Algorithm can infer velocity and pressure from video of fluid flows

A technique for estimating velocities and pressures from videos of fluid flows could help in studying everything from hurricanes to vascular disease.

PROVIDENCE, R.I. [Brown University] — Researchers from Brown University have developed a computer algorithm that can infer the velocities and pressures of a fluid flow just by analyzing video of that flow.

In a study in the journal Science, the researchers showed that the technique could potentially be used to analyze magnetic resonance imagery of blood flow through a brain aneurysm and compute the stress being placed on an arterial wall, which could help doctors better predict the likelihood that the aneurysm may rupture.

The researchers say the technique could also be used to calculate wind speeds and barometric pressures from satellite imagery of hurricanes, or to calculate forces on vehicles in wind tunnel experiments. 

“We refer to the technique as ‘hidden fluid mechanics,’” said George Karniadakis, a professor of applied mathematics at Brown and the study’s senior author. “We’re taking in data from things we can see in a video, and using equations describing the underlying physics to infer the velocities and pressures even though we can not see the values directly.”

The technique makes use of artificial neural networks that are encoded with the Navier Stokes equations, the partial differential equations that describe the flow of incompressible fluids. The system inputs video data depicting the movement of a passive scalar, which could be smoke carried along in airflow, dye carried in a liquid or a contrast agent in blood flow. The physics-informed neural networks use that data to derive values for quantities of the “hidden” variables. 

Having the physical laws governing the system baked into the algorithm reduces the amount of data needed to make accurate predictions, according to Karniadakis. That gives the system the ability to make useful predictions from just a few seconds of video in some cases. 

“You can think of this as learning from small data as opposed to big data,” Karniadakis said. “The physics constrains the search space for the correct predictions, and so a little bit of data will get us there.”

Karniadakis says that the general approach of encoding physics into artificial neural networks could be applicable in domains other than visualizations of fluid flows. For example, networks equipped with equations describing the mechanical behavior of materials could be combined with ultrasound data to predict crack propagation in a structure. Electrical phenomena could be analyzed by encoding the Maxwell equations describing electrical and magnetic fields.

“There’s a lot we can do when we can combine data with the underlying physics,” Karniadakis said.

Co-authors on the paper were Maziar Raissi and Alireza Yazdani. This work received support by the Defense Advanced Research Projects Agency (N66001-15-2-4055, HR00111990025), the Air Force Office of Scientific Research (FA9550-17-1-0013), the National Institutes of Health (U01HL142518) and the Department of Energy (DE-AC05-76RL01830).