Data-driven prediction of fluid flow and temperature distribution in marine and aerospace engineering has received extensive research and demonstrated its potential in real-time prediction recently. However, usually large amounts of high-fidelity data are required to describe and accurately predict the complex physical information, while in reality, only limited high-fidelity data is available due to the high experiment/computational cost. Therefore, this work proposes a novel multi-fidelity learning method based on the Fourier Neural Operator by jointing abundant low-fidelity data and limited high-fidelity data under transfer learning paradigm. First, as a resolution-invariant operator, the Fourier Neural Operator is first and gainfully applied to integrate multi-fidelity data directly, which can utilize the scarce high-fidelity data and abundant low-fidelity data simultaneously. Then, the transfer learning framework is developed for the current task by extracting the rich low-fidelity data knowledge to assist high-fidelity modeling training, to further improve data-driven prediction accuracy. Finally, three typical fluid and temperature prediction problems are chosen to validate the accuracy of the proposed multi-fidelity model. The results demonstrate that our proposed method has high effectiveness when compared with other high-fidelity models, and has the high modeling accuracy of 99% for all the selected physical field problems. Significantly, the proposed multi-fidelity learning method has the potential of a simple structure with high precision, which can provide a reference for the construction of the subsequent model.

翻译：在航空航天与海洋工程中，基于数据驱动的流体流动与温度分布预测已获得广泛研究，并展现出实时预测的潜力。然而，描述和准确预测复杂物理信息通常需要大量高保真度数据，而现实中高保真度数据因高昂的实验/计算成本而极为有限。为此，本文提出一种基于傅里叶神经算子的新型多保真度学习方法，通过迁移学习范式融合丰富的低保真度数据和有限的高保真度数据。首先，傅里叶神经算子作为一种分辨率不变的算子，被首次且有效地应用于直接整合多保真度数据，能同时利用稀缺的高保真数据与丰富的低保真数据。随后，针对当前任务开发了迁移学习框架，通过提取丰富的低保真度数据知识辅助高保真度建模训练，以进一步提升数据驱动预测精度。最后，选取三个典型的流体与温度预测问题验证所提多保真度模型的准确性。结果表明，与其他高保真度模型相比，本文方法具有高效性，且对所有选定的物理场问题实现了99%的建模精度。值得注意的是，该多保真度学习方法兼具结构简单与高精度的潜力，可为后续模型构建提供参考。