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We propose a non-intrusive, reduced-basis, and data-driven method forapproximating both eigenvalues and eigenvectors in parametric eigenvalueproblems. We generate the basis of the reduced space by applying the properorthogonal decomposition (POD) approach on a collection of pre-computed,full-order snapshots at a chosen set of parameters. Then, we use Bayesianlinear regression (a.k.a. Gaussian Process Regression) in the online phase topredict both eigenvalues and eigenvectors at new parameters. A split of thedata generated in the offline phase into training and test data sets isutilized in the numerical experiments following standard practices in the fieldof supervised machine learning. Furthermore, we discuss the connection betweenGaussian Process Regression and spline methods, and compare the performance ofGPR method against linear and cubic spline methods. We show that GPRoutperforms other methods for functions with a certain regularity. To this end,we discuss various different covariance functions which influence theperformance of GPR. The proposed method is shown to be accurate and efficientfor the approximation of multiple 1D and 2D affine and non-affineparameter-dependent eigenvalue problems that exhibit crossing of eigenvalues.

A data-driven method for parametric PDE Eigenvalue Problems using Gaussian Process with different covariance functions