AttentionCap: Transformer Based Capacitance Matrix Learning Toward Full-Chip Extraction

2026-06-06

AI Summary

This work addresses the insufficient accuracy of traditional capacitance extraction methods and the limited generalization of existing deep learning models at advanced process nodes. The authors propose AttentionCap, a customized Transformer architecture tailored for capacitance matrix learning, which introduces attention mechanisms into capacitance modeling for the first time. Key innovations include Gram matrix representation, a physically aligned symmetric attention output layer, a normalized Laplacian loss function, and process node embeddings, collectively enabling cross-node transferability and few-shot fine-tuning. Evaluated on unseen real-world designs, AttentionCap achieves remarkably low errors of 0.67% for self-capacitance and 3.99% for coupling capacitance—reducing baseline CNN-Cap errors by 4.6–5.7×—while accelerating inference by 192×.

Abstract

As capacitance extraction accuracy of rule-based pattern matching becomes difficult to sustain at advanced nodes, a growing trend emerges to develop deep-learning-based 2D capacitance models. However, existing MLP- and CNN-based methods constrain their input to fixed metal-layer combinations in a specific process node, limiting their usability in practice. Recognizing the inherent similarity between capacitance matrix and the prevailing attention mechanism, we propose AttentionCap, a customized Transformer for capacitance matrix learning, with a Gram representation framework, a physics-aligned symmetric-attention output layer, and a novel normalized Laplacian loss. We also introduce a process-node embedding to enable multi-node learning. Trained on synthetic data, AttentionCap attains 0.67\%/3.99\% self/coupling-capacitance error on unseen real designs under a multi-layer and multi-node setting, surpassing the CNN-Cap baseline with 4.6$\times$/5.7$\times$ lower self/coupling error and 192$\times$ faster inference speed. A pretrained AttentionCap accurately transfers to an unseen node with only 5K samples and 4K finetuning steps. With sufficient accuracy on unseen real designs and strong transferability to new process nodes, AttentionCap offers highly practical value for modern EDA workflows. Code and data are available at https://github.com/THU-numbda/AttentionCap.

Problem

• capacitance extraction
• deep learning
• process node generalization
• EDA
• parasitic modeling

Innovation

• Transformer
• Capacitance Extraction
• Attention Mechanism
• Multi-Node Learning
• EDA