基于算子学习的MOOSE增材制造模型的快速准确降阶建模
Fast and Accurate Reduced-Order Modeling of a MOOSE-based Additive Manufacturing Model with Operator Learning
AI总结：
本工作针对MOOSE框架下的增材制造模型，利用FNO和DeepONet等算子学习方法构建快速准确的降阶模型，在保持预测精度的同时显著提升了仿真速度并降低了优化成本。
摘要：
增材制造（AM）领域的一个主要挑战是通过在运行时操纵制造工艺参数来实现特定的材料性能。这种操纵往往会增加AM中使用的现有仿真工具的计算负荷。本工作的目标是为在多物理场面向对象仿真环境（MOOSE）框架内开发的AM模型构建一个快速且准确的降阶模型（ROM），最终降低AM控制和优化过程的时间/成本。我们采用的算子学习（OL）方法使我们能够学习通过改变激光高斯点热源中的工艺变量而产生的一族微分方程。更具体地说，我们使用傅里叶神经算子（FNO）和深度算子网络（DeepONet）来开发用于时间相关响应的ROM。此外，我们将这些OL方法的性能与传统的基于深度神经网络（DNN）的ROM进行了基准比较。最终，我们发现OL方法提供了相当的性能，并且在准确性和泛化能力方面，甚至在预测标量模型响应时优于DNN。基于DNN的ROM提供了最快的训练时间。此外，所有ROM都比原始MOOSE模型更快，但仍提供了准确的预测。FNO的平均预测误差比DeepONet小，但在时间相关响应上具有更大的方差。与DNN不同，FNO和DeepONet都能够模拟时间序列数据，而无需降维技术。本工作通过实现仿真工具的更快执行同时保持评估准确性，有助于促进AM优化过程。
英文摘要：
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.
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