- covariance_functionsCovariance functions that this covariance function depends on.
C++ Type:std::vector<UserObjectName>
Unit:(no unit assumed)
Controllable:No
Description:Covariance functions that this covariance function depends on.
- num_outputs1The number of outputs expected for this covariance function.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of outputs expected for this covariance function.
LMC
Covariance function for multioutput Gaussian Processes based on the Linear Model of Coregionalization (LMC).
The linear model of co-regionalization (LMC) distinctly models the covariances between the inputs and the outputs. Mathematically, the LMC is defined as (Liu et al., 2018; Cheng et al., 2020):
(1)
where, denotes the latent basis index, output covariance matrix of size for the -th covariate, is the input covariance matrix of size for the -th covariate, is the total number of basis functions, and denotes the Kronecker product. is further defined as the sum of two matrices of weights (Cheng et al., 2020):
(2)
where, and are vectors (size ) of hyper-parameters, both for the -th basis. The size is user-defined and it can be greater than or equal to 1. The larger the , the more sophisticated the multi-output Gaussian Process in modeling complex outputs.
If , the LMC reduces to the intrinsic co-regionalization model (ICM).
Example Input File Syntax
(contrib/moose/modules/stochastic_tools/test/tests/surrogates/multioutput_gp/mogp_lmc.i)Input Parameters
- num_latent_funcs1The number of latent functions for the expansion of the outputs.
Default:1
C++ Type:unsigned int
Unit:(no unit assumed)
Controllable:No
Description:The number of latent functions for the expansion of the outputs.
Optional Parameters
- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Unit:(no unit assumed)
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
Unit:(no unit assumed)
Controllable:No
Description:Set the enabled status of the MooseObject.
Advanced Parameters
References
- L. F. Cheng, B. Dumitrascu, G. Darnell, C. Chivers, M. Draugelis, K. Li, and B. E. Engelhardt.
Sparse multi-output gaussian processes for online medical time series prediction.
BMC medical informatics and decision making, 20(1):1–23, 2020.[BibTeX]
- H. Liu, J. Cai, and Y. S. Ong.
Remarks on multi-output gaussian process regression.
Knowledge-Based Systems, 144:102–112, 2018.[BibTeX]