Physics-Informed Flow Field Tomography with UQ using a B-PINN

Planar and volumetric flow field measurements play an important role in the observation of novel phenomena and validation of numerical models. Tomography is increasingly used to record these measurements due to the limited optical access required for 2D tomography and the potential to conduct instantaneous or time-resolved 3D imaging. Reconstruction is inherently ill-posed so information in addition to the projection data is required to obtain realistic estimates of a flow field. This is usually done with a smoothness prior or maximum entropy constraint. However, existing algorithms give rise to non-physical errors that cannot be fully-corrected in post-processing (PP). We introduce a novel form of flow field tomography using a physics-informed neural net (PINN) to directly reconstruct a flow from a set of coupled projections, as opposed to PINN-based PP of conventional reconstructions. Our approach can be employed in conjunction with numerous modalities in 2D or 3D. Moreover, we show how a Bayesian PINN facilitates uncertainty quantification and enables robust reconstructions of noisy data. We demonstrate our method using synthetic projections of a 2D flow. Our reconstructions are superior to those produced by state-of-the-art algorithms even when a PINN is used for PP.