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

Calculating analytic solutions to the Schrödinger equation is impossible except in a small number of special cases. Approximate solutions typically impose a fixed functional form on the wavefunction. Neural networks have shown impressive power as accurate practical function approximators¹ and have been recently used in bosonic² and lattice systems³. 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 a combination of variational Monte Carlo (VMC) and optimisation methods from machine learning⁴. 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 and small molecules and outperform VMC using conventional Slater-Jastrow wavefunctions.

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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, arXiv:1909.02487 (2019).

DP and JS contributed equally to this work.