[rsfern]

More physical ML force fields is a super interesting topic that I feel like blurs the line between ML and actually just doing physics. My favorite topic lately is parametrizing tight binding models with neural nets, which hopefully would lead to more transferable potentials, but also let you predict electronic properties directly since you’re explicitly modeling the valence electrons

Context for the non-mat-sci crowd - numerically solving Schrodinger essentially means constructing a large matrix that describes all the electron interactions and computing its eigenvalues (iterated to convergence because the electron interactions are interdependent on the solutions). Density functional theory (for solids) uses a Fourier expansion for each electron (these are the one-electron wave functions), so the complexity of each eigensolve is cubic in the number of valence electrons times the number of Fourier components

The tight binding approximation is cool because it uses a small spherical harmonic basis set to represent the wavefunctions in real space - you still have the cubic complexity of the eigensolve, and you can model detailed electronic behavior, but the interaction matrix you’re building is much smaller.

Back to the ML variant: it’s a hard problem because ultimately you’re trying to predict a matrix that has the same eigenvalues as your training data, but there are tons of degeneracies that lead to loads of unphysical local minima (in my experience anyway, this is where I got stuck with it). The papers I’ve seen deal with it by basically only modeling deviations from an existing tight binding model, which in my opinion only kind of moves to problem upstream