# In which part of the Hartree–Fock algorithm (or DFT one) could a neural network be most effectively used?

I understand that the task of implementing machine learning in DFT and Hartree–Fock (HF) algorithm has already been solved, perhaps to some extent, but it is interesting to think about how to implement, for example, a neural network (NN) such a way that NN would be balanced towards the speed of calculation execution rather than training: (1) using several NNs in various parts of the algorithm; (2) using one single NN into one part of the algorithm; (3) using one common NN for the entire algorithm; (4) or something else?

I have seen that NNs are used for the matrix diagonalization procedure. The procedure is used, for example, by the HF algorithm.

• I've thought about this a decent amount before and I think one of the best things that could be done which would still give you the exact answer, is to machine learn a better guess for the converged orbitals. That is, most of the time in HF and DFT is spent optimizing the orbitals iteratively. Minimizing the number of iterations is very important for getting solutions quickly. If you're interested in ML that gives you solutions other than the appropriate HF or DFT energy, then literally anything is on the table and you're only limited by your imagination. Jun 10, 2022 at 15:28
• Could you share the link to the article implementing NN-based matrix diagonalization? That sounds interesting Jun 10, 2022 at 17:21
• I would agree with the above - I think better initial guess might help. For example @susilehtola published papers on the superposition of atomic potentials: doi.org/10.1021/acs.jctc.8b01089 and arxiv.org/pdf/2002.02587.pdf - one could imagine an ML model adjusting these based on atomic environments / neighborhoods. Jun 13, 2022 at 0:56
• Calculating 2-electron integrals with Gaussian or plane wave basis functions is by now so optimized that NN methods will have a hard time competing. But if sufficient accuracy and speed could be attained by NN to provide 2-electron integrals with Slater type basis functions, that could be interesting. Jun 13, 2022 at 8:51
• Well, 2-electron integrals can be computed efficiently with Slater-type basis sets using resolutions of the identity and quadrature, so ML would have a hard time in that as well... Jun 26, 2022 at 18:46