Non-intrusive reduced order modeling of parametric electromagnetic scattering problems through Gaussian process regression

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.