Convergence to the fixed-node limit in deep variational Monte Carlo

Abstract

Variational quantum Monte Carlo (QMC) is an ab-initio method for solving the electronic Schrödinger equation that is exact in principle, but limited by the flexibility of the available ansatzes in practice. The recently introduced deep QMC approach, specifically two deep-neural-network ansatzes PauliNet and FermiNet, allows variational QMC to reach the accuracy of diffusion QMC, but little is understood about the convergence behavior of such ansatzes. Here, we analyze how deep variational QMC approaches the fixed-node limit with increasing network size. First, we demonstrate that a deep neural network can overcome the limitations of a small basis set and reach the mean-field complete-basis-set limit. Moving to electron correlation, we then perform an extensive hyperparameter scan of a deep Jastrow factor for LiH and H${}_4$ and find that variational energies at the fixed-node limit can be obtained with a sufficiently large network. Finally, we benchmark mean-field and many-body ansatzes on H${}_2$O, increasing the fraction of recovered fixed-node correlation energy of single-determinant Slater--Jastrow-type ansatzes by half an order of magnitude compared to previous variational QMC results and demonstrate that a single-determinant Slater--Jastrow--backflow version of the ansatz overcomes the fixed-node limitations. This analysis helps understanding the superb accuracy of deep variational ansatzes in comparison to the traditional trial wavefunctions at the respective level of theory, and will guide future improvements of the neural network architectures in deep QMC.

arXiv commentThis article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Chem. Phys., vol. 154, no. 12, p. 124108, Mar. 2021 and may be found at https://doi.org/10.1063/5.0032836

References in corpus (16)

• SchNet - a deep learning architecture for molecules and materials
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Recent developments in the PySCF program package
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Continuum variational and diffusion quantum Monte Carlo calculations
• Jastrow correlation factor for atoms, molecules, and solids
• Fermionic neural-network states for ab-initio electronic structure
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Scheme for adding electron-nucleus cusps to Gaussian orbitals
• Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach
• Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm
• Dissociation energy of the water dimer from Quantum Monte Carlo calculations
• A deep neural network for molecular wave functions in quasi-atomic minimal basis representation
• On Representing (Anti)Symmetric Functions

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