Density functional theory is still quantum mechanics, but operating on the expected electron density itself, rather than the many-body problem of all the electrons. It's pretty good, but not fast - around a CPU-minute for a medium-sized molecule.
I'm working on approximating the electron density using just the nuclei positions and some neural networks. The throughput is tens of thousands of times higher than for DFT. But since the model itself contains little or no physics, the training data has to be very clean and complete.
Would you be able to leverage any of the work that's being done around so called "neural ODE's"?
The Julia community seems to be doing some really cool at the intersection of the 2 fields and it seems like it could be useful if you've already got some kind of pre-existing model/structure to hang the ML part off:
