High-fidelity, data-driven models that can quickly simulate thermal behavior during additive manufacturing (AM) are crucial for improving the performance of AM technologies in multiple areas, such as part design, process planning, monitoring, and control. However, the complexities of part geometries make it challenging for current models to maintain high accuracy across a wide range of geometries. Additionally, many models report a low mean square error (MSE) across the entire domain (part). However, in each time step, most areas of the domain do not experience significant changes in temperature, except for the heat-affected zones near recent depositions. Therefore, the MSE-based fidelity measurement of the models may be overestimated. This paper presents a data-driven model that uses Fourier Neural Operator to capture the local temperature evolution during the additive manufacturing process. In addition, the authors propose to evaluate the model using the $R^2$ metric, which provides a relative measure of the model's performance compared to using mean temperature as a prediction. The model was tested on numerical simulations based on the Discontinuous Galerkin Finite Element Method for the Direct Energy Deposition process, and the results demonstrate that the model achieves high fidelity as measured by $R^2$ and maintains generalizability to geometries that were not included in the training process.

翻译：高保真、数据驱动的模型能够快速模拟增材制造过程中的热行为，这对于提升增材制造技术在零件设计、工艺规划、监测与控制等多个领域的性能至关重要。然而，零件几何结构的复杂性使得现有模型难以在广泛几何范围内保持高精度。此外，许多模型在整体计算域（零件）上报告的均方误差较低，但在每个时间步中，除近期沉积区域附近的热影响区外，计算域内大部分区域的温度变化并不显著。因此，基于均方误差的模型保真度评估可能被高估。本文提出一种采用傅里叶神经算子的数据驱动模型，用于捕获增材制造过程中的局部温度演变。同时，作者建议使用$R^2$指标评估模型性能，该指标通过对比均值温度预测方法，提供模型性能的相对度量。该模型在基于不连续伽辽金有限元法的定向能量沉积工艺数值模拟上进行了测试，结果表明：模型在$R^2指标下实现了高保真度，并对未参与训练过程的几何结构保持了良好的泛化能力。