  In this article, we propose a data-driven reduced basis (RB) method for the
approximation of parametric eigenvalue problems. The method is based on the
offline and online paradigms. In the offline stage, we generate snapshots and
construct the basis of the reduced space, using a POD approach. Gaussian
process regressions (GPR) are used for approximating the eigenvalues and
projection coefficients of the eigenvectors in the reduced space. All the GPR
corresponding to the eigenvalues and projection coefficients are trained in the
offline stage, using the data generated in the offline stage. The output
corresponding to new parameters can be obtained in the online stage using the
trained GPR. The proposed algorithm is used to solve affine and non-affine
parameter-dependent eigenvalue problems. The numerical results demonstrate the
robustness of the proposed non-intrusive method.
