If you pour honey into a colander with a hundred small holes, it will drip in thin streams, but each stream will swirl around the edge of the hole. Engineers need to understand such swirls: they affect how quickly water filters, how oil comes out of a reservoir, or how a drug seeps through tissues. But the more holes there are, the harder it is for a computer to calculate every detail at the edges.
An ordinary neural network, trained on examples, tries to guess the flow across the entire colander at once. It gets penalized if it errs near the walls and starts flailing like a student given a hundred contradictory instructions. The authors used the finite basis method: they divided the colander into many small zones and placed a tiny neural network in each. To ensure it knows exactly where the wall is, they 'sewed in' a hard rule from the start: at the boundary, the velocity is always zero. It's like telling each painter: 'Your wall is this square, and don't go beyond its edge.' The result is that the painters work in harmony and quickly, and the seams between squares are nearly invisible.
This approach resembles assembling a huge mosaic: each piece is simple, but together they create a picture of the flow. And importantly, all pieces can be assembled simultaneously on different computers. In the end, we get not just a fast calculation but a reliable tool for designing new materials — from water purification membranes to artificial vessels where every microchannel must work without failure.
The number of holes in the experiment reached up to several hundred per square millimeter — about like a foam sponge, but strictly ordered.
In Vernor Vinge's novel 'A Fire Upon the Deep,' a civilization is described whose consciousness is distributed across many separate bodies, like fluid flow through pores — losing one element does not disrupt the overall flow of thought.