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:数据驱动的预测海洋和航空工程中的流体流动和温度分布最近受到了广泛的研究,并展示了其在实时预测中的潜力。但通常需要大量高保真度数据来描述和准确地预测复杂的物理信息,而在现实中,由于高实验/计算成本,只有有限的高保真度数据可用。因此,本研究提出了一种基于傅里叶神经算子的多保真度学习方法,该方法利用迁移学习范式下的丰富低保真度数据和有限高保真度数据。首先,作为一种分辨率不变算子,傅立叶神经算子首先被成功应用于直接集成多种数据,可以同时利用稀缺的高保真度数据和丰富的低保真度数据。然后,提出了迁移学习框架,通过提取低保真度数据中的丰富知识来协助高保真度建模训练,进一步提高数据驱动预测的准确性。最后,选择了三个典型的流体和温度预测问题来验证所提出的多保真度模型的准确性。结果表明,与其他高保真模型相比,所提出的方法具有高效性,对于所选择的所有物理场问题的建模精度均为99%。值得注意的是,所提出的多保真度学习方法具有简单结构和高精度的潜力,可以为后续模型的构建提供参考。