Inferring Flows with Neural Networks

Drawings by Leonardo Da Vinci showing water flow around and past different objects.

Fluid dynamicists have long used flow visualization methods to get a qualitative sense for flows, but it’s rare to derive much quantitative data from this imagery. But that may soon change thanks to a new computational technique, called Hidden Fluid Mechanics, that uses data from flow visualizations combined with physics-informed neural networks to derive the underlying velocities and pressures in a flow.

The technique relies on two important ideas. One is that the dye, smoke, or other method of visualizing the flow does not alter the underlying flow; it’s just something carried along by the fluid. In other words, the flow behaves exactly the same whether or not you inserted dye or smoke.

The second key idea is that the Navier-Stokes equations — which are derived from conservation of mass, momentum, and energy — accurately describe the physics of a flow. That assumption is critical to the technique since it uses those equations to constrain the flow fields the algorithm reconstructs.

So here, roughly speaking, is what the algorithm actually does: researchers feed it concentration data from a flow visualization — essentially how much smoke or dye is present at every point in space and time — and the neural network reconstructs, based on the Navier-Stokes equations, what velocity and pressure field would produce that concentration data.

The researchers demonstrate the capabilities of their algorithm by comparing its results to flows where all the information is known. The first image in the gallery above shows concentration data for the flow in an aneurysm. The full flow field is known already from a numerical simulation, but the researchers gave their new algorithm only the concentration data. From that, it reconstructed the streamlines for the aneurysm’s flow, shown in the second image as “Learned”. The “Exact” streamlines on the left are taken from the original numerical simulation data. As you can see, the results are remarkably similar. (Image credit: drawings – L. da Vinci, others – M. Raissi et al.; research credit: M. Raissi et al.; submitted by Stuart H.)

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