  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.
