Patterns in latent space change over temperature

In searching for physical meaning to the latent space, I've been looking closely at how these latent features change with temperature.

We started by seeing how, even from ground state, we could already pick out clusters in the latent space where the highest-temperature superconductors would be. If this was the case, could we just skip the MD and predict Tc directly? We had tried this approach first but what we came to was that it was mostly learning material classification, not superconducting state requirements. Additionally, it failed to predict out of target distribution.

Doing this latent space evolution study shows that we cannot determine Tc just from initial conditions, the ground state.

We do this study by looking at each material's latent feature changes from 0 K to 40 K and calculating the change in that range. This also means that all of these materials have a Tc greater than or equal to 40 to ensure we have the data. I should include all materials in further study so we can look at the movements in non-superconductors.

We can also look at the same data with an alternate visualization that makes it easier to quantitatively see the changes.

We can see that there are indeed some patterns here. We learn from the first plot that the starting value of the feature doesn't necessitate high temperature superconductivity. While it is true that all the high-Tc superconductors generally fall within a certain feature range (as demonstrated by other clustering and feature visualizations), there are also low-Tc superconductors within that range too.

It becomes somewhat clearer in the second plot that there is also a certain level of resistivity or fluidity in feature changes that shows high-Tc materials close together.

For example:

• Feature 165, you want to minimize the amount the feature decreases

• Feature 10, you generally want to decrease with temperature instead of increase

• Feature 155, you generally want to increase and the more the better

It's hard to say exactly what to do with this information at this time. I suppose it is good evidence that all the computation and time spent doing the molecular dynamics is important. Perhaps it's also another bit of evidence to the idea of computational irreducibility.