One predominant challenge in additive manufacturing (AM) is to achieve specific material properties by manipulating manufacturing process parameters during the runtime. Such manipulation tends to increase the computational load imposed on existing simulation tools employed in AM. The goal of the present work is to construct a fast and accurate reduced-order model (ROM) for an AM model developed within the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, ultimately reducing the time/cost of AM control and optimization processes. Our adoption of the operator learning (OL) approach enabled us to learn a family of differential equations produced by altering process variables in the laser's Gaussian point heat source. More specifically, we used the Fourier neural operator (FNO) and deep operator network (DeepONet) to develop ROMs for time-dependent responses. Furthermore, we benchmarked the performance of these OL methods against a conventional deep neural network (DNN)-based ROM. Ultimately, we found that OL methods offer comparable performance and, in terms of accuracy and generalizability, even outperform DNN at predicting scalar model responses. The DNN-based ROM afforded the fastest training time. Furthermore, all the ROMs were faster than the original MOOSE model yet still provided accurate predictions. FNO had a smaller mean prediction error than DeepONet, with a larger variance for time-dependent responses. Unlike DNN, both FNO and DeepONet were able to simulate time series data without the need for dimensionality reduction techniques. The present work can help facilitate the AM optimization process by enabling faster execution of simulation tools while still preserving evaluation accuracy.

翻译：增材制造（AM）中的一项主要挑战是在运行过程中通过调整制造工艺参数来实现特定的材料性能。这种调整往往会增加AM中现有仿真工具的计算负荷。本工作旨在为多物理场面向对象模拟环境（MOOSE）框架内开发的AM模型构建快速精确的降阶模型（ROM），最终减少AM控制与优化过程的时间/成本。我们采用算子学习（OL）方法，能够学习通过改变激光高斯点热源中工艺变量而产生的微分方程族。具体而言，我们使用傅里叶神经算子（FNO）和深度算子网络（DeepONet）为时间相关响应开发了ROM。此外，我们将这些OL方法的性能与传统基于深度神经网络（DNN）的ROM进行了基准测试。最终发现，在预测标量模型响应方面，OL方法性能相当，且在精度和泛化能力上甚至优于DNN。基于DNN的ROM实现了最快的训练时间。此外，所有ROM均比原始MOOSE模型运行更快，同时仍能提供精确预测。对于时间相关响应，FNO的均值预测误差小于DeepONet，但方差更大。与DNN不同，FNO和DeepONet均能模拟时间序列数据，无需降维技术。本工作通过实现仿真工具的快速执行并保持评估精度，有助于促进AM优化过程。