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A multi-fidelity regression model is proposed for combining multiple datasetswith different fidelities, particularly abundant low-fidelity data and scarcehigh-fidelity observations. The model builds upon recent multi-fidelityframeworks based on neural networks, which employ two distinct networks forlearning low- and high-fidelity data, and extends them by feeding the gradientsinformation of low-fidelity data into the second network, while the gradientsare computed using automatic differentiation with minimal computationaloverhead. The accuracy of the proposed framework is demonstrated through avariety of benchmark examples, and it is shown that the proposed model performsbetter than conventional multi-fidelity neural network models that do not usegradient information. Additionally, the proposed model is applied to thechallenging case of turbulent flow reconstruction. In particular, we study theeffectiveness of the model in reconstructing the instantaneous velocity fieldof the decaying of homogeneous isotropic turbulence givenlow-resolution/low-fidelity data as well as small amount ofhigh-resolution/high-fidelity data. The results indicate that the proposedmodel is able to reconstruct turbulent field and capture small scale structureswith good accuracy, making it suitable for more practical applications.

Gradient enhanced multi-fidelity regression with neural networks: application to turbulent flow reconstruction