  A non-intrusive model order reduction (MOR) method for solving parameterized
electromagnetic scattering problems is proposed in this paper. A database
collecting snapshots of high-fidelity solutions is built by solving the
parameterized time-domain Maxwell equations for some values of the material
parameters using a fullwave solver based on a high order discontinuous Galerkin
time-domain (DGTD) method. To perform a prior dimensionality reduction, a set
of reduced basis (RB) functions are extracted from the database via a two-step
proper orthogonal decomposition (POD) method. Projection coefficients of the
reduced basis functions are further compressed through a convolutional
autoencoder (CAE) network. Singular value decomposition (SVD) is then used to
extract the principal components of the reduced-order matrices generated by
CAE, and a cubic spline interpolation-based (CSI) approach is employed for
approximating the dominating time- and parameter-modes of the reduced-order
matrices. The generation of the reduced basis and the training of the CAE and
CSI are accomplished in the offline stage, thus the RB solution for given
time/parameter values can be quickly recovered via outputs of the interpolation
model and decoder network. In particular, the offline and online stages of the
proposed RB method are completely decoupled, which ensures the validity of the
method. The performance of the proposed CAE-CSI ROM is illustrated with
numerical experiments for scattering of a plane wave by a 2-D dielectric disk
and a multi-layer heterogeneous medium.

Numerical Analysis;Numerical Analysis