Fiber reinforcement and polymer matrix respond differently to manufacturing conditions due to mismatch in coefficient of thermal expansion and matrix shrinkage during curing of thermosets. These heterogeneities generate residual stresses over multiple length scales, whose partial release leads to process-induced deformation (PID), requiring accurate prediction and mitigation via optimized non-isothermal cure cycles. This study considers a unidirectional AS4 carbon fiber/amine bi-functional epoxy prepreg and models PID using a two-mechanism framework that accounts for thermal expansion/shrinkage and cure shrinkage. The model is validated against manufacturing trials to identify initial and boundary conditions, then used to generate PID responses for a diverse set of non-isothermal cure cycles (time-temperature profiles). Building on this physics-based foundation, we develop a data-driven surrogate based on Deep Operator Networks (DeepONets). A DeepONet is trained on a dataset combining high-fidelity simulations with targeted experimental measurements of PID. We extend this to a Feature-wise Linear Modulation (FiLM) DeepONet, where branch-network features are modulated by external parameters, including the initial degree of cure, enabling prediction of time histories of degree of cure, viscosity, and deformation. Because experimental data are available only at limited time instances (for example, final deformation), we use transfer learning: simulation-trained trunk and branch networks are fixed and only the final layer is updated using measured final deformation. Finally, we augment the framework with Ensemble Kalman Inversion (EKI) to quantify uncertainty under experimental conditions and to support optimization of cure schedules for reduced PID in composites.

翻译：纤维增强相与聚合物基体在固化过程中因热膨胀系数失配及基体收缩，对制造条件呈现差异化响应。这种多尺度非均质性产生的残余应力部分释放会导致工艺诱导变形（PID），因此需通过优化非等温固化周期实现精确预测与调控。本研究以单向AS4碳纤维/胺双官能环氧预浸料为对象，采用双机制框架（包含热膨胀/收缩与固化收缩效应）构建PID模型。通过制造试验验证模型以确定初始条件与边界条件，进而生成不同非等温固化周期（时间-温度曲线）下的PID响应。基于此物理模型，我们开发了基于深度算子网络（DeepONet）的数据驱动代理模型。该DeepONet融合高保真仿真数据与目标实验测量的PID数据构成训练集，并进一步拓展为特征线性调制（FiLM）DeepONet：通过外部参数（包括初始固化度）调制分支网络特征，实现固化度、粘度及变形时间历程的预测。针对实验数据仅能获取有限时间点（如最终变形量）的局限性，我们采用迁移学习策略：固定经仿真数据训练的干线与分支网络，仅利用实测最终变形更新末层参数。最后，通过集成卡尔曼反演（EKI）框架量化实验条件不确定性，为优化复合材料固化工艺周期以降低PID提供支撑。