In this next experiment, I'm going to try to build more of an intuition and physical understanding of some of our most important latent features, as they relate to importance of predicting the superconducting state.
This work is a continuation of some prior work trying to tie the latent space variables to real physical properties we can design materials with:
By looking at our superconducting state classifier model feature importance, we can understand what features we should be looking at. From there, we can start to study how these features change across
Let's start looking as some specific latent features.
Okay this is really exciting. 63 seems to be related to volume of the crystal. By scaling all three lattice vectors by the same factor, we can measure how the latent vector changes. We find that 63 is the most significantly impacted, growing as the lattice expands and shrinking as the lattice compresses.
Measuring the impact scaling the crystal lattice has on different select latent features.
This matches up well with what we've seen in the trends of 63 over time and how it grows with heating. Our SHAP values tell us that smaller values of the 63 vector lead to more pressure predicting the superconducting state!
This tells us we need a material that is resistant to thermal expansion! Ceramics are already pretty good at this, but maybe there's something we can learn from heat shielding for rockets that could inform us on how to improve the thermomechanical properties.
Unsurprisingly, many of our other features have a response to isotropic scaling. But it's interesting to notice that increasing the scale doesn't really have an effect and only when shrinking do we see most of the changes. Notice how 156 (the top dark blue when shrunk) has a significant change upward when shrunk but very little effect when expanded. We'll see what more we can learn about it in other studies.
Okay this is sick. In our studies, we've often found that 91 and 93 are the first features that start to show up that start pushing down on predicting the superconducting state. Their influence becomes more pronounced as temperature rises, where actually the value of 91 decreases. Our SHAP values tell us we want large values to promote supercondcuting.
Simulating the effect changing the spacing between the layers of a cuprate has on the latent vectors that represent that material.
This analysis of scaling the c-axis shows us there are optimizations we can make! We follow 91 in gray, seeing how shrinking the space between layers of this cuprate we're studying can, within a range, increase 91. Reducing spacing too much and we start to decrease! So there's a sweet spot to find that gives us what we're looking for.
Again, we see that over expanding the cell has negative ramifications, shown by 63 increasing and 91 decreasing significantly.
As promised, we're back and looking at 220. It's by far our most important feature, where large values increase superconducting probability and smaller values decrease it. If there's something we can engineer to increase 220 consistently across all temperatures, we going to be on to something.
Earlier, I had the idea that maybe it was tied to temperature, kinetic energy, or something volume related but I don't think that anymore. Exactly what'd hope for because now it's something we can design for.
Measuring the effect of changing the spacing of a layer in the crystal and how it changes the latent space representation of that material.
This experiment shows us the effect of layers in the material being shifted, specifically adjusting the spacing between a barium oxide layer and a mercury atom.
220 is the dark blue on the bottom, we find we're already in the most optimal arrangement? Increasing the space between the layers reduces the feature value, and decreasing the space reduces it too. I'll try some middle-of-the-pack materials and see how this holds.
It did not hold. It seems this behavior is common and perhaps it relates more to the stability or relaxation of the material. A non-superconducting material exhibits the same behavior.
So what's the difference between 220 and 63 other than them often being inverses of each other to some degree?
[IN PROGRESS]