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.

中文翻译：

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应用于微波滤波器的大范围参数建模的并行分解方法

本文提出了一种新的分解技术来解决电磁 (EM) 参数建模的挑战，其中几何参数的值在大范围内变化。在该方法中，提出了一种基于二阶导数信息的系统自动化算法，将整体几何范围分解为一组子范围。使用所提出的技术，平滑区域被分解成几个大的子区域，而高度非线性的区域被分解成许多小的子区域。所提出的技术提供了一种有效的数学方法来在系统和自动化的过程中执行分解。具有简单结构的人工神经网络（ANN）模型，在此称为子模型，是在每个子区域中以几何参数作为变量开发的。当几何参数的值从一个子模型的区域变化到另一个子模型时，在相邻子模型之间的边界处观察到电磁响应的不连续性。整体模型中有很多子模型边界，导致复杂的多维不连续性问题。提出了一个子模型修改过程来解决这个多维不连续问题，以获得整个区域的连续模型。提出了并行数据生成、并行子模型训练和并行子模型修改以加快建模开发过程。与使用单一模型覆盖整个宽几何范围的标准建模方法相比，该方法可以在较短的模型开发时间下获得更好的模型精度。