Hidden Fluid Mechanics: Navier-Stokes Informed Deep Learning from the Passive Scalar Transport

Inspired by the recent developments in physics-informed deep learning framework, we propose a novel Navier-Stokes informed neural networks that encodes the governing equations of fluid motions i.e., mass, momentum and transport equations to infer hidden quantities of interest such as velocity and pressure fields merely from spatio-temporal visualizations of a passive scaler (e.g. dye or smoke) transported in arbitrarily complex domains. Our approach towards solving the aforementioned data assimilation problem is unique as we design an algorithm that is agnostic to the geometry or the initial and boundary conditions. This makes the algorithm highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. The proposed algorithm achieves accurate predictions of the pressure and velocity fields in both two and three dimensional flows for several benchmark problems motivated by real-world applications. Our results demonstrate that this relatively simple methodology can be used in physical and biomedical problems to extract valuable quantitative information (e.g. lift and drag forces or wall shear stresses in arteries) for which direct measurements may not be possible.