Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

TLDR

Flow visualization has long enabled the visual study of fluid motion in physical and biological systems, yet extracting velocity and pressure fields directly from images remains challenging despite the Navier‑Stokes equations providing a theoretical description. The authors aim to develop hidden fluid mechanics (HFM), a physics‑informed deep‑learning framework that encodes Navier‑Stokes equations into neural networks while remaining agnostic to geometry and boundary conditions. HFM integrates Navier‑Stokes constraints into neural networks, allowing it to infer velocity and pressure fields from flow visualizations without requiring explicit geometry or boundary data. HFM successfully extracts quantitative velocity and pressure information for various physical and biomedical problems, demonstrating robustness to low resolution and substantial noise, thereby enabling applications where direct measurements are infeasible.

Abstract

For centuries, flow visualization has been the art of making fluid motion visible in physical and biological systems. Although such flow patterns can be, in principle, described by the Navier-Stokes equations, extracting the velocity and pressure fields directly from the images is challenging. We addressed this problem by developing hidden fluid mechanics (HFM), a physics-informed deep-learning framework capable of encoding the Navier-Stokes equations into the neural networks while being agnostic to the geometry or the initial and boundary conditions. We demonstrate HFM for several physical and biomedical problems by extracting quantitative information for which direct measurements may not be possible. HFM is robust to low resolution and substantial noise in the observation data, which is important for potential applications.