Approximation of IMSE-optimal Designs via Quadrature Rules and Spectral Decomposition

We address the problem of computing IMSE (Integrated Mean-Squared Error) optimal designs for random fields interpolation with known mean and covariance. We both consider the IMSE and truncated-IMSE (approximation of the IMSE by spectral truncation). We assume that the MSE is integrated through a discrete measure and restrict the design space to the support of the considered measure. The IMSE and truncated-IMSE of such designs can be easily evaluated at the cost of some simple preliminary computations, making global optimization affordable. Numerical experiments are carried out and illustrate the interest of the considered approach for the approximation of IMSE optimal designs.