Approximating Many-Electron Wave Functions using Neural Networks

William Foulkes
Imperial College London

Given access to accurate solutions of the many-electron Schrödinger equation, most of condensed matter physics, chemistry and materials physics could be derived from first principles. Exact wave functions of systems with more than a few electrons 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 an approximate parameterized wave function, which must trade accuracy for efficiency. Neural networks have shown impressive power as practical function approximators and promise as a way of representing wave functions for spin systems, but electronic wave functions have to obey Fermi-Dirac statistics. This talk introduces a deep learning architecture, the Fermionic neural network, which is capable of approximating many-electron wavefunctions and greatly outperforms conventional approximations. The use of FermiNet wave functions boosts the accuracy of the simple and appealing variational quantum Monte Carlo method until it rivals the very best conventional quantum chemical approaches.

Matthew Foulkes, Gino Cassella, Wan Tong Lou, Halvard Sutterud Imperial College London

David Pfau, James Spencer
DeepMind Ltd.

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