Fast and Accurate Reduced-Order Modeling of a MOOSE-based Additive
  Manufacturing Model with Operator Learning
Mahmoud Yaseen Dewen Yushu Peter German Xu Wu
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.