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

Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operator