Given access to accurate solutions of the many-electron Schrödinger equation, nearly all chemistry could be derived from first principles. Exact wave functions 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 wave function 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 wave-function Ansatz for spin systems, but problems in electronic structure require wave functions that obey Fermi-Dirac statistics. Here we introduce a novel deep learning architecture, the Fermionic neural network, as a powerful wave-function Ansatz for many-electron systems. The Fermionic neural network is able to achieve accuracy beyond other variational quantum Monte Carlo Ansatz 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 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, opening the possibility of accurate direct optimization of wave functions for previously intractable many-electron systems.
The khmer package is a freely available software library for working efficiently with fixed length DNA words, or k-mers. khmer provides implementations of a probabilistic k-mer counting data structure, a compressible De Bruijn graph representation, De Bruijn graph partitioning, and digital normalization. khmer is implemented in C++ and Python, and is freely available under the BSD license at https://github.com/dib-lab/khmer/.
Improving DFT with deep learning In the past 30 years, density functional theory (DFT) has emerged as the most widely used electronic structure method to predict the properties of various systems in chemistry, biology, and materials science. Despite a long history of successes, state-of-the-art DFT functionals have crucial limitations. In particular, significant systematic errors are observed for charge densities involving mobile charges and spins. Kirkpatrick et al . developed a framework to train a deep neural network on accurate chemical data and fractional electron constraints (see the Perspective by Perdew). The resulting functional outperforms traditional functionals on thorough benchmarks for main-group atoms and molecules. The present work offers a solution to a long-standing critical problem in DFT and demonstrates the success of combining DFT with the modern machine-learning methodology. —YS
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the Beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.
The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.
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