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

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.