geopfa.extrapolation.build_rbf_kernel_global

build_rbf_kernel_global(X_stdized, Y_stdized, input_dim=2, lower_frac=0.02, upper_frac=0.2)[source]

Construct an RBF kernel whose ARD lengthscale bounds are derived from the global radius of the standardized training coordinates.

Parameters:

  • X_stdized (numpy.ndarray) – Standardized training coordinates, shape (N, 2).

  • Y_stdized (numpy.ndarray) – Standardized training targets, shape (N, 1).

  • input_dim (int, optional) – Dimensionality of the input space. Default is 2.

  • lower_frac (float, optional) – Fraction of the global radius used as the lower lengthscale bound.

  • upper_frac (float, optional) – Fraction of the global radius used as the upper lengthscale bound.

Returns:

(GPy.kern.RBF, dict) – The constructed RBF kernel and a dictionary describing the applied constraints and initialization values.

Notes

  • The global radius stabilizes ARD lengthscale bounds across datasets with different spatial extents.

  • Variance is initialized based on the variance of Y_stdized and constrained with a Gamma prior.