UCLA

When adjusting the geometric, material, and boundary properties of an electromagnetic (EM) system, the system's response varies with the design variables. While full-wave simulations can estimate the response for a fixed set of design variables, they do not model the relationship between the design variables and EM system responses. Parametric modeling is essential for design sensitivity analysis, statistical analysis, and optimization. EM parametric modeling research could revolutionize EM simulation and design. Historically, engineers faced long wait times (hours or even days) for simulation completion and relied on trial-and-error schemes to tune design parameters. Incorporating parametric modeling in EM designs has the potential to significantly decrease EM design and optimization time to a tolerable level (seconds or minutes), consequently reducing design costs and electronic devices' time to market. In this study, we have researched on several parametric modeling techniques in EM applications. The parametric modeling techniques fall into two main categories: intrusive and non-intrusive. Non-intrusive parametric modeling assumes the response-parameter relation as a mathematical function and uses training data samples to train the model. We first investigate the classical continuous function reconstruction using Nyquist-Shannon sampling and sinc interpolations to reconstruct the Mie scattering formula. Surrogate models estimate the response-parameter relationship through orthogonal basis expansion or interpolation. Trained with a limited number of full-wave simulation training samples, surrogate models are constructed to estimate statistics of RF human exposure. We also demonstrate the efficiency of surrogate-based optimization in the design of an embroidery textile patch antenna. The Fourier neural operator (FNO), a recently-proposed neural network dedicated for solving partial differential equations (PDE), is investigated to accelerate EM simulations. The unique features of FNO, such as global convolution and multilayer iterative processes, make it suitable for fast solving integral equations. Neural networks with FNO are implemented to accelerate EM simulations and perform as EM parametric modeling in electrostatic and electromagnetic problems. As another type of parametric modeling, intrusive parametric modeling incorporates underlying physics into the modeling. The first-order Taylor expansion expresses employs the first-order gradient with respect to design parameters. The gradient is obtained by adjoint variation methods (AVM) applied on finite element method (FEM) solutions. The method requires only one evaluation to get the gradient with respect to design parameters, compared to the finite difference method, which requires multiple evaluations. Additionally, we introduce the use of PyTorch's auto-gradient tool to calculate derivatives conveniently for the first time. Inspired by FNO, we introduce a Conjugate-Gradient Fast-Fourier-Transform (CGFFT) iterative solver for volume integral equations as a neural network configuration. The method employs intrusive modeling techniques, while it is accelerated by advanced hardware and software technologies developed for artificial intelligence (AI). Research in EM parametric modeling not only provides fast and easy-to-use engineering design tools and methodology, but also paves the way for further investigation into expressing PDE solutions on compressed function bases. Moreover, researchers can incorporate rapidly evolving AI techniques into EM modeling and simulations in the future.