On application of Physics-Informed Neural Networks to Improve Noisy Data of Incompressible Flows

This study explores a novel approach for improving the noisy data of incompressible flow fields by leveraging the Physics Informed Neural Networks (PINNs). Two examples are considered: inviscid flow over a circular cylinder and the 3D axisymmetric Hill Vortex. A neural network is constructed for the spatial variation of the stream-function, to determine the velocity field. Hence, continuity of the flow field is automatically satisfied. Then, the network is trained to minimize the deviation of the constructed flow field from the original field to find the closest divergence-free velocity field for the given flow data. Accordingly, any component, which is not divergence-free (violating continuity) is considered induced by noise and is automatically filtered out. To ensure the accuracy of the corrected data, boundary conditions are introduced into the cost function during training. These boundary conditions guide the filtration process, and help refining the flow field data. One current application of this approach is to improve noisy data obtained from Particle Image Velocimetry (PIV) measurements. This study shows the PINNs' potential in denoising flow fields via incorporating physical knowledge into neural network-based modeling.