Training Set Optimization in an Artificial Neural Network Constructed for High Bandwidth Interconnects Design

In this article, a novel training set optimization method in an artificial neural network (ANN) constructed for high bandwidth interconnects design is proposed based on rigorous probability analysis. In general, the accuracy of an ANN is enhanced by increasing training set size. However, generating large training sets is inevitably time-consuming and resource-demanding, and sometimes even impossible due to limited prototypes or measurement scenarios. Especially, when the number of channels in required design are huge such as graphics double data rate (GDDR) memory and high bandwidth memory (HBM). Therefore, optimizing the training set selection process is crucial to minimizing the training datasets for developing an efficient ANN. According to rigorous mathematical analysis of the uniformity of the training data by probability distribution function, optimization flow of the range selection is proposed to improve accuracy and efficiency. The optimal number of training data samples is further determined by studying the prediction error rates. The performance of the proposed method in terms of accuracy is validated by comparing the scattering parameters of arbitrarily chosen strip and microstrip type GDDR interconnects obtained from EM simulations with those predicted by ANNs using default and the proposed training-set selection methods.

I. Introduction

Electromagnetic (EM) modeling is regarded as an effective way to characterize the microwave components. Several methods based on computational EM have been developed for an accurate characterization, such as finite-difference time-domain (FDTD) [1], finite element method (FEM) [2], method of moment (MoM) [3], and partial element equivalent circuit (PEEC) [4], etc. Those methods have been widely implemented in modeling microstrip lines, stripline, and coplanar structures [5]–[10]. The above-mentioned methods are all grid-based or cell-based techniques. A meshless modeling approach was proposed to avoid the very complicated and even time-consuming demerit caused by the practical structure with complex geometries [11]. In general, conventional numerical methods ensure accurate modeling by analyzing the inherent characteristics of microwave structures. Comprehensive understanding of complicated microwave theory and mathematics is the prerequisite to make use of those methods. To bring a convenience to a practical engineering level, complicated numerical methods have been realized by commercial simulation tools, and users do not need to face the original numerical challenges in their realistic usage. However, simulator-based approaches embody the following disadvantages: time-consuming, costly license fees, and expensive hardware resources [12].