  The data driven extrapolation requires the definition of a functional model
depending on the available data and has the application scope of providing
reliable predictions on the unknown dynamics. Since data might be scattered, we
drive our attention towards kernel models that have the advantage of being
meshfree. Precisely, the proposed numerical method makes use of the so-called
Variably Scaled Kernels (VSKs), which are introduced to implement a feature
augmentation-like strategy based on discrete data. Due to the possible
uncertainty on the data and since we are interested in modelling the behaviour
of the considered dynamics, we seek for a regularized solution by ridge
regression. Focusing on polyharmonic splines, we investigate their
implementation in the VSK setting and we provide error bounds in Beppo-Levi
spaces. The performances of the method are then tested on functions which are
common in the framework of the Laplace transform inversion. Comparisons with
Support Vector Regression (SVR) are also carried out and show that the proposed
method is effective particularly since it does not require to train complex
architecture constructions.
