The fusion of flow field data with multiple fidelities

We propose a spatial-temporal multi-fidelity Gaussian process regression framework for the fusion of flow field data with various availabilities and fidelities but not sufficiently large to train neural networks commonly encountered in fluid mechanics studies. For example, fluid experiments lead to data with high fidelity but sparse in time and space, while most of the numerical data are generally regarded as less accurate but are spatially temporally continuous. The proposed framework aims at generating a new set of fused data by combining the merits of those in the spatial-temporal space. Numerical simulations [e.g., direct numerical simulation (DNS), large eddy simulation, Reynolds-averaged Navier-Stokes] of flow around a National Advisory Committee for Aeronautics 0012 airfoil are performed to collect the original raw data with various fidelities, and a fraction of the DNS result is used to mimic the high-fidelity but sparse experimental data. It is found that the accuracy of the fused data increases with the density of high-fidelity points until reaching a threshold, above which the fusion accuracy becomes insensitive. This limit can be overcome by introducing extra dimensions, such as the gradients of the low-fidelity data field. By examining the error fields, it is found that the high-fidelity points can tune low-fidelity fields but only within a limited local region. The accuracy can be firmly improved by introducing more high-fidelity points or higher levels of spatial gradients if the data set captures the temporal development.