

doi:10.1137/16m106193x

Cited by 38 publications

(35 citation statements)

References 45 publications

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“…Computing Sobol' indices, however, is a computationally demanding task. Availability of a surrogate model typically enables efficient computation of Sobol' indices [11][12][13][14][15]. This has enabled performing global sensitivity analysis on a wide range of applications including in ocean modeling [16,17], geosciences [18][19][20], and chemical kinetics [21][22][23] to name a few.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

et al. 2018

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We develop a systematic approach for surrogate model construction in reduced input parameter spaces. A sparse set of model evaluations in the original input space is used to approximate derivative based global sensitivity measures (DGSMs) for individual uncertain inputs of the model. An iterative screening procedure is developed that exploits DGSM estimates in order to identify the unimportant inputs. The screening procedure forms an integral part of an overall framework for adaptive construction of a surrogate in the reduced space. The framework is tested for computational efficiency through an initial implementation in simple test cases such as the classic Borehole function, and a semilinear elliptic PDE with a random source term. The framework is then deployed for a realistic application from chemical kinetics, where we study the ignition delay in an H 2 /O 2 reaction mechanism with 19 uncertain rate constants. It is observed that significant computational gains can be attained by constructing accurate low-dimensional surrogates using the proposed framework.

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Section: Introductionmentioning

confidence: 99%

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

et al. 2018

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“…In this context, uncertainty quantification and reduction methods have been developed 2 . As mentioned by Hart et al, 3 even the concept of sensitivity is delicate when dealing with stochastic models, as the one in our industrial application whose stochasticity is due to the stochastic nature of the wind external solicitation. Note also that the models used in wind energy applications are often time consuming 4,5 .…”

Section: Introduction and Scopementioning

confidence: 93%

Quantification and reduction of uncertainties in a wind turbine numerical model based on a global sensitivity analysis and a recursive Bayesian inference approach

Hirvoas

Prieur

Arnaud

et al. 2021

Numerical Meth Engineering

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A framework to perform quantification and reduction of uncertainties in a wind turbine numerical model using a global sensitivity analysis and a recursive Bayesian inference method is developed in this article. We explain how a prior probability distribution on the model parameters is transformed into a posterior probability distribution, by incorporating a physical model and real field noisy observations. Nevertheless, these approaches suffer from the so‐called curse of dimensionality. In order to reduce the dimension, Sobol' indices approach for global sensitivity analysis, in the context of wind turbine modeling, is presented. A major issue arising for such inverse problems is identifiability, that is, whether the observations are sufficient to unambiguously determine the input parameters that generated the observations. Global sensitivity analysis is also used in the context of identifiability.

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“…In [19], to the best of my understanding, the authors carry out the sensitivity analysis of a stochastic model based on a joint metamodel. In [10], a stochastic model is seen as a functional relation of the form Y (ϑ, ω) = f (X(ϑ), ω), where the X is a random vector on some probability space, ω is a point in some probability space distinct from that on which X is defined, f is some function and Y (ϑ, ω) is a random variable on the induced product probability space. The quantity f (X(ϑ), ω) represents the output of the stochastic model run with input X(ϑ); the point ω represents the intrinsic randomness.…”

mentioning

confidence: 99%

A Trade-Off Between Explorations and Repetitions for Estimators of Two Global Sensitivity Indices in Stochastic Models Induced by Probability Measures

Mazo¹

2021

SIAM/ASA J. Uncertainty Quantification

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Sobol sensitivity indices assess how the output of a given mathematical model is sensitive to its inputs. If the model is stochastic then it cannot be represented as a function of the inputs, thus raising questions as how to do a sensitivity analysis in those models. Practitioners have been using a method that exploits the availability of softwares for deterministic models. For each input, the stochastic model is repeated and the outputs are averaged. These averages are seen as if they came from a deterministic model and hence Sobol's method can be used. However, in the context of limited computational resources, one must ensure that the number of repetitions of the stochastic model multiplied by the number of explorations of the input space is less than a fixed threshold. The problem of finding an optimal tradeoff between the repetitions and the explorations is addressed. A bound on an error criterion that penalizes bad rankings of the inputs' sensitivities is minimized. The estimator induced by the empirical method described above is shown to be asymptotically biased if the number of repetitions goes to infinity too slowly. A functional relationship between the output, the input and some random noise is derived from minimal distributional assumptions, which leads to a new sensitivity index with better statistical properties. The theory is illustrated on numerical experiments.

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Efficient Computation of Sobol' Indices for Stochastic Models

Cited by 38 publications

References 45 publications

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

Sensitivity-Driven Adaptive Construction of Reduced-space Surrogates

Quantification and reduction of uncertainties in a wind turbine numerical model based on a global sensitivity analysis and a recursive Bayesian inference approach

A Trade-Off Between Explorations and Repetitions for Estimators of Two Global Sensitivity Indices in Stochastic Models Induced by Probability Measures

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