Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and manufacturing process. Current approaches employ numerical simulations, which however quickly becomes computation-intensive, especially for iterative optimization. Data-driven machine learning methods can be used to replace time- and resource-intensive numerical simulations. In particular, MeshGraphNets (MGNs) have shown promising results. They enable fast and accurate predictions on unseen mesh geometries while being fully differentiable for optimization. However, these models rely on large amounts of expensive training data, such as numerical simulations. Physics-informed neural networks (PINNs) offer an opportunity to train neural networks with partial differential equations instead of labeled data, but have not been extended yet to handle time-dependent simulations of arbitrary meshes. This work introduces PI-MGNs, a hybrid approach that combines PINNs and MGNs to quickly and accurately solve non-stationary and nonlinear partial differential equations (PDEs) on arbitrary meshes. The method is exemplified for thermal process simulations of unseen parts with inhomogeneous material distribution. Further results show that the model scales well to large and complex meshes, although it is trained on small generic meshes only.

翻译：工程部件必须在日益缩短的开发周期内满足不断增长的技术需求。为应对这些挑战，需采用一种能够并行开发部件设计、材料系统与制造工艺的整体性方法。现有方法依赖数值仿真，但在迭代优化过程中会迅速变得计算密集。数据驱动的机器学习方法可用于替代耗时耗资源的数值仿真，其中MeshGraphNets（MGNs）展现出显著潜力——它们能在未见网格几何结构上实现快速精准预测，且完全可微以支持优化。然而，此类模型依赖大量高成本训练数据（如数值仿真结果）。物理引导神经网络（PINNs）可通过偏微分方程替代标签数据训练网络，但尚未扩展至任意网格上的时变仿真场景。本文提出PI-MGNs这一混合方法，融合PINNs与MGNs以在任意网格上快速精准求解非稳态非线性偏微分方程。以材料非均匀分布的新部件热过程仿真为例验证该方法。进一步结果表明，尽管模型仅基于小型通用网格训练，却能良好扩展至大型复杂网格。