WarPGNN: A Parametric Thermal Warpage Analysis Framework with Physics-aware Graph Neural Network

2026-03-19

AI Summary

This work addresses the critical challenge of thermally induced warpage in 2.5D/3D heterogeneous integrated chip packaging, which severely compromises reliability and is traditionally analyzed using computationally expensive finite element methods (FEM). To overcome this limitation, the authors propose an efficient graph neural network–based parametric warpage analysis framework. The approach constructs a reduced transitive closure graph (rTCG) from layout data and employs a GCN encoder coupled with a U-Net decoder to rapidly predict warpage distributions. By incorporating a physics-informed loss function and an enhanced GIN message-passing mechanism, the model significantly improves its ability to capture long-tail extreme warpage cases and generalizes robustly across diverse designs. Compared to 2D and 3D FEM simulations, the method achieves acceleration ratios of 205.91× and 119,766.64×, respectively, with a normalized RMSE of only 1.26% and warpage error of 2.21%, while demonstrating 3.4× higher training efficiency than DeepONet.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

With the advent of system-in-package (SiP) chiplet-based design and heterogeneous 2.5D/3D integration, thermal-induced warpage has become a critical reliability concern. While conventional numerical approaches can deliver highly accurate results, they often incur prohib- itively high computational costs, limiting their scalability for complex chiplet-package systems. In this paper, we present WarPGNN, an ef- ficient and accurate parametric thermal warpage analysis framework powered by Graph Neural Networks (GNNs). By operating directly on graphs constructed from the floorplans, WarPGNN enables fast warpage-aware floorplan exploration and exhibits strong transfer- ability across diverse package configurations. Our method first en- codes multi-die floorplans into reduced Transitive Closure Graphs (rTCGs), then a Graph Convolution Network (GCN)-based encoder extracts hierarchical structural features, followed by a U-Net inspired decoder that reconstructs warpage maps from graph feature embed- dings. Furthermore, to address the long-tailed pattern of warpage data distribution, we developed a physics-informed loss and revised a message-passing encoder based on Graph Isomorphic Network (GIN) that further enhance learning performance for extreme cases and expressiveness of graph embeddings. Numerical results show that WarPGNN achieves more than 205.91x speedup compared with the 2-D efficient FEM-based method and over 119766.64x acceleration with 3-D FEM method COMSOL, respectively, while maintaining comparable accuracy at only 1.26% full-scale normalized RMSE and 2.21% warpage value error. Compared with recent DeepONet-based model, our method achieved comparable prediction accuracy and in- ference speedup with 3.4x lower training time. In addition, WarPGNN demonstrates remarkable transferability on unseen datasets with up to 3.69% normalized RMSE and similar runtime.

Problem

• thermal warpage
• system-in-package
• heterogeneous integration
• computational efficiency
• reliability

Innovation

• Graph Neural Network
• Thermal Warpage
• Physics-informed Learning
• Parametric Modeling
• Chiplet Integration