Learning-based physics-enhanced modeling and inline material characterization for electromagnetics
TL;DR
This thesis explores possibilities for combining physics-based and learning-based techniques to create efficient hybrid methods for electromagnetic problems and proposes and evaluates Gradient-Informed Attentive Normalization Training (GIANT), a neural network training procedure for constructing computationally efficient surrogate models for CEM methods.
Abstract
This thesis explores data-driven modeling and inline material characterization methods for electromagnetic problems. In particular, it explores possibilities for combining physics-based and learning-based techniques to create efficient hybrid methods. The field of computational electromagnetics (CEM) offers many numerical methods to solve Maxwell's equations. However, they tend to be computationally demanding, especially in three spatial dimensions. In the first part of the thesis, we propose and evaluate Gradient-Informed Attentive Normalization Training (GIANT), a neural network training procedure for constructing computationally efficient surrogate models for CEM methods. GIANT consists of two parts: (i) Attentive Normalization (AttNorm), a reparameterization procedure that enables efficient training of very deep fully-connected neural networks; and (ii) gradient-informed training, which is used to minimize the number of samples that are needed to train the neural network. For the reciprocal microwave problems that we consider, we use continuum sensitivity analysis to compute these gradients at a very low computational cost. We demonstrate GIANT by constructing accurate surrogate models for a cylindrical resonator that is filled with an inhomogeneous dielectric and for an H-plane waveguide filter. In the second part of the thesis, we develop two inline material characterization techniques. The first is a method for determining unknown parameters that describe the materials of an electric motor. The method is based on a computationally efficient physics-based model of the motor, to which we apply a Bayesian estimation framework to exploit prior knowledge about the sought parameters. The second is an auto-calibration method that, given uncalibrated observations of scattering parameters, simultaneously determines the averaged permittivity of an inhomogeneous dielectric in the measurement domain and calibrates the measurement system. We demonstrate the methods by applying them to both synthetic and measured data.