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Tomographic background oriented schlieren (Tomo-BOS) imaging measures densityor temperature fields in 3D using multiple camera BOS projections, and isparticularly useful for instantaneous flow visualizations of complex fluiddynamics problems. We propose a new method based on physics-informed neuralnetworks (PINNs) to infer the full continuous 3D velocity and pressure fieldsfrom snapshots of 3D temperature fields obtained by Tomo-BOS imaging. PINNsseamlessly integrate the underlying physics of the observed fluid flow and thevisualization data, hence enabling the inference of latent quantities usinglimited experimental data. In this hidden fluid mechanics paradigm, we trainthe neural network by minimizing a loss function composed of a data mismatchterm and residual terms associated with the coupled Navier-Stokes and heattransfer equations. We first quantify the accuracy of the proposed method basedon a 2D synthetic data set for buoyancy-driven flow, and subsequently apply itto the Tomo-BOS data set, where we are able to infer the instantaneous velocityand pressure fields of the flow over an espresso cup based only on thetemperature field provided by the Tomo-BOS imaging. Moreover, we conduct anindependent PIV experiment to validate the PINN inference for the unsteadyvelocity field at a center plane. To explain the observed flow physics, we alsoperform systematic PINN simulations at different Reynolds and Richardsonnumbers and quantify the variations in velocity and pressure fields. Theresults in this paper indicate that the proposed deep learning technique canbecome a promising direction in experimental fluid mechanics.

journal of fluid mechanics

Flow over an espresso cup: Inferring 3D velocity and pressure fields  from tomographic background oriented schlieren videos via physics-informed  neural networks