Nonuniform frequency sampling with active learning: Application to wide-band frequency-domain modeling and design

One must employ many frequency points to synthesize a wide-band time-domain signal scattered or radiated from a given linear device. If the structure is large relative to wavelengths of interest, the large number of required frequency-domain computations may require significant computational resources. An active learning framework is introduced to reduce the number of frequencies needed for frequency-domain numerical computations or measurements. This method is used to optimally select frequency points at which a computation of measurement should be performed, resulting in nonuniform frequency sampling and often a reduced number of total frequency points (vis-a-vis uniform sampling). In this paper we focus on wide-band frequency-domain numerical modeling, demonstrating a reduction in the required number of computations. The method consists of two basic steps, tied to fitting the frequency-domain data to a simple parametric model. One step involves estimation of model parameters using a least-square (LS) algorithm. This process is based on data from frequency points computed thus far by the rigorous numerical model. The next step is to optimally choose the next frequency point for analysis by the numerical model. This new frequency point is selected with the goal of reducing uncertainty in the simplified parametric model (quantified via the Fisher information matrix). Iterating these two steps, a sequence of numerical computations are performed, each at the most informative frequency for learning the parameters of the associated simpler parametric model. After demonstrating this technique with scattering problems, the idea is employed for design of an ultrawide-band antenna. In this design, a genetic algorithm (GA) is employed to optimize the geometry and the resistive loading of an antenna, with the number of required frequency-domain numerical computations reduced by the parametric model and active learning.