Biomechanical Surrogate Modelling Using Stabilized Vectorial Greedy Kernel Methods

Greedy kernel approximation algorithms are successful techniques for sparse and accurate data-based modelling and function approximation. Based on a recent idea of stabilization (Wenzel et al., A novel class of stabilized greedy kernel approximation algorithms: convergence, stability & uniform point distribution. e-prints. arXiv:1911.04352, 2019) of such algorithms in the scalar output case, we here consider the vectorial extension built on VKOGA (Wirtz and Haasdonk, Dolomites Res Notes Approx 6:83–100, 2013. We introduce the so called γ-restricted VKOGA, comment on analytical properties and present numerical evaluation on data from a clinically relevant application, the modelling of the human spine. The experiments show that the new stabilized algorithms result in improved accuracy and stability over the non-stabilized algorithms