Data-driven reduced order modeling for parametric PDE eigenvalue problems using Gaussian process regression

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.