Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks

Approximate solutions to the Schrödinger equation typically impose a fixed functional form on the wavefunction. Neural networks have shown impressive power as accurate practical function approximators[1] and have been recently used in bosonic[2] and lattice systems[3]. We show that deep neural networks can learn the ground state wavefunction of chemical systems given only the positions and charges of the nuclei using variational Monte Carlo[4]. We find it crucial to use the second-order optimization algorithm KFAC[5], which uses curvature information from the wavefunction distribution. The neural network Ansatz, FermiNet, is compact yet flexible and gives more accurate energies than conventional Ansätze. We obtain ground state energies, ionisation potentials and electron affinities to within chemical accuracy on a variety of atoms, small molecules, and model reactions.

JS and DP contributed equally to this work.

[1] A. Krizhevsky, I. Sutskever, G.E. Hinton, NIPS’12 1097-1105 (2012).
[2] G. Carleo, M. Troyer, Science 356, 602-606 (2017).
[3] D. Luo, B.K. Clark Phys. Rev. Lett. 122, 226401 (2019).
[4] D. Pfau, J. S. Spencer, A. G. de G. Matthews, W. M. C. Foulkes, Phys. Rev. Research 2, 033429 (2020).
[5] J. Martens, R. Grosse, ICML 2408–2417 (2015).