Learning Nonlinear Responses in PET Bottle Buckling With a Hybrid DeepONet–Transolver Framework

Abstract

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize solutions across varying nonparametric geometric domains. In this work, we address this challenge in the context of polyethylene terephthalate (PET) bottle buckling analysis, a representative packaging design problem conventionally solved using computationally expensive finite element analysis (FEA). We introduce a hybrid DeepONet-Transolver framework that simultaneously predicts nodal displacement fields and the time evolution of reaction forces during top load compression. Our methodology is evaluated on two families of bottle geometries parameterized by two and four design variables. Training data is generated using nonlinear FEA simulations in Abaqus for 254 unique designs per family. The proposed framework achieves mean relative $L^2$ errors ranging from 2.5% to 13% for displacement fields and approximately 2.4% for time-dependent reaction forces for the four-parameter bottle family. Point-wise error analyses further show absolute displacement errors on the order of $10^{-4}$–$10^{-3}$, with the largest discrepancies confined to localized geometric regions. Importantly, the model accurately captures key physical phenomena, such as buckling behavior, across diverse bottle geometries. These results highlight the potential of our framework as a scalable and computationally efficient surrogate, particularly for multitask predictions in computational mechanics and applications requiring rapid design evaluation.