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

TL;DR

This paper introduces Hidden Fluid Mechanics (HFM), a physics-informed deep learning framework that infers velocity and pressure fields from flow visualizations, applicable to complex geometries and passive scalar data, without prior knowledge of boundary conditions.

Contribution

HFM is a novel, geometry-agnostic deep learning approach that encodes Navier-Stokes laws to infer hidden fluid quantities solely from visual data, surpassing traditional methods.

Findings

Accurately predicts velocity and pressure in 2D and 3D flows.

Effective in complex, real-world biomedical applications.

Outperforms pure machine learning or scientific computing alone.

Abstract

We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) 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 (e.g., in human arteries or brain aneurysms). 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 HFM highly flexible in choosing the spatio-temporal domain of interest for data acquisition as well as subsequent training and predictions. Consequently, the predictions made by HFM are among those cases where a pure machine learning strategy or a mere scientific computing approach simply cannot reproduce. 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.