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Solving the Many-Electron Schrödinger Equation with Deep Neural Networks

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Exact wavefunctions of interesting many-electron systems are NP-hard to compute in general, but approximations can be found using polynomially-scaling algorithms. The challenge is to find an approximate wavefunction that is simple enough to evaluate and yet has enough variational freedom to produce accurate results. Neural networks have shown impressive power as accurate practical function approximators and promise as compact wavefunctions for spin systems, but the Pauli principle complicates network representations of many-fermion wavefunctions. Here we introduce a fully antisymmetric deep learning architecture, Fermi Net, able to approximate the wavefunctions of atoms and small molecules to remarkable accuracy. For example, we predict the dissociation curves of the nitrogen molecule and the hydrogen chain, two challenging strongly-correlated systems, to significantly higher precision than the coupled cluster method, widely considered the best scalable method for quantum chemistry. This work opens the possibility of accurate direct optimisation of wavefunctions for previously intractable molecules and solids.

This talk is part of the Theory of Condensed Matter series.

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