ExpectedImprovementGlobalFit

Expected improvement for global fit (EIGF) by Lam and Notz 2008.

Overview

The ExpectedImprovementGlobalFit acquisition function for parallel active learning (global surrogate fitting) is given by (Lam, 2008):

$(1)var element = document.getElementById("moose-equation-182efba6-f388-41a7-8022-65f271723d01");katex.render(" a(\\pmb{x}) = (\\mu - f(\\pmb{x}^*))^2 + \\sigma^2", element, {displayMode:true,throwOnError:false});$

where, $var element = document.getElementById("moose-equation-2c85a730-6c84-4fb9-898a-e4c4439bccd5");katex.render("f(\\pmb{x}^*)", element, {displayMode:false,throwOnError:false});$ is the computational model output at $var element = document.getElementById("moose-equation-95c441a8-70f1-4f10-9663-6d6572bda113");katex.render("\\pmb{x}^*", element, {displayMode:false,throwOnError:false});$ which is the closest point to $var element = document.getElementById("moose-equation-7264190a-3715-4e10-87db-59bcfdea855b");katex.render("\\pmb{x}", element, {displayMode:false,throwOnError:false});$ , $var element = document.getElementById("moose-equation-c767dc13-ea32-4a35-a9c7-a3f7d706666d");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ is the Gaussian process mean prediction, and $var element = document.getElementById("moose-equation-7954ef29-16c8-45d7-86fe-2b01a5b21a37");katex.render("\\sigma", element, {displayMode:false,throwOnError:false});$ is the Gaussian process standard deviation.

Input Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:No
Description:Set the enabled status of the MooseObject.

References

C. Q. Lam. Sequential adaptive designs in computer experiments for response surface model fit. PhD thesis, The Ohio State University, 2008.

@phdthesis{Lam2008thesis,
    author = "Lam, C. Q.",
    title = "Sequential adaptive designs in computer experiments for response surface model fit",
    school = "The Ohio State University",
    year = "2008"
}

Overview
Input Parameters
References