Parallel Decomposition Approach to Wide-Range Parametric Modeling With Applications to Microwave Filters

This article proposes a novel decomposition technique to address the challenges of electromagnetic (EM) parametric modeling, where the values of geometrical parameters change in a large range. In this method, a systematic and automated algorithm based on second-order derivative information is proposed to decompose the overall geometrical range into a set of subranges. Using the proposed technique, a smooth region is decomposed into a few large subregions, while a highly nonlinear region is decomposed into many small subregions. The proposed technique provides an efficient mathematical methodology to perform the decomposition in a systematic and automated process. An artificial neural network (ANN) model with a simple structure, hereby referred to as a submodel, is developed with geometrical parameters as variables in each subregion. When the values of geometrical parameters change from the region of one submodel to another submodel, the discontinuity of the EM responses is observed at the boundary between the adjacent submodels. There are many submodel boundaries in the overall model resulting in the complex multidimensional discontinuity problem. A submodel modification process is proposed to solve this multidimensional discontinuity problem to obtain a continuous model over the entire region. Parallel data generation, parallel submodel training, and parallel submodel modification are proposed to speed up the modeling development process. Compared with standard modeling methods using a single model to cover the entire wide geometrical range, the proposed method can obtain better model accuracy with short model-development time. Two microwave filter examples are used to illustrate the validity of the proposed technique.