Add MCMC GP training

[xianjian-xie]

closes #28103

[moosebuild]

Job Precheck on cdecc0e 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/28166/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 182f6e0bf02749ec553df32dda8e607a0cc589fc

[grmnptr]

I have one quick comment: we will need tests for the new code. Check the tests files on how to specify one. The gold folder contains the files that you can compare results with.

[github-actions[bot]]

This pull request has been automatically marked as stale because it has not had recent activity in the last 100 days. It will be closed in 7 days if no further activity occurs. Thank you for your contributions.

[GiudGiud]

@xianjian-xie what's the status here? Do you have time to address the test failures? There are in the "precheck recipe" and are fairly simple to address

ERROR: The following files do not contain a newline character before EOF:
	modules/navier_stokes/test/tests/finite_element/uq_paper/Navier_Stokes.i
	modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_tuned_adam2.i
	modules/stochastic_tools/test/tests/surrogates/gaussian_process/GP_squared_exponential_tuned_adam3.i
	modules/stochastic_tools/test/tests/surrogates/gaussian_process/Navier_Stokes.i

Run the "delete_trailing_whitespace.sh" script in your $MOOSE_DIR/scripts directory.

ERROR: The following files contain banned keywords (std::cout, std::cerr, sleep, print_trace):
	modules/stochastic_tools/src/surrogates/GaussianProcessSurrogate.C
	modules/stochastic_tools/src/surrogates/TwoLayerGaussianProcessSurrogate.C
	modules/stochastic_tools/src/trainers/TwoLayerGaussianProcessTrainer.C
	modules/stochastic_tools/src/utils/GaussianProcess.C
	modules/stochastic_tools/src/utils/Standardizer.C
	modules/stochastic_tools/src/utils/TwoLayerGaussianProcess.C
##########################################################################

[grmnptr]

I am reviewing this right now. If the timeline changes we will take this over.

[github-actions[bot]]

This pull request has been automatically marked as stale because it has not had recent activity in the last 100 days. It will be closed in 7 days if no further activity occurs. Thank you for your contributions.