Deep learning (DL) has achieved remarkable successes in many disciplines such
as computer vision and natural language processing due to the availability of
``big data''. However, such success cannot be easily replicated in many nuclear
engineering problems because of the limited amount of training data, especially
when the data comes from high-cost experiments. To overcome such a data
scarcity issue, this paper explores the applications of deep generative models
(DGMs) that have been widely used for image data generation to scientific data
augmentation. DGMs, such as generative adversarial networks (GANs), normalizing
flows (NFs), variational autoencoders (VAEs), and conditional VAEs (CVAEs), can
be trained to learn the underlying probabilistic distribution of the training
dataset. Once trained, they can be used to generate synthetic data that are
similar to the training data and significantly expand the dataset size. By
employing DGMs to augment TRACE simulated data of the steady-state void
fractions based on the NUPEC Boiling Water Reactor Full-size Fine-mesh Bundle
Test (BFBT) benchmark, this study demonstrates that VAEs, CVAEs, and GANs have
comparable generative performance with similar errors in the synthetic data,
with CVAEs achieving the smallest errors. The findings shows that DGMs have a
great potential to augment scientific data in nuclear engineering, which proves
effective for expanding the training dataset and enabling other DL models to be
trained more accurately.

本研究探讨深度生成模型在核工程中扩增科学数据的应用，发现变分自编码器（VAEs）、条件变分自编码器（CVAEs）和生成对抗网络（GANs）具有相当的生成性能，使合成数据集的误差较小，证明深度生成模型在核工程中具有扩增训练数据集并让其他深度学习模型更准确训练的巨大潜力。

基于深度生成建模的数据增强与演示，使用 BFBT 基准空隙率数据集

Deep Generative Modeling-based Data Augmentation with Demonstration  using the BFBT Benchmark Void Fraction Datasets

This research introduces the Deep Operator Network (DeepONet) as a robust
surrogate modeling method within the context of digital twin (DT) systems for
nuclear engineering. With the increasing importance of nuclear energy as a
carbon-neutral solution, adopting DT technology has become crucial to enhancing
operational efficiencies, safety, and predictive capabilities in nuclear
engineering applications. DeepONet exhibits remarkable prediction accuracy,
outperforming traditional ML methods. Through extensive benchmarking and
evaluation, this study showcases the scalability and computational efficiency
of DeepONet in solving a challenging particle transport problem. By taking
functions as input data and constructing the operator $G$ from training data,
DeepONet can handle diverse and complex scenarios effectively. However, the
application of DeepONet also reveals challenges related to optimal sensor
placement and model evaluation, critical aspects of real-world implementation.
Addressing these challenges will further enhance the method's practicality and
reliability. Overall, DeepONet presents a promising and transformative tool for
nuclear engineering research and applications. Its accurate prediction and
computational efficiency capabilities can revolutionize DT systems, advancing
nuclear engineering research. This study marks an important step towards
harnessing the power of surrogate modeling techniques in critical engineering
domains.

该研究介绍了 Deep Operator Network (DeepONet) 的应用，作为一个强大的代理建模方法，用于数字孪生系统，应用于核工程领域。DeepONet 展现了出色的预测准确性，优于传统机器学习方法。通过广泛的基准测试和评估，研究展示了 DeepONet 在解决复杂粒子传输问题方面的可伸缩性和计算效率。该研究对优化传感器布置和模型评估提出了挑战，这是实际实施中的关键问题。总的来说，DeepONet 为核工程研究和应用提供了一个有希望和具有变革性的工具，其准确的预测和高效的计算能力可以推动数字孪生系统的进一步发展，推进核工程研究，实现对关键工程领域的代理建模技术的有效利用。