The objective of this study is to evaluate whether the number of requisite
training samples can be reduced with the use of various transfer learning
models for predicting, for example, the chemical source terms of the
data-driven reduced-order model that represents the homogeneous ignition
process of a hydrogen/air mixture. Principal component analysis is applied to
reduce the dimensionality of the hydrogen/air mixture in composition space.
Artificial neural networks (ANNs) are used to tabulate the reaction rates of
principal components, and subsequently, a system of ordinary differential
equations is solved. As the number of training samples decreases at the target
task (i.e.,for T0 > 1000 K and various phi), the reduced-order model fails to
predict the ignition evolution of a hydrogen/air mixture. Three transfer
learning strategies are then applied to the training of the ANN model with a
sparse dataset. The performance of the reduced-order model with a sparse
dataset is found to be remarkably enhanced if the training of the ANN model is
restricted by a regularization term that controls the degree of knowledge
transfer from source to target tasks. To this end, a novel transfer learning
method is introduced, parameter control via partial initialization and
regularization (PaPIR), whereby the amount of knowledge transferred is
systemically adjusted for the initialization and regularization of the ANN
model in the target task. It is found that an additional performance gain can
be achieved by changing the initialization scheme of the ANN model in the
target task when the task similarity between source and target tasks is
relatively low.

通过使用各种迁移学习模型来预测氢 / 空气混合物的均相点火过程数据驱动的降阶模型的化学源项等目标，本研究评估了是否可以减少所需的训练样本数量。

化学反应流中主成份传输源项预测的迁移学习

Transfer learning for predicting source terms of principal component  transport in chemically reactive flow

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.

通过运用运算符学习方法构建 AM 模型的快速准确的降阶模型，以提高 AM 控制和优化过程的时间 / 成本，同时保持评估准确性。

基于 MOOSE 的添加制造模型的快速准确降阶建模与操作学习

Fast and Accurate Reduced-Order Modeling of a MOOSE-based Additive  Manufacturing Model with Operator Learning

One possible way of making thermal processing controllable is to gather
real-time information on the product's current state. Often, sensory equipment
cannot capture all relevant information easily or at all. Digital Twins close
this gap with virtual probes in real-time simulations, synchronized with the
process. This paper proposes a physics-based, data-driven Digital Twin
framework for autonomous food processing. We suggest a lean Digital Twin
concept that is executable at the device level, entailing minimal computational
load, data storage, and sensor data requirements. This study focuses on a
parsimonious experimental design for training non-intrusive reduced-order
models (ROMs) of a thermal process. A correlation ($R=-0.76$) between a high
standard deviation of the surface temperatures in the training data and a low
root mean square error in ROM testing enables efficient selection of training
data. The mean test root mean square error of the best ROM is less than 1
Kelvin (0.2 % mean average percentage error) on representative test sets.
Simulation speed-ups of Sp $\approx$ 1.8E4 allow on-device model predictive
control.
The proposed Digital Twin framework is designed to be applicable within the
industry. Typically, non-intrusive reduced-order modeling is required as soon
as the modeling of the process is performed in software, where root-level
access to the solver is not provided, such as commercial simulation software.
The data-driven training of the reduced-order model is achieved with only one
data set, as correlations are utilized to predict the training success a
priori.

本文提出了一种基于物理和数据驱动的数字孪生框架，用于自主食品加工，该框架含有最小计算负载、数据存储和传感器数据要求的精益数字孪生概念，并采用一个节俭的实验设计用于训练热处理的非侵入式降阶模型，其最佳模型的测试均方根误差小于 1 开尔文（0.2％平均百分比误差），模拟速度加快达到 1.8E4 Sp，可用于设备内的模型预测控制。