基於向量電路壓降(vectored IR-drop)分析在晶片簽收(sign off)階段是其中一個重要的步驟用來確保功率(power)在電源分布網路(power distribution network)的完整性，然而動態(dynamic) IR-drop的分析是一個非常耗時的過程，本文利用機器學習來建立一個predictor，用來預測電路上的元件(standard cells)
本文中我們利用機器學習計算IR-drop提出兩個創新的想法。第一，由於 IR-drop 本身是一個極端不平衡的資料集，因此提出一個新的兩階段模型(two-stage model)來改善那些高IR-drop 元件的表現。在此架構下我們達到了20%的改善。第二，由於我們的架構中與分類的表現有關，我們使用了Remix這個原先用來改善不平衡圖像分類的技巧到扁平數據(tabular data)上以提升模型的表現。經過實驗證明，兩階段模型可令高IR的單元表現上升20%，再加上Remix更可以提升80%以上，同時可輕易的應用到其他IR-drop的情景。

Vectored IR-drop analysis is a crucial component of the chip signoff phase, as it is indispensable for ensuring power integrity within the power distribution network. Yet, dynamic IR-drop analysis is highly time-consuming. In this thesis, we utilize machine learning to devise a predictor that forecasts the IR-drop for all standard cells in the circuit. Furthermore, we introduce two novel concepts regarding IR-drop estimation through machine learning.

Firstly, to counter the severe imbalance in the IR-drop dataset, we suggest a unique two-stage model aimed at enhancing the performance of cells with high IR-drop. This approach has achieved a 20% improvement in performance. Secondly, given that our model's efficacy can be affected by classification, we implement the 'Remix' technique. Originally used to bolster imbalanced image classification, we apply it to tabular data to improve our model's performance. Our experiments reveal that the straightforward two-stage model alone can amplify performance by 20%. When supplemented with the 'Remix' technique, the performance of cells with high IR-drop can improve by over 80%. This method is also versatile, as it can be conveniently applied to other IR-drop scenarios.

Abstract (Chinese) I
Contents III
List of Figures V
List of Tables VI
1 Introduction 1
2 Background 5
2.1 Features engineering . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Machine Learning for Tabular Data . . . . . . . . . . . . . . . . . . 6
2.2.1 Tree-based model study . . . . . . . . . . . . . . . . . . . . 6
2.2.2 XGBoost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Mixup-based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Proposed Method 10
3.1 Proposed Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 Two-stage model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.3 Remix for tabular data . . . . . . . . . . . . . . . . . . . . . . . . . 12
4 Experiments 16
4.1 Evaluation Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
III
4.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.4 Features Ablation Study . . . . . . . . . . . . . . . . . . . . . . . . 19
5 Conclusion 21
Reference 22

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