Article,
Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
(2019)cite arxiv:1909.02487.
Abstract
Given access to accurate solutions of the many-electron Schrödinger
equation, nearly all chemistry could be derived from first principles. Exact
wavefunctions of interesting chemical systems are out of reach because they are
NP-hard to compute in general, but approximations can be found using
polynomially-scaling algorithms. The key challenge for many of these algorithms
is the choice of wavefunction approximation, or Ansatz, which must trade off
between efficiency and accuracy. Neural networks have shown impressive power as
accurate practical function approximators and promise as a compact wavefunction
Ansatz for spin systems, but problems in electronic structure require
wavefunctions that obey Fermi-Dirac statistics. Here we introduce a novel deep
learning architecture, the Fermionic Neural Network, as a powerful wavefunction
Ansatz for many-electron systems. The Fermionic Neural Network is able to
achieve accuracy beyond other variational Monte Carlo Ansätze on a variety of
atoms and small molecules. Using no data other than atomic positions and
charges, we predict the dissociation curves of the nitrogen molecule and
hydrogen chain, two challenging strongly-correlated systems, to significantly
higher accuracy than the coupled cluster method, widely considered the gold
standard for quantum chemistry. This demonstrates that deep neural networks can
outperform existing ab-initio quantum chemistry methods, opening the
possibility of accurate direct optimisation of wavefunctions for previously
intractable molecules and solids.
