隨著半導體製程的進步，電源完整性問題是積體電路實體設計中需要考慮的一環。
電路壓降，屬於電源完整性的其中一個項目，指的是電流通過電源供應網路時，由於
金屬導線電阻引起的電路壓降，過高的電壓損耗會使得訊號及電源傳遞到電晶體時無
法正確的驅動，引起電路功能完整性的問題，因此在設計規則檢查中占有重要地位。
傳統上，要得到精確的靜態電路壓降值需要等到電路繞線完畢，使用克希荷夫電壓定
律進行節點分析來得知電路壓降的狀況。然而數萬個節點會使得聯立方程組過於龐大，
求精確解的過程過於耗時。在本論文中，我們提出一個使用卷積神積網路的機器學習
模型和改進的資料處理，在尚未繞線前，能夠預測出當前的靜態電路壓降的方法，相
對先前的研究，我們能以更好的平均絕對誤差及 F1 分數，有效地預測靜態電路壓降。

As the semiconductor manufacturing process advances, power integrity issues
have become an important design rule check during physical design. Voltage drop,
part of power integrity, refers to the voltage drop caused by the resistance of metal
conductors in the power delivery network when current flows from the power pad
to the transistor. Excessive voltage drops can prevent signals from correctly driving
the transistors, leading to functional behavior issues. Hence, it holds a significant
place in design rule checks. Traditionally, obtaining precise static voltage drop
values requires completing the circuit routing and using Kirchhoff’s voltage law
for node analysis to identify where voltage drop issues occur. However, analyzing
tens of millions of nodes results in a system of equations that is too large, making
the time to find an exact solution excessively long. In this thesis, we propose a
machine learning model using convolutional neural networks and improved data
extraction to predict static voltage drop in the layout design before the routing stage
once we have the placement result and the powerplan. Compare to the previous
work, we can have a better prediction quality in terms of both MAE and F1 score.

[1] G. S. P. Kadagala and V. A. Chhabria, “Invited Paper: 2023 ICCAD CAD Contest Problem
C: Static IR Drop Estimation Using Machine Learning,” 2023 IEEE/ACM International
Conference on Computer Aided Design (ICCAD), San Francisco, CA, USA, 2023, pp.
1-5, doi: 10.1109/ICCAD57390.2023.10323767.
[2] O. Ronneberger, P. Fischer and T. Brox,“U-Net: Convolutional Networks for Biomedical
Image Segmentation.＂Medical Image Computing and Computer-Assisted Intervention–
MICCAI 2015, Springer International Publishing, 2015, pp. 234–41. doi: 10.1007/978-3-
319-24574-4_28.
[3] M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. Corrado, A. Davis, J.
Dean, M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, R. Jozefowicz,
Y. Jia, L. Kaiser, M. Kudlur, J. Levenberg, D. Mané, M. Schuster, R. Monga, S. Moore, D.
Murray, C. Olah, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke,
V. Vasudevan, F. Viégas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X.
Zheng, “TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems,” 2015.
Software available from tensorflow.org.
[4] Retrieved from https://github.com/ASU-VDA-Lab/ML-for-IR-drop.git
[5] Retrieved from https://si2.org/open-cell-and-free-pdk-libraries/
[6] V. A. Chhabria, V. Ahuja, A. Prabhu, N. Patil, P. Jain and S. S. Sapatnekar, “Thermal
and IR Drop Analysis Using Convolutional Encoder-Decoder Networks,” 2021 26th Asia
and South Pacific Design Automation Conference (ASP-DAC), Tokyo, Japan, 2021, pp.
690-696.
[7] K. He, X. Zhang, S. Ren, J. Sun, “Deep Residual Learning for Image Recognition,” doi:
10.48550/arXiv.1512.03385
[8] C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke,
A. Rabinovich, “Going Deeper with Convolutions,” doi: 10.48550/arXiv.1409.4842
[9] C.-T. Ho and A. B. Kahng, “IncPIRD: Fast Learning-Based Prediction of Incremental IR
Drop,” 2019 IEEE/ACM International Conference on Computer-Aided Design (ICCAD),
Westminster, CO, USA, 2019, pp. 1-8, doi: 10.1109/ICCAD45719.2019.8942110.
[10] Z. Xie, H. Li, X. Xu, J. Hu and Y. Chen, “Fast IR Drop Estimation with Machine Learning
: Invited Paper,” 2020 IEEE/ACM International Conference On Computer Aided Design
(ICCAD), San Diego, CA, USA, 2020, pp. 1-8.
[11] Z. Xie et al., “PowerNet: Transferable Dynamic IR Drop Estimation via Maximum
Convolutional Neural Network,” 2020 25th Asia and South Pacific Design Automa-
tion Conference (ASP-DAC), Beijing, China, 2020, pp. 13-18, doi: 10.1109/ASP-
DAC47756.2020.9045574.
[12] C.-H. Pao, A.-Y. Su and Y.-M. Lee, “XGBIR: An XGBoost-based IR Drop Pre-
dictor for Power Delivery Network,” 2020 Design, Automation & Test in Europe
Conference & Exhibition (DATE), Grenoble, France, 2020, pp. 1307-1310, doi:
10.23919/DATE48585.2020.9116327.
[13] H. Zhou, W. Jin and S. X.-D. Tan, “GridNet: Fast Data-Driven EM-Induced IR Drop
Prediction and Localized Fixing for On-Chip Power Grid Networks,” 2020 IEEE/ACM
International Conference On Computer Aided Design (ICCAD), San Diego, CA, USA,
2020, pp. 1-9.
[14] S. Lin and N. Chang, “Challenges in power-ground integrity,” 2001 IEEE/ACM Interna-
tional Conference On Computer Aided Design (ICCAD), San Jose, CA, USA, 2001, pp.
651-654, doi: 10.1109/ICCAD.2001.968730.
[15] L. T. Wang, Y. W. Chang, and K. T. Cheng, “Electronic Design Automation: Synthesis,
Verification, and Test,” Elsevier Science, 2009, ch. 13, sec. 2-4, pp. 760-763, 829-850.
[16] C. White, W. Neiswanger, S. Nolen, and Y. Savani, “A Study on Encodings for Neural
Architecture Search,” 2020 Advances in Neural Information Processing Systems, vol. 33,
H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin, Eds. Curran Associates,
Inc., 2020, pp. 20309-20319, doi: 10.48550/arXiv.2007.04965
[17] Q. K. Zhu, “Power Distribution Network Design For VLSI”, John Wiley & Sons, Ltd,
2004, ch. 4, pp. 87-104. doi: https://doi.org/10.1002/0471660302.ch4
[18] VoltageStorm Transistor-Level PGS User Guide, Cadence Design Systems, Inc., 2002.
[19] T. Ajayi, V. A. Chhabria, M. Fogaça, S. Hashemi, A. Hosny, A. B. Kahng, M. Kim, J. Lee,
U. Mallappa, M. Neseem, G. Pradipta, S. Reda, M. Saligane, S. S. Sapatnekar, C. Sechen,
M. Shalan, W. Swartz, L. Wang, Z. Wang, M. Woo, and B. Xu, “Toward an Open-Source
Digital Flow: First Learnings from the OpenROAD Project,” in Proceedings of the 56th
Annual Design Automation Conference 2019, Las Vegas, NV, USA, 2019, pp. 1-4, Art.
no. 76. doi: 10.1145/3316781.3326334.
[20] S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager,
E. Gouillart, T. Yu, and the scikit-image contributors, “scikit-image: Image Processing in
Python,” PeerJ, vol. 2, p. e453, Jun. 2014. doi: 10.7717/peerj.453.
[21] V. A. Chhabria, K. Kunal, M. Zabihi and S. S. Sapatnekar, “BeGAN: Power Grid Bench-
mark Generation Using a Process-portable GAN-based Methodology,” 2021 IEEE/ACM
International Conference On Computer Aided Design (ICCAD), Munich, Germany, 2021,
pp. 1-8, doi: 10.1109/ICCAD51958.2021.9643566.
[22] V. A. Chhabria, K. Kunal, M. Zabihi and S. S. Sapatnekar, “BeGAN-benchmarks,” 2021.
[Online]. Available: https://github.com/UMN-EDA/BeGAN-benchmarks.
[23] V. A. Chhabria, et al., “ThermEDGe-and-IREDGe,＂2021. [Online]. Available:
https://github.com/VidyaChhabria/ThermEDGe-and-IREDGe.
[24] J. Bergstra and Y. Bengio, “Random search for hyper-parameter optimization,” The Jour-
nal of Machine Learning Research, vol. 13, pp. 281–305, Feb. 2012.