Multi output Gaussian process (MOGP) surrogate for field quantities

[somu15]

Reason

MOGP will allow the prediction of field quantities like temperature distribution in the domain and also quantify the prediction uncertainties.

Design

MultiOutputGaussianProcessTrainer, MultiOutputGaussianProcess surrogate objects will be created. In addition, OutputCovariance covariance class will be created. Also, MultiOutputGaussianProcessHanlder utils class will be created for hyper-parameter optimization.

Impact

No expected impact to existing objects.

Closes #25438

[moosebuild]

Job Documentation on cb79d21 wanted to post the following:

View the site here

This comment will be updated on new commits.

[moosebuild]

Job Coverage on cb79d21 wanted to post the following:

Framework coverage

	62dc98	#27132 cb79d2
	Total	Total	+/-	New
Rate	85.06%	85.05%	-0.01%	0.00%
Hits	104412	104413	+1	0
Misses	18335	18350	+15	16

Diff coverage report

Full coverage report

Modules coverage

Stochastic tools

	62dc98	#27132 cb79d2
	Total	Total	+/-	New
Rate	90.61%	90.66%	+0.05%	95.86%
Hits	7922	7991	+69	649
Misses	821	823	+2	28

Diff coverage report

Full coverage report

Full coverage reports

Reports

• framework
• chemical_reactions
• combined
• contact
• electromagnetics
• external_petsc_solver
• fluid_properties
• fsi
• functional_expansion_tools
• geochemistry
• heat_transfer
• level_set
• misc
• navier_stokes
• optimization
• peridynamics
• phase_field
• porous_flow
• ray_tracing
• rdg
• reactor
• richards
• scalar_transport
• solid_mechanics
• solid_properties
• stochastic_tools
• thermal_hydraulics
• xfem

Warnings

• framework new line coverage rate 0.00% is less than the suggested 90.0%

This comment will be updated on new commits.

[moosebuild]

Job Precheck on 4fd5ba9 wanted to post the following:

Your code requires style changes.

A patch was auto generated and copied here
You can directly apply the patch by running, in the top level of your repository:

curl -s https://mooseframework.inl.gov/docs/PRs/27132/clang_format/style.patch | git apply -v

Alternatively, with your repository up to date and in the top level of your repository:

git clang-format be45bd992c48626133350fd34dfcb0d4db71293d

[grmnptr]

@loganharbour , this is ready!