Solution of the many-electron Schrödinger equation with deep neural networks

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 approximate wavefunction, which must find a balance between efficiency and accuracy. Neural networks have shown impressive power as accurate practical function approximators and promise as a compact approximate wavefunction for spin systems, but problems in electronic structure require wavefunctions that obey Fermi-Dirac statistics. In a very recent preprint (arXiv:1909.02487), we introduced a novel deep learning architecture, the Fermionic Neural Network, as a powerful approximate wavefunction for many-electron systems and showed that this can be combined with the well-known and appealingly simple variational quantum Monte Carlo (VMC) method to achieve accuracy well beyond that achieved in previous VMC simulations atoms and small molecules. Using no data other than atomic positions and charges, we predicted 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 most accurate scalable method for quantum chemistry at equilibrium geometry. This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab-initio quantum chemistry methods.
Mr Cassella's PhD project will build on this promising start by using neural network trial wavefunctions to study simple solids. For simplicity, we will start by looking at the uniform electron gas (which will require substantial code development) before moving on to solid hydrogen and perhaps other simple solids. We will also investigate using fermionic neural networks to improve the accuracy of the more sophisticated diffusion quantum Monte Carlo method.