Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Palar, Pramudita Satria; Zuhal, Lavi Rizki; Shimoyama, Koji; Tsuchiya, Takeshi

doi:10.1016/j.ress.2017.10.013

Cited by 63 publications

(26 citation statements)

References 80 publications

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“…LSSs have large numbers of free parameters (sometimes including parameters that are hard coded and thus easily overlooked, Mendoza et al, ) whose values are uncertain. Sensitivity analysis can be used to understand how certain parameters affect certain model outputs (Bastidas, Hogue, Sorooshian, Gupta, & Shuttleworth, ; Palar, Zuhal, Shimoyama, & Tsuchiya, ; Sieber & Uhlenbrook, ; Slater et al, ). However, this can be challenging when the number of parameters is large (Cadero et al, ), when the influences of different parameters are not independent, and when we are potentially interested in multiple output metrics.…”

Section: Methodsmentioning

confidence: 99%

Controls on evapotranspiration from jack pine forests in the Boreal Plains Ecozone

Nazarbakhsh

Ireson

Barr

2019

Hydrological Processes

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The exchanges of water, energy and carbon between the land surface and the atmosphere are tightly coupled, so that errors in simulating evapotranspiration lead to errors in simulating both the water and carbon balances. Areas with seasonally frozen soils present a particular challenge due to the snowmelt-dominated hydrology and the impact of soil freezing on the soil hydraulic properties and plant root water uptake. Land surface schemes that have been applied in high latitudes often have reported problems with simulating the snowpack and runoff. Models applied at the Boreal Ecosystem Research and Monitoring Sites in central Saskatchewan have consistently over-predicted evapotranspiration as compared with flux tower estimates.We assessed the performance of two Canadian land surface schemes (CLASS and CLASS-CTEM) for simulating point-scale evapotranspiration at an instrumented jack pine sandy upland site in the southern edge of the boreal forest in Saskatchewan, Canada. Consistent with past reported results, these models over-predicted evapotranspiration, as compared with flux tower observations, but only in the spring period. Looking systematically at soil properties and vegetation characteristics, we found that the dominant control on evapotranspiration within these models was the canopy conductance. However, the problem of excessive spring ET could not be solved satisfactorily by changing the soil or vegetation parameters. The model overestimation of spring ET coincided with the overestimation of spring soil liquid water content. Improved algorithms for the infiltration of snowmelt into frozen soils and plant-water uptake during the snowmelt and soil thaw periods may be key to addressing the biases in spring ET. K E Y W O R D S

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Section: Methodsmentioning

confidence: 99%

Controls on evapotranspiration from jack pine forests in the Boreal Plains Ecozone

Nazarbakhsh

Ireson

Barr

2019

Hydrological Processes

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“…To calculate the PCE coefficients, one may use the traditional projection technique or regression method . However, it is known that these methods suffer from the “curse of dimensionality.” To overcome this issue, Blatman and Sudret proposed several adaptive algorithms to identify the most relevant basis functions sequentially from full PCE using only few samples.…”

Section: Polynomial Chaos Approximationmentioning

confidence: 99%

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Cheng

Lü

2020

Numerical Meth Engineering

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Assessing the failure probability of complex aeronautical structure is a difficult task in presence of uncertainties. In this paper, active learning polynomial chaos expansion (PCE) is developed for reliability analysis. The proposed method firstly assigns a Gaussian Process (GP) prior to the model response, and the covariance function of this GP is defined by the inner product of PCE basis function. Then, we show that a PCE model can be derived by the posterior mean of the GP, and the posterior variance is obtained to measure the local prediction error as Kriging model. Also, the expectation of the prediction variance is derived to measure the overall accuracy of the obtained PCE model. Then, a learning function, named expected indicator function prediction error (EIFPE), is proposed to update the design of experiment of PCE model for reliability analysis.This learning function is developed under the framework of the variance-bias decomposition. It selects new points sequentially by maximizing the EIFPE that considers both the variance and bias information, and it provides a dynamic balance between global exploration and local exploitation. Finally, several test functions and engineering applications are investigated, and the results are compared with the widely used Kriging model combined with U and expected feasibility function learning function. Results show that the proposed method is efficient and accurate for complex engineering applications.

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“…Here, we build on the MFMC method [38] and present new multifidelity estimators for the variance and main effect sensitivity indices. Multifidelity formulations which target estimation of Sobol' indices have been presented in [15,26,27,37]. The work in [15] considers a setting where, in addition to having random inputs, the model itself is stochastic.…”

mentioning

confidence: 99%

“…In this approach, lower-fidelity models can be introduced via a cokriging model, thus increasing the quality of the Gaussian process approximation without incurring additional evaluations of the expensive high-fidelity model. In [37], the Sobol' indices are obtained from a polynomial chaos expansion derived from a low-fidelity model with a correction polynomial chaos expansion derived from the difference between the low-and the high-fidelity model at some inputs. In both [27,37], the Sobol' indices are obtained for a surrogate model, and the multifidelity formulation serves to efficiently increase the quality of the surrogate employed.…”

mentioning

confidence: 99%

“…In [37], the Sobol' indices are obtained from a polynomial chaos expansion derived from a low-fidelity model with a correction polynomial chaos expansion derived from the difference between the low-and the high-fidelity model at some inputs. In both [27,37], the Sobol' indices are obtained for a surrogate model, and the multifidelity formulation serves to efficiently increase the quality of the surrogate employed. This means that the result will be biased relative to the original high-fidelity model.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices

Qian¹,

Peherstorfer²,

O’Malley³

et al. 2018

SIAM/ASA J. Uncertainty Quantification

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Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This work presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusionreaction model that demonstrate up to 10× speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

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Global sensitivity analysis via multi-fidelity polynomial chaos expansion

Cited by 63 publications

References 80 publications

Controls on evapotranspiration from jack pine forests in the Boreal Plains Ecozone

Controls on evapotranspiration from jack pine forests in the Boreal Plains Ecozone

Active learning polynomial chaos expansion for reliability analysis by maximizing expected indicator function prediction error

Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices

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