SquaredExponentialCovariance

Squared Exponential covariance function.

Overview

A widely used, general purpose isotropic covariance function is

is a scaled distance based on the length factor , defined as

Hyperparameters

Table 1: Hyperparameters for Squared Exponential Covariance Function

VariableDomainDescription
Length factors corresponding to input parameters*
Signal variance*
Noise variance*

*See the Gaussian Process Trainer documentation for more in depth explanation of , , and hyperparameters.

Example Input File Syntax

[Covariance]
  [covar]
    type = SquaredExponentialCovariance
    signal_variance = 1 #Use a signal variance of 1 in the kernel
    noise_variance = 1e-6 #A small amount of noise can help with numerical stability
    length_factor = '0.38971 0.38971' #Select a length factor for each parameter (k and q)
  []
[]
(modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential.i)

Input Parameters

  • length_factorLength Factor to use for Covariance Kernel

    C++ Type:std::vector<double>

    Controllable:No

    Description:Length Factor to use for Covariance Kernel

  • noise_variance0Noise Variance ($\sigma_n^2$) to use for kernel calculation.

    Default:0

    C++ Type:double

    Controllable:No

    Description:Noise Variance ($\sigma_n^2$) to use for kernel calculation.

  • signal_varianceSignal Variance ($\sigma_f^2$) to use for kernel calculation.

    C++ Type:double

    Controllable:No

    Description:Signal Variance ($\sigma_f^2$) to use for kernel calculation.

Required 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.

Advanced Parameters

Input Files