论文标题
使用基质分解和深神经网络的参数化电磁问题的模型订购降低
Model order reduction for parameterized electromagnetic problems using matrix decomposition and deep neural networks
论文作者
论文摘要
本文提出了一种用于解决参数化电磁散射问题的非侵入模型阶数（MOR）方法。通过求解基于高阶不连续的Galerkin Time-time-time-timain（DGTD）方法的某些值的参数化时间域麦克斯韦方程来构建高保真解决方案快照的数据库。为了进行先前的维度降低，通过两步正确的正交分解（POD）方法从数据库中提取一组减少基础（RB）函数。通过卷积自动编码器（CAE）网络进一步压缩了降低基础功能的投影系数。然后，使用CAE产生的还原级矩阵的主要成分来提取奇异值分解（SVD），并采用了基于立方样条插值（CSI）方法来近似降低矩阵的主导时间和参数模式。在离线阶段完成了减少基础和CAE和CSI的训练，因此可以通过插值模型和解码器网络的输出快速恢复给定时间/参数值的RB解决方案。特别是，提出的RB方法的离线和在线阶段被完全解耦，从而确保了该方法的有效性。通过2-D介电磁盘和多层异质培养基散射平面波的数值实验，用数值实验说明了所提出的CAE-CSI ROM的性能。
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.
