- gammaGamma to use for Exponential Covariance Kernel
C++ Type:double
Controllable:No
Description:Gamma to use for Exponential Covariance Kernel
- 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.
ExponentialCovariance
Exponential covariance function.
Overview
A simple exponential covariance function can be constructed as
which is valid for . is a scaled distance based on the length factor , defined as
When is is equivalent to SquaredExponentialCovariance, save a factor of (which can be absorbed into ).
Hyperparameters
Table 1: Hyperparameters for Exponential Covariance Function
| Variable | Domain | Description |
|---|---|---|
| Length factors corresponding to input parameters* | ||
| Signal variance* | ||
| Noise variance* | ||
| Exponential factor |
*See the Gaussian Process Trainer documentation for more in depth explanation of , , and hyperparameters.
Example Input File Syntax
[Covariance]
[covar]
type = ExponentialCovariance
gamma = 1 #Define the exponential factor
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 = '0.551133 0.551133' #Select a length factor for each parameter (k and q)
[]
[]
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.