A fast surrogate cross validation algorithm for meshfree RBF collocation approaches

Francesco Marchetti

Abstract: Highlights•Cross-validation is an important tool for tuning parameters in kernel-based interpolation and collocation frameworks.•The extended Rippa's algorithm is a well-established strategy to reduce the computational cost required by cross-validation in the interpolation setting. However, in literature, the proposed adaptations of this approach to the collocation context consist of empirical adjustments with limited theoretical insights.•We propose and analyze a surrogate cross-validation algorithm that approximates the true validation error, and can be considered as the natural extension of Rippa's scheme into the collocation setting.•The efficiency of the proposed surrogate scheme, as well as its effectiveness when compared to the empirical adaptations proposed in literature, are proved by means of various numerical experiments involving various PDE collocation settings.