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):

$(1)var element = document.getElementById("moose-equation-49914444-0094-431e-ade0-af35a72a9574");katex.render(" a(\\pmb{x}) = (\\mu - f(\\pmb{x}^*))^2 + \\sigma^2", element, {displayMode:true,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$

where, $var element = document.getElementById("moose-equation-d384fa88-4119-48fb-9a48-a2e770a91428");katex.render("f(\\pmb{x}^*)", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the computational model output at $var element = document.getElementById("moose-equation-820d902f-bd4d-4176-9e8a-bd7461113f78");katex.render("\\pmb{x}^*", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ which is the closest point to $var element = document.getElementById("moose-equation-65266bc0-6e13-4510-abd5-25cc8973f28d");katex.render("\\pmb{x}", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ , $var element = document.getElementById("moose-equation-30471206-1c1e-4add-861f-9eee5953f1d8");katex.render("\\mu", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ is the Gaussian process mean prediction, and $var element = document.getElementById("moose-equation-5a4e9062-7e79-48b2-9330-9dd9c4b88802");katex.render("\\sigma", element, {displayMode:false,throwOnError:false,macros:{"\\eqc":"\\,,","\\eqp":"\\,.","\\pd":"\\frac{\\partial #1}{\\partial #2}","\\pr":"\\left(#1\\right)","\\ddt":"\\frac{d #1}{d t}"}});$ 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