Multi-fidelity prediction of fluid flow based on transfer learning using Fourier neural operator

Data-driven prediction of laminar flow and turbulent flow 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 reality, only limited high-fidelity data are available due to the high experimental/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 limited 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 engineering application 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. Additionally, the low-fidelity model without transfer learning has the modeling accuracy of 86%. Significantly, the proposed multi-fidelity learning method has the potential of a simple structure with high precision for fluid flow problems, which can provide a reference for the construction of the subsequent model.