We present hidden fluid mechanics (HFM), a physics informed deep learning capable of encoding an important class of physical laws governing motions, namely the Navier-Stokes equations. In particular, we seek to the underlying conservation laws (i.e., for mass, momentum, and) to infer hidden quantities of interest such as velocity and pressure merely from spatio-temporal visualizations of a passive scaler (e.g., or smoke), transported in arbitrarily complex domains (e.g., in human or brain aneurysms). Our approach towards solving the aforementioned assimilation problem is unique as we design an algorithm that is agnostic the geometry or the initial and boundary conditions. This makes HFM highly in choosing the spatio-temporal domain of interest for data as well as subsequent training and predictions. Consequently, the made by HFM are among those cases where a pure machine learning or a mere scientific computing approach simply cannot reproduce. The algorithm achieves accurate predictions of the pressure and velocity in both two and three dimensional flows for several benchmark problems by real-world applications. Our results demonstrate that this simple methodology can be used in physical and biomedical problems extract valuable quantitative information (e.g., lift and drag forces or shear stresses in arteries) for which direct measurements may not be.
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Raissi et al. (2018) studied this question.