電壓降和有效電阻是評估現代積體電路設計中電源傳輸網路穩健性的關鍵指標。在現今積體電路設計流程中的工程改變命令（ECO）階段需要對電源傳輸網路進行迭代調整，過程中需要多次啟動電源傳輸網路分析工具來評估改進結果。傳統上，積體電路設計中的靜態電壓降使用修正節點分析系統（MNA）為基礎的電源線路分析工具進行計算，而有效電阻則通過拉普拉斯系統進行推導。然而，這兩種方法都受到運行時間限制的影響。
在工程改變命令階段，即使對電源傳輸網路進行微小的局部調整，使用傳統的拉普拉斯系統和修正節點分析系統驅動的電源傳輸網路分析工具也會需要不成比例的運行時間。這主要是因為使用拉普拉斯系統計算電源傳輸網路中任意節點的有效電阻需要考慮整個電源傳輸網路中的所有節點。同樣地，使用修正節點分析系統為基礎的電源線路分析工具進行積體電路設計中的靜態電壓降分析也需要考慮整個電源傳輸網路中的所有節點。
為了應對這些問題，本研究提出利用兩個基於機器學習方法的流程。這些基於機器學習方法的流程旨在提高計算電源傳輸網路中區域性有效電阻和計算積體電路設計中區域性靜態電壓降的速度。實驗結果表明，與拉普拉斯系統為基礎的商業工具和與修正節點分析系統為基礎的商業工具相比，所提出的方法在運行時間上實現了顯著的改進。估計積體電路設計中區域性靜態電壓降速度大約是以修正節點分析系統為基礎的商業工具的四倍，誤差在20%的範圍內。同樣地，估計電源傳輸網路中區域性有效電阻的速度大約是以拉普拉斯系統為基礎的商業工具的四倍，誤差約為1%。

Voltage (IR) drop and effective resistance (effR) are key metrics for assessing the robustness of the Power Delivery Network (PDN) in Very-Large-ScaleIntegration (VLSI) circuit designs. The Engineering Change Order (ECO) phase of the modern design cycle requires iterative tuning of PDNs, necessitating multiple launches of rail analysis tools to guide the refinement process. Traditionally, the static IR drop in VLSI circuit designs is computed using Modified Nodal Analysis System (MNA)-driven rail analysis tools, while effR is derived through a Laplacian System. However, both approaches suffer from significant runtime limitations.
During the ECO phase, even minor local adjustments to the PDN entail disproportional amount of run-time when using traditional Laplacian System and MNA-driven rail analysis tools. This is primarily due to the need to consider the entire PDN for computing the effR of any individual network node in the Laplacian System. Similarly, using MNA-driven rail analysis tools to calculate the IR drop of modules caused by PDN-induced ablation encounters challenges of massive run-time cost. Consequently, there is a need to address these limitations.
To tackle these issues, this research proposes the utilization of two machine learning (ML) models, and both models are U-Net-based models. These ML-based approaches aim to expedite the estimation of regional static IR drop and effRs. Experimental results demonstrate that the proposed methodology achieves significant run-time improvements compared to an MNA-driven commercial tool and a commercial tool employing a Laplacian System. The estimated static IR drop is approximately four times faster than the Commercial MNA-driven tool, with errors within the range of 20%, comparable to other proposed IR drop prediction works. Similarly, the estimation of effRs is approximately four times faster than the Laplacian System tool, with errors around 1%.

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