Water swirling into a vortex eventually stops being smooth: foam and spray appear. Mathematicians describe such flows with equations, but there's a puzzle — sometimes the solution 'explodes,' becoming infinite, and no one knows why. Stochastic modeling doesn't help here; we need a precise tool.
The authors took a small neural network with an unusual design: instead of straight lines, it uses waves. Such a network can't draw sharp corners, so when a rupture appears in the flow, it starts making errors, and the error concentrates exactly where the liquid tears. It's like trying to draw a crack on glass with a soft pencil: the pencil slips and leaves a mark right at the fracture line.
The method was tested on a classic example — the Taylor–Green vortex, where fluid swirls in a cube. At normal viscosity, the network's error was weak, but when the fluid became nearly weightless, the error grew 13-fold and gathered at a single point — where theory predicts a rupture. The network also found a boundary: if viscosity exceeds a certain value, ruptures disappear and the flow stays smooth.
This approach is like a sensor on an airplane wing that senses in advance where the air is about to break into a vortex. For now, it's a mathematical tool, but it could help engineers predict dangerous swirls in turbines or around hulls.
The classic Taylor–Green vortex, on which the method was tested, was first described in 1937 to study turbulence, and since then it has remained a benchmark for testing new ideas in fluid dynamics.
In Stanislaw Lem's novel 'Solaris,' the ocean behaves like a fluid with unpredictable ruptures — perhaps similar methods could help understand its nature.