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.

翻译：随着基于系统级封装（SiP）芯粒设计的异构2.5D/3D集成技术的出现，热致翘曲已成为关键可靠性问题。传统数值方法虽能提供高精度结果，但通常面临高昂计算成本，限制了其在复杂芯粒-封装系统中的可扩展性。本文提出WarPGNN——一种基于图神经网络（GNN）的高效精准参数化热致翘曲分析框架。该框架直接对从布局规划构建的图结构进行操作，支持快速翘曲感知布局探索，并展现出跨不同封装配置的强迁移能力。该方法首先将多裸片布局规划编码为简化传递闭包图（rTCG），然后采用基于图卷积网络（GCN）的编码器提取层次化结构特征，最后通过受U-Net启发的解码器从图特征嵌入重建翘曲分布图。此外，针对翘曲数据分布的长尾特性，我们开发了物理信息损失函数，并基于图同构网络（GIN）改进消息传递编码器，进一步增强了极端情况下的学习性能和图嵌入的表达能力。数值结果表明：与基于二维高效有限元法（FEM）的方法相比，WarPGNN实现超过205.91倍加速；与基于三维FEM的COMSOL方法相比，加速比达119766.64倍以上，同时保持可比精度——全尺度归一化均方根误差（RMSE）仅1.26%，翘曲值误差2.21%。与近期基于DeepONet的模型相比，该方法在预测精度和推理加速方面性能相当，而训练时间降低3.4倍。此外，WarPGNN在未见数据集上展现出卓越迁移能力，归一化RMSE达3.69%，且运行时间相近。