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We present hidden fluid mechanics (HFM), a physics informed deep learningframework capable of encoding an important class of physical laws governingfluid motions, namely the Navier-Stokes equations. In particular, we seek toleverage the underlying conservation laws (i.e., for mass, momentum, andenergy) to infer hidden quantities of interest such as velocity and pressurefields merely from spatio-temporal visualizations of a passive scaler (e.g.,dye or smoke), transported in arbitrarily complex domains (e.g., in humanarteries or brain aneurysms). Our approach towards solving the aforementioneddata assimilation problem is unique as we design an algorithm that is agnosticto the geometry or the initial and boundary conditions. This makes HFM highlyflexible in choosing the spatio-temporal domain of interest for dataacquisition as well as subsequent training and predictions. Consequently, thepredictions made by HFM are among those cases where a pure machine learningstrategy or a mere scientific computing approach simply cannot reproduce. Theproposed algorithm achieves accurate predictions of the pressure and velocityfields in both two and three dimensional flows for several benchmark problemsmotivated by real-world applications. Our results demonstrate that thisrelatively simple methodology can be used in physical and biomedical problemsto extract valuable quantitative information (e.g., lift and drag forces orwall shear stresses in arteries) for which direct measurements may not bepossible.

Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data