Deep neural network solution of the electronic Schrödinger equation

The electronic Schrödinger equation describes fundamental properties of molecules and materials, but cannot be solved exactly for larger systems than a hydrogen atom. Quantum Monte Carlo is an apt approach for high-quality approximations, because its accuracy is limited in principle only by the flexibility of the used wave-function ansatz, but traditional trial wave functions are too rigid to take full advantage of this potential. Here, we greatly increase the flexibility of existing ansatzes by incorporating deep neural networks, which are known as superb universal function approximators. Our architecture, dubbed PauliNet, is built around the Hartree–Fock solution as a baseline, includes analytical cusp conditions, and uses the Jastrow-factor and backflow constructions as entry points for graph-convolutional neural networks, which ensure the exact permutational antisymmetry. We demonstrate that PauliNet outperforms comparable state-of-the-art trial wave functions on atoms, small molecules, and a strongly correlated model system. Our approach opens a new path towards highly accurate and systematically improvable electronic structure methods with explicit access to the corresponding wave function and hence a variety of electronic properties.