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

Abstract: A multi-fidelity regression model is proposed for combining multiple datasets with different fidelities, particularly abundant low-fidelity data and scarce high-fidelity observations. The model builds upon recent multi-fidelity frameworks based on neural networks, which employ two distinct networks for learning low- and high-fidelity data, and extends them by feeding the gradients information of low-fidelity data into the second network, while the gradients are computed using automatic differentiation with minimal computational overhead. The accuracy of the proposed framework is demonstrated through a variety of benchmark examples, and it is shown that the proposed model performs better than conventional multi-fidelity neural network models that do not use gradient information. Additionally, the proposed model is applied to the challenging case of turbulent flow reconstruction. In particular, we study the effectiveness of the model in reconstructing the instantaneous velocity field of the decaying of homogeneous isotropic turbulence given low-resolution/low-fidelity data as well as small amount of high-resolution/high-fidelity data. The results indicate that the proposed model is able to reconstruct turbulent field and capture small scale structures with good accuracy, making it suitable for more practical applications.