Do you think that human theorists are near the limit of what kind of approximations we should use to calculate the band structure of diamond (and therefore a superintelligent AI couldn’t outsmart human theorists by doing their job better)? Like if you left physics to stew for a century and came back, we’d still be using the GW approximation?
This seems unlikely to me, but I don’t really know much about DFT (I was an experimentalist). Maybe there are so few dials to turn that picking the best approximation for diamond is an easy game. Intuitively I’d expect that if a clever theorist knew that they were trying to just predict the band structure of diamond (but didn’t know the answer ahead of time), there are bespoke things they could do to try to get a better answer (abstract reasoning about what factors are important, trying to integrate DFT and a tight binding model, something something electron phonon interactions), and that is effectively equivalent to an efficient approximation that beats DFT+GWA.
Definitely we’re still making progress for more interesting materials (e.g. cuprates) - or at least people are still arguing. So even if we really can’t do better than what we have now for diamond, we should still expect a superintelligent AI to be better at numerical modeling for lots of cases of interest.
Do you think that human theorists are near the limit of what kind of approximations we should use to calculate the band structure of diamond (and therefore a superintelligent AI couldn’t outsmart human theorists by doing their job better)? Like if you left physics to stew for a century and came back, we’d still be using the GW approximation?
This seems unlikely to me, but I don’t really know much about DFT (I was an experimentalist). Maybe there are so few dials to turn that picking the best approximation for diamond is an easy game. Intuitively I’d expect that if a clever theorist knew that they were trying to just predict the band structure of diamond (but didn’t know the answer ahead of time), there are bespoke things they could do to try to get a better answer (abstract reasoning about what factors are important, trying to integrate DFT and a tight binding model, something something electron phonon interactions), and that is effectively equivalent to an efficient approximation that beats DFT+GWA.
Definitely we’re still making progress for more interesting materials (e.g. cuprates) - or at least people are still arguing. So even if we really can’t do better than what we have now for diamond, we should still expect a superintelligent AI to be better at numerical modeling for lots of cases of interest.