Multi-fidelity non-intrusive polynomial chaos based on regression

Palar, Pramudita Satria; Tsuchiya, Takeshi; Parks, Geoffrey T.

doi:10.1016/j.cma.2016.03.022

Cited by 69 publications

(47 citation statements)

References 32 publications

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“…Herein, the Sobol low‐discrepancy sequence is used to generate the LF and HF sample data. In addition, the computational cost ratio H l / H h of LF and HF simulations is defined by Reference :

H_{l} / H_{h} = C_{l} / C_{h},

where C 1 and C 2 represent the computational times of LF and HF simulations, respectively. Therefore, the total computational cost C T of the proposed hierarchical surrogate model method can be computed as

C_{T} = N_{h} + N_{l} C_{l} / C_{h} .

…”

Section: Numerical Examplementioning

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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H_{l} / H_{h} = C_{l} / C_{h},

C_{T} = N_{h} + N_{l} C_{l} / C_{h} .

…”

Section: Numerical Examplementioning

confidence: 99%

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

Cheng

Lü

2019

Numerical Meth Engineering

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“…Given a small number of f H ( m ) evaluations and a much larger number of f L ( m ) evaluations, the multifidelity simulation can take advantage of both the efficiency of f L ( m ) and the accuracy of f H ( m ). The integrated system can be constructed with many methods, for example, polynomial chaos expansion (Narayan et al, ; Palar et al, ; Zhu et al, ) and Gaussian process (GP) (Kennedy & O'Hagan, ; Le Gratiet & Garnier, ; Parussini et al, ; Raissi et al, ). GP is a generic supervised learning method that uses a (multivariate) Gaussian distribution to predict the quantity of interest based on a set of training data (Williams & Rasmussen, ).…”

Section: Introductionmentioning

confidence: 99%

Inverse Modeling of Hydrologic Systems with Adaptive Multifidelity Markov Chain Monte Carlo Simulations

Zhang

Man

Lin

et al. 2018

Water Resources Research

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Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU‐intensive and high dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU‐efficient while less accurate low‐fidelity model (e.g., a numerical model with a coarser discretization or a data‐driven surrogate) is usually adopted. Nowadays, multifidelity simulation methods that can take advantage of both the efficiency of the low‐fidelity model and the accuracy of the high‐fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high‐fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multifidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high‐fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process system that is adaptively constructed with multifidelity simulation. The error of the Gaussian process system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high‐fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.

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“…On the other hand, the iteration for the partially converged simulation to be used as the LF simulations is set to 100, which means that the computational cost ratio between the LF and HF simulation is 0.2 for this case. This fully and partially converged simulation strategy has been employed for optimization [83,84], surrogate model construction [85], and UQ [71]. One advantage of this strategy is that some LF samples are evaluated together with the HF samples, which leads to further reduction in the computational cost.…”

Section: Transonic Airfoil In Inviscid Flowmentioning

confidence: 99%

“…The method works by combining the LF and correction PCE into a single MF-PCE [69]. The coefficients of the LF and correction PCE can be obtained by employing spectral projection [69] or regression-based technique [70,71]. Another similar technique is the MF stochastic collocation that relies on Lagrange-polynomial interpolation [72].…”

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confidence: 99%

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Palar

Zuhal

Shimoyama

et al. 2018

Reliability Engineering & System Safety

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The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations are required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the lowfidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy.

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Multi-fidelity non-intrusive polynomial chaos based on regression

Cited by 69 publications

References 32 publications

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

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

Inverse Modeling of Hydrologic Systems with Adaptive Multifidelity Markov Chain Monte Carlo Simulations

Global sensitivity analysis via multi-fidelity polynomial chaos expansion

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