Functional gaussian processes

Methodology
1

Not sure if this is the correct location for this topic.

Within the openturns library, I see there is something called “ConditionedGaussianProcess”.

Having only worked with Kriging method before, can someone explain the difference between Kriging approach and the conditioned gaussian process. My understanding is that the kriging process is assuming a zero mean some covariance and useful for stationary problems, e.g. estimating the surface of the Earth. Whereas the conditioned gaussian process can account for some trend within the mean, e.g. temporal variance. In simple terms, is that more or less correct?

The second thing is that upon reviewing the literature, I come across the term “functional gaussian process regression”:
https://www.sciencedirect.com/science/article/pii/S0031320322006094?ref=cra_js_challenge&fr=RR-1

I understand this as the situation where the mean of a gaussian process is assumed to be a function. This sounds quite similar to the “conditioned gaussian process” of openturns. Is this terminology interchangeable?

2

ConditionedGaussianProcess is a class that can be used after Kriging. It lets you sample trajectories from the Kriging Gaussian Process, conditioned on the observations (that is, trajectories interpolate the data).

Please have a look at this example:

https://openturns.github.io/openturns/1.23/auto_meta_modeling/kriging_metamodel/plot_kriging_simulate.html

The class is called at the end:

process = ot.ConditionedGaussianProcess(krigingResult, myRegularGrid)

As you can see, the arguments are a KrigingResult (obtained from a KrigingAlgorithm that has been run) and a discretization grid for the trajectories.