Physics

Flow velocity

Fluid mechanics

Mechanics

Vector field

Motion (physics)

Artificial intelligence

Stokes flow

Visualization

Flow (mathematics)

Computer science

Navier–Stokes equations

Compressibility

Classical mechanics

Flow visualization

Fluid dynamics

Science

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.

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