Sparse Collocation Methods for Stochastic Interpolation and Quadrature

Gunzburger, Max; Webster, Clayton G.; Zhang, Guannan

doi:10.1007/978-3-319-11259-6_29-1

Cited by 1 publication

(1 citation statement)

References 61 publications

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“…Recently, the SG interpolation is developed with the aim of using fewer interpolation points to achieve a comparable accuracy with the full tensor interpolation (Barthelmann et al, ; Gunzburger et al ):

{frakturT}^{L, d} ([]|, η) (|, bold-italicθ) ≔ \underset{{L + 1 \leq |ℓ|}_{1} \leq L + d}{false\sum} {{(|, - 1)}^{L - {(|||, bold-scriptℓ)}_{1}} (|, \frac{0pt}{d - 1}) scriptU}^{{N_{scriptℓ}}_{1}} \otimes \dots \otimes {scriptU}^{N_{{scriptℓ}_{d}}} ([]|, η) .

The SG interpolant

{frakturT}^{L, d} ([]|, η) (|, bold-italicθ)

in equation is a weighted sum of a series of tensor‐product interpolants

{scriptU}^{N_{{scriptℓ}_{1}}} \otimes \dots \otimes {scriptU}^{N_{{scriptℓ}_{d}}} ([]|, η)

. Each of these interpolants is similar to the one in equation , but defined on a coarse grid with different resolution levels in different dimensions, i.e .,

{scriptℓ}_{i}

and

N_{{scriptℓ}_{i}}

may differ from each other for

i = 1, \dots, d

.…”

Section: Methodsmentioning

confidence: 99%

Calibration of the E3SM Land Model Using Surrogate‐Based Global Optimization

Ricciuto

Stoyanov

et al. 2018

J Adv Model Earth Syst

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Calibration of the Energy Exascale Earth System Model (E3SM), land model (ELMv0) is challenging because of its model complexity, strong model nonlinearity, and significant computational requirements. Therefore, only a limited number of simulations can be allowed in any attempt to find a near‐optimal solution within an affordable time. The goal of this study is to calibrate some of the ELMv0 parameters to improve model projection of carbon fluxes. We propose a computationally efficient global optimization procedure using sparse‐grid based surrogates. We first use advanced sparse grid (SG) interpolation to construct a surrogate system of the ELMv0, and then calibrate the surrogate model in the optimization process. As the surrogate model is a polynomial whose evaluation is fast, it can be efficiently evaluated a sufficiently large number of times in the optimization, which facilitates the global search. We calibrate eight parameters against five years of net ecosystem exchange, total leaf area index, and latent heat flux data from the U.S. Missouri Ozark flux tower. The calibrated model is then used for predicting the three variables in the following 4 years. The results indicate that an accurate surrogate model can be created for the ELMv0 with a relatively small number of SG points, i.e., a few ELMv0 simulations that can be fully parallel. And, the application of the optimized parameters leads to a better model performance and a higher predictive capability than the default parameter values in the ELMv0.

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{frakturT}^{L, d} ([]|, η) (|, bold-italicθ) ≔ \underset{{L + 1 \leq |ℓ|}_{1} \leq L + d}{false\sum} {{(|, - 1)}^{L - {(|||, bold-scriptℓ)}_{1}} (|, \frac{0pt}{d - 1}) scriptU}^{{N_{scriptℓ}}_{1}} \otimes \dots \otimes {scriptU}^{N_{{scriptℓ}_{d}}} ([]|, η) .

The SG interpolant

{frakturT}^{L, d} ([]|, η) (|, bold-italicθ)

in equation is a weighted sum of a series of tensor‐product interpolants

{scriptU}^{N_{{scriptℓ}_{1}}} \otimes \dots \otimes {scriptU}^{N_{{scriptℓ}_{d}}} ([]|, η)

. Each of these interpolants is similar to the one in equation , but defined on a coarse grid with different resolution levels in different dimensions, i.e .,