Saving a smoothed function of two variables

[#1]

I need to not only visualize a smoothed function of two variables Y(X1, X2), which is what I can do with a Contour plot in Graph builder with an adjustable smoothness parameter lambda, but also save a table of smoothed Y values Ysmooth(X1, X2). How would I go about it?

[#2]

Try either the Neural or Gaussian process platforms. They should be able to fit a smoothed model to the data, and the prediction formula for that model that can be used create a table of smoothed Y values.  You can also use that prediction formula in the Profilers (Profiler, Contour Profiler) and Surface Plot to visualize the smooth fit to the data.  

[#3]

I've considered a parametric fit, but the model has to be really complex to capture many extrema and saddle points I need to have in the smoothed surface. I was looking for a 2D counterpart of a smoother with a flexible lambda. Am I out of luck with JMP here and have to resort to Python programming?

[#4]

[#5]

Thanks! The Gaussian process does work as a 2D smoother Y(X1, X2) I can save, but I have one complication in my smoothing task: the degrees of smoothing (lambdas, Gaussian widths or some other smoothing parameters) have to be very different for X1 and X2, because I know there is lots of noise I need to filter out along X1, but along X2 the complicate change profile is the actual signal I want to capture in the smoother. In other words, I need anisotropic smoothing. I tried "Estimate Nugget" option, but it seems to also be isotropic (no difference in degree of smoothing along X1 and X2).