應用高斯過程迴歸法於訊號完整度與天線的代理模型與設計

Abstract

本論文應用高斯過程迴歸法 (Gaussian Process Regression, GPR) 於訊號完整度分析，藉由具備物理意義之簡化變數取代原始多維設計參數，從而建立傳輸訊號系統所響應眼圖之預測模型；爰此，僅需少量訓練資料即可達到高準確度之眼圖預測，並且大幅地降低模擬時間與資料需求。此外，結合導線的導電係數與介電常數隨溫度變化之關係，所建立之GPR模型可以有效地考慮熱效應之影響，快速地建構符合JEDEC規範之設計範圍，而適用High Bandwidth Memory (HBM) 連線於Chip-on-Wafer-on-Substrate (CoWoS) 與Integrated Fan-Out (InFO) 等電子封裝結構，以提升高速連線系統之設計效率。就延伸之應用，本研究亦將GPR與主動子空間法 (Active Subspace Method) 結合應用於天線設計問題，藉由降維分析而建立共振頻率與輸入阻抗之近似解析設計關係，再以微帶天線為例，求得幾何參數之低維設計空間，能快速地設計天線之長寬尺寸與饋入位置。綜上所述，本論文所提出之方法可在維持預測準確度之情況下，大幅地降低計算成本，並且可應用於高速連線結構與微帶天線設計之問題，展現良好之效率與實用性。

Based on the Gaussian Process Regression (GPR), the reduced variables with a physics meaning are investigated in this thesis to replace the high-dimensional design parameters so as to analyze the signal integrity of a transmission system by constructing an efficiently responded eye-digram prediction model. This proposed approach achieves high prediction accuracy by employing only a small amount of training data, yet significantly reducing both the simulation time and data requirements. Concerning the temperature-dependent behavior of the metal conductivity and dielectric permittivity through the interconnect, this developed GPR model effectively accounts for its thermal effect to enable a rapid construction of the design solution-spaces that comply with JEDEC specifications. The method further applies to the HBM link in such as the CoWoS and InFO packaging structures, thereby improving the design efficiency of the high-speed interconnect systems. For a patch-antenna design, this thesis integrates GPR with Active Subspace Method through dimensionality reduction to approximate the analytical design relationships between the resonant frequency and input impedance. A reduced design space of the patch antenna is thus exploited to tune its dimensions and feeding positions to meet the specific frequency responses. Overall, the proposed methodology maintains the high prediction accuracy while significantly reducing the computational cost to be applied for both the SI analysis of high-speed links and the agile design of patch antennas, demonstrating strong efficiency and practical value.