Parametric PDE with a large number of parameters, perhaps in the hundreds, face the “Curse of dimensionality”. This talk will describe recent work on a kernel interpolation method applied to a many-parameter elliptic PDE . The first step is to transform the parameters of the parametric PDE so that they become 1- periodic. The PDE is then solved by a finite-element method at each point of a well-chosen lattice of points of the periodic parametric variables. Kernel interpolation is then used to interpolate beween the points of the lattice, with the lattice structure making kernel interpolation very efficient. Collaborators ar, e Frances Kuo, Alec Gilbert, Vesa Kaarnioja, Fabio Nobile and Yoshihito Kazashi.