Reconstructing Experimental Measurements of Supersonic Flow via Physics-Informed BOS

We report a new workflow for background-oriented schlieren (BOS) to extract density, velocity, and pressure fields from reference and distorted images. Our method uses a physics-informed neural network (PINN) to represent a high-speed flow, for which we specify a physics loss based on the Euler and irrotationality equations. In BOS, images of a background pattern are processed using computer vision and tomography algorithms to determine the density field. Crucially, BOS features a series of ill-posed problems that require supplemental information. Current workflows interpolate the images or add a penalty term to promote globally- or piecewise-smooth solutions. However, these algorithms are incompatible with the flow physics, leading to reconstruction artifacts. Physics-informed BOS directly reconstructs all the flow fields using a PINN that includes the measurement model and governing equations. This improves the accuracy of density estimates and also yields (previously unavailable) velocity and pressure data. We demonstrate our approach with synthetic and experimental data. Reconstructions produced by physics-informed BOS are significantly more accurate than conventional estimates, and this work is the first use of a PINN to reconstruct a supersonic flow from experimental data.