Differentiable Graph Neural Networks for Wirelength Estimation

A model that utilizes a graph neural network (GNN) is proposed to estimate wirelength in the early stages of physical design. The model predicts the post-routing wirelength of a net, which addresses the limitations of current estimators including half-perimeter wirelength (HPWL) that tend to under-estimate the true post-routed wirelength of complex nets. Utilizing a dataset of 18 benchmark circuits, the GNN achieves an average R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of 0.825, outperforming HPWL, which yields an R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of 0.764. The GNN demonstrates consistent performance across nets of varying lengths, providing significantly improved accuracy over HPWL for long and multi-path nets. The GNN model is differentiable and compatible with gradient-based optimization methods, while providing an 8× improvement in inference time.