Trade-off between reconstruction accuracy and physical validity in modeling turbomachinery particle image velocimetry data by physics-informed convolutional neural networks

Particle image velocimetry (PIV) data are a valuable asset in fluid mechanics. It is capable of visualizing flow structures even in complex physics scenarios, such as the flow at the exit of the rotor of a centrifugal fan. Machine learning is also a successful companion to PIV in order to increase data resolution or impute experimental gaps. While classical algorithms focus solely on replicating data using statistical metrics, the application of physics-informed neural networks (PINN) contributes to both data reconstruction and adherence to governing equations. The present study utilizes a convolutional physics-informed auto-encoder to reproduce planar PIV fields in the gappy regions while also satisfying the mass conservation equation. It proposes a novel approach that compromises experimental data reconstruction for compliance with physical restrictions. Simultaneously, it is aimed to ensure that the reconstruction error does not considerably deviate from the uncertainty band of the test data. A turbulence scale approximation is employed to set the relative weighting of the physical and data-driven terms in the loss function to ensure that both objectives are achieved. All steps are initially evaluated on a set of direct numerical simulation data to demonstrate the general capability of the network. Finally, examination of the PIV data indicates that the proposed PINN auto-encoder can enhance reconstruction accuracy by about 28% and 29% in terms of mass conservation residual and velocity statistics, respectively, at the expense of up to a 5% increase in the number of vectors with reconstruction error higher than the uncertainty band of the PIV test data.