Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

Cheng, Kai; Lü, Zhenzhou

doi:10.1016/j.compstruc.2017.09.002

Cited by 109 publications

(31 citation statements)

References 37 publications

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“…Another line of research focuses on reducing the problem dimension by using advanced methods for solving nonlinear regression problems. For instance, sparse PCE coefficients can be computed efficiently through the application of support vector regression [56] or preconditioned conjugate gradient [57] techniques. Another direction of development relies on coupling the iterative solvers with algorithms for ranking the importance of the basis polynomials (e.g.…”

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confidence: 99%

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Tarakanov¹,

Elsheikh²

2019

Journal of Computational Physics

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Surrogate-modelling techniques including Polynomial Chaos Expansion (PCE) is commonly used for statistical estimation (aka. Uncertainty Quantification) of quantities of interests obtained from expensive computational models. PCE is a data-driven regression-based technique that relies on spectral polynomials as basis-functions. In this technique, the outputs of few numerical simulations are used to estimate the PCE coefficients within a regression framework combined with regularization techniques where the regularization parameters are estimated using standard cross-validation as applied in supervised machine learning methods.In the present work, we introduce an efficient method for estimating the PCE coefficients combining Elastic Net regularization with a data-driven feature ranking approach. Our goal is to increase the probability of identifying the most significant PCE components by assigning each of the PCE coefficients a numerical value reflecting the magnitude of the coefficient and its stability with respect to perturbations in the input data. In our evaluations, the proposed approach has shown high convergence rate for high-dimensional problems, where standard feature ranking might be challenging due to the curse of dimensionality.The presented method is implemented within a standard machine learning library (scikit-learn [1]) allowing for easy experimentation with various solvers and regularization techniques (e.g. Tikhonov, LASSO, LARS, Elastic Net) and enabling automatic cross-validation techniques using a widely used and well tested implementation. We present a set of numerical tests on standard analytical functions, a two-phase subsurface flow model and a simulation dataset for CO2 sequestration in a saline aquifer. For all test cases, the proposed approach resulted in a significant increase in PCE convergence rates.

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confidence: 99%

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Tarakanov¹,

Elsheikh²

2019

Journal of Computational Physics

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“…To address the problem of “curse of dimensionality,” one may utilize the dimensionality reduction technique, for example, sensitivity analysis . This method ranks the input variables with respect to their significance for the response variability.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical surrogate model with dimensionality reduction technique for high‐dimensional uncertainty propagation

Cheng

Lü

2019

Numerical Meth Engineering

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Summary In this article, hierarchical surrogate model combined with dimensionality reduction technique is investigated for uncertainty propagation of high‐dimensional problems. In the proposed method, a low‐fidelity sparse polynomial chaos expansion model is first constructed to capture the global trend of model response and exploit a low‐dimensional active subspace (AS). Then a high‐fidelity (HF) stochastic Kriging model is built on the reduced space by mapping the original high‐dimensional input onto the identified AS. The effective dimensionality of the AS is estimated by maximum likelihood estimation technique. Finally, an accurate HF surrogate model is obtained for uncertainty propagation of high‐dimensional stochastic problems. The proposed method is validated by two challenging high‐dimensional stochastic examples, and the results demonstrate that our method is effective for high‐dimensional uncertainty propagation.

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“…Another way of finding the coefficients is by regression method, which utilizes a finite set of MCS results to evaluate the unknown coefficients. This process is known as nonintrusive method . However, in both the methods, as the number of random variables or the order of expansion increases, the size of the system matrix increases exponentially.…”

Section: Introductionmentioning

confidence: 99%

“…This process is known as nonintrusive method. 2,3,[17][18][19] However, in both the methods, as the number of random variables or the order of expansion increases, the size of the system matrix increases exponentially. To overcome this, many researchers proposed a sparse PC expansion.…”

Section: Introductionmentioning

confidence: 99%

An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non‐Gaussian randomness

Nath

Dutta

Hazra

2019

Numerical Meth Engineering

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Summary Stochastic analysis of structure with non‐Gaussian material property and loading in the framework of polynomial chaos (PC) is considered. A new approach for the solution of stochastic mechanics problem with random coefficient is presented. The major focus of the method is to consider reduced size of expansion in an iterative manner to overcome the problem of large system matrix in conventional PC expansion. The iterative method is based on orthogonal expansion of stochastic responses and generation of an iterative PC based on the responses of the previous iteration. The polynomials are evaluated using Gram‐Schmidt orthogonalization process. The numbers of random variables in PC expansion are reduced by considering only the dominant components of the response characteristics, which is evaluated using Karhunen‐Loève (KL) expansion. In case of random material field problem, the KL expansion is used to discretize and simulate the non‐Gaussian random field. Independent component analysis (ICA) is carried out on the non‐Gaussian KL random variables to minimize statistical dependence. The usefulness of the proposed method in terms of accuracy and computational efficiency is examined. From the numerical analysis of three different types of structural mechanics problems, the proposed iterative method is observed to be computationally more efficient and accurate than conventional PC method for solution of linear elastostatic structural mechanics problems.

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Adaptive sparse polynomial chaos expansions for global sensitivity analysis based on support vector regression

Cited by 109 publications

References 37 publications

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Regression-based sparse polynomial chaos for uncertainty quantification of subsurface flow models

Hierarchical surrogate model with dimensionality reduction technique for high‐dimensional uncertainty propagation

An iterative polynomial chaos approach toward stochastic elastostatic structural analysis with non‐Gaussian randomness

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