Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

NAS-Cap: Deep-Learning Driven 3-D Capacitance Extraction with Neural Architecture Search and Data Augmentation

Haoyuan Li, Dingcheng Yang, Chunyan Pei, Wenjian Yu

TL;DR

The paper tackles the challenge of accurate and efficient 3-D capacitance extraction for IC interconnects by applying neural architecture search (DrNAS-style) to design a CNN tailored for 3-D data, complemented by a data augmentation strategy that multiplies training instances by 8×. It introduces NAS-Cap, a cell-based CNN with normal and reduction cells that optimizes architecture weights and connection weights to minimize mean square relative error for total and coupling capacitances, while avoiding BN in most cells. The approach yields substantial accuracy gains over the prior CNN-Cap, particularly for coupling capacitance, and reduces model size and inference time, with demonstrated transferability across different designs and process technologies. Overall, NAS-Cap offers a practical, scalable route to surpass pattern-matching accuracy and approach field-solver-like precision for full-chip capacitance extraction in complex ICs.

Abstract

More accurate capacitance extraction is demanded for designing integrated circuits under advanced process technology. The pattern matching approach and the field solver for capacitance extraction have the drawbacks of inaccuracy and large computational cost, respectively. Recent work \cite{yang2023cnn} proposes a grid-based data representation and a convolutional neural network (CNN) based capacitance models (called CNN-Cap), which opens the third way for 3-D capacitance extraction to get accurate results with much less time cost than field solver. In this work, the techniques of neural architecture search (NAS) and data augmentation are proposed to train better CNN models for 3-D capacitance extraction. Experimental results on datasets from different designs show that the obtained NAS-Cap models achieve remarkably higher accuracy than CNN-Cap, while consuming less runtime for inference and space for model storage. Meanwhile, the transferability of the NAS is validated, as the once searched architecture brought similar error reduction on coupling/total capacitance for the test cases from different design and/or process technology.

NAS-Cap: Deep-Learning Driven 3-D Capacitance Extraction with Neural Architecture Search and Data Augmentation

TL;DR

The paper tackles the challenge of accurate and efficient 3-D capacitance extraction for IC interconnects by applying neural architecture search (DrNAS-style) to design a CNN tailored for 3-D data, complemented by a data augmentation strategy that multiplies training instances by 8×. It introduces NAS-Cap, a cell-based CNN with normal and reduction cells that optimizes architecture weights and connection weights to minimize mean square relative error for total and coupling capacitances, while avoiding BN in most cells. The approach yields substantial accuracy gains over the prior CNN-Cap, particularly for coupling capacitance, and reduces model size and inference time, with demonstrated transferability across different designs and process technologies. Overall, NAS-Cap offers a practical, scalable route to surpass pattern-matching accuracy and approach field-solver-like precision for full-chip capacitance extraction in complex ICs.

Abstract

More accurate capacitance extraction is demanded for designing integrated circuits under advanced process technology. The pattern matching approach and the field solver for capacitance extraction have the drawbacks of inaccuracy and large computational cost, respectively. Recent work \cite{yang2023cnn} proposes a grid-based data representation and a convolutional neural network (CNN) based capacitance models (called CNN-Cap), which opens the third way for 3-D capacitance extraction to get accurate results with much less time cost than field solver. In this work, the techniques of neural architecture search (NAS) and data augmentation are proposed to train better CNN models for 3-D capacitance extraction. Experimental results on datasets from different designs show that the obtained NAS-Cap models achieve remarkably higher accuracy than CNN-Cap, while consuming less runtime for inference and space for model storage. Meanwhile, the transferability of the NAS is validated, as the once searched architecture brought similar error reduction on coupling/total capacitance for the test cases from different design and/or process technology.
Paper Structure (12 sections, 5 equations, 11 figures, 6 tables)

This paper contains 12 sections, 5 equations, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background
  3. CNN-Cap Model for Capacitance Extraction
  4. Neural Architecture Search
  5. Methodology
  6. The Idea and Architecture Settings
  7. NAS-Cap Model for Capacitance Extraction
  8. Training NAS-Cap Models with Data Augmentation
  9. Experimental Results
  10. Results on Dataset 1
  11. Results on Dataset 2 and Dataset 3
  12. Conclusions

Figures (11)

  • Figure 1: The process of building CNN-Cap models and using them for predicting 2-D capacitances. (a) The training stage. (b) The prediction stage yang2023cnn.
  • Figure 2: An example of a metal layer's data representation for 3-D interconnect structure. The case includes three conductors where the master conductor is in the middle. (a) The data representation for calculating the total capacitance $C_{11}$. (b) The data representation for calculating the coupling capacitance $C_{12}$ (Conductor 2 is on the left) yang2023cnn.
  • Figure 3: The architecture of the proposed model. (a) Overview of the whole network model, (b) Connection among cells in the cell series.
  • Figure 4: The directed acyclic graph (DAG) representing a cell, where each block with "?" represents an operation.
  • Figure 5: The workflow of the proposed deep-learning based method with neural architecture search.
  • ...and 6 more figures