  This paper is concerned with the design of a non-intrusive model order
reduction (MOR) for the system of parametric time-domain Maxwell equations. A
time- and parameter-independent reduced basis (RB) is constructed by using a
two-step proper orthogonal decomposition (POD) technique from a collection of
full-order electromagnetic field solutions, which are generated via a
discontinuous Galerkin time-domain (DGTD) solver. The mapping between the
time/parameter values and the projection coefficients onto the RB space is
approximated by a Gaussian process regression (GPR). Based on the data
characteristics of electromagnetic field solutions, the singular value
decomposition (SVD) is applied to extract the principal components of the
training data of each projection coefficient, and the GPR models are trained
for time- and parameter-modes respectively, by which the final global
regression function can be represented as a linear combination of these time-
and parameter-Gaussian processes. The extraction of the RB and the training of
GPR surrogate models are both completed in the offline stage. Then the field
solution at any new input time/parameter point can be directly recovered in the
online stage as a linear combination of the RB with the regression outputs as
the coefficients. In virtue of its non-intrusive nature, the proposed POD-GPR
framework, which is equation-free, decouples the offline and online stages
completely, and hence can predict the electromagnetic solution fields at unseen
parameter locations quickly and effectively. The performance of our method is
illustrated by a scattering problem of a multi-layer dielectric cylinder.
