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.

翻译：本研究将深度算子网络（DeepONet）引入核工程数字孪生（DT）系统，作为其鲁棒的代理建模方法。随着核能作为碳中和解决方案的重要性日益凸显，采用数字孪生技术对于提升核工程应用中的运行效率、安全性和预测能力变得至关重要。DeepONet展现出卓越的预测精度，优于传统机器学习方法。通过广泛的基准测试与评估，本研究展示了DeepONet在解决具有挑战性的粒子输运问题时的可扩展性与计算效率。通过将函数作为输入数据，并从训练数据中构建算子$G$，DeepONet能够有效处理多样化且复杂的场景。然而，DeepONet的应用也揭示了与最优传感器布设和模型评估相关的挑战，这些是实际部署中的关键方面。应对这些挑战将进一步增强该方法的实用性与可靠性。总体而言，DeepONet为核工程研究与应用提供了一种富有前景且变革性的工具。其精准预测与计算效率能力可革新数字孪生系统，推动核工程研究进展。本研究标志着在关键工程领域利用代理建模技术迈出的重要一步。