I can't read the research article now, but from the press article, it looks like they are explaining a known experimental result that was unexplained (or confusing) until now.

IIUC in a previous real life experiment other group put a tiny amount of Potassium under very high pressure, and they uses x-ray diffraction to "see" the structure of the sample. At low temperature they saw regular arrangement of atoms that has slots (like a "sponge", but a regular sponge). In these slots there were more atoms in some fixed positions.

When they increase the temperature, the "sponge" part didn't change, but the atoms in the slots began to move like in a liquid. In the x-ray you get sharp point for the atoms that are essentially still and in a regular arrangement (the points are not the atoms), but the atoms that can move or are in irregular positions don't produce sharp point.

So IIUC in a previous real life experiment other group saw a change. My guess is that the atoms that can move don't drip. They keep trapped inside the "sponge" part (like a small amount of water in a towel). The dripping part is probably a bad metaphor.

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In spite we know all the quantum mechanic rules to simulate this, the problem is that the runtime grows exponentially with the number of atoms. So an exact simulation is only possible with only a few small atoms (5-10 Carbons, perhaps 10-20 Hydrogens (but not 10 Carbons and 20 Hydrogens). Potassium has a lot of electrons, so it is more difficult.) (And the simulation is not as exact as a Mathematician would like to call it exact.)

There are some tricks to avoid the exponential time. Like assuming that the atoms/electrons only interact with nearby atoms/electrons. It's quite true, but not 100% true. You can also use some model of how the electrons in one atom interact with the electrons in the other atom. But electrons like to wander, specially inside a conductor, so you must consider the electrons that live between the atoms. It's a lot of fun, there are plenty of model to approximate how the electrons behave in some situation, but each model is good for one situation and bad for other situations.

If you want to go down the rabbit hole https://en.wikipedia.org/wiki/Density_functional_theory , but it is not the only method to try to solve the problem. There are a few rabbit holes, because the exact problem has exponential complexity.

In this work, they use a neural network to approximate the behavior of the electrons in each atom (and between atoms). I guess that they are assuming that they interact almost locally, and hopefully they can get the result in linear time instead of exponential. I'm not sure if this can be classified as DFT or other technique, or they are digging a brand new rabbit hole.

It's difficult to judge the work by reading only a press article, but the abstract of the research paper says:

> Calculations necessitated the development of an interatomic forcefield using machine learning, which we show fully reproduces potassium’s phase diagram, including the chain-melted state and 14 known phase transitions.

It looks very promising, specially because in each phase the conditions are different and that makes the use of a single model very difficult.