Vandermonde Wave Function Ansatz for Improved Variational Monte Carlo

Acevedo, Alberto; Curry, Michael J.; Joshi, Shantanu H.; Brett, Leroux,; Malaya, Nicholas

doi:10.1109/dls51937.2020.00010

Cited by 10 publications

(5 citation statements)

References 6 publications

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“…Research into neural network Ansätze has covered Boltzmann machines and feed-forward neural networks over 235139-2 a wide range of systems [23,[36][37][38], including more recent Slater determinant Ansätze [39,40]. Other more recent examples incorporate physics-based structure [3], or large and deep networks [2,24,26] on molecular systems.…”

Section: Related Workmentioning

confidence: 99%

Neural network ansatz for periodic wave functions and the homogeneous electron gas

et al. 2023

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We design a neural network Ansatz for variationally finding the ground-state wave function of the homogeneous electron gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarized and paramagnetic phases with 7, 14, and 19 electrons over a broad range of densities from r s = 1 to r s = 100, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ansätze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. We illustrate the advantage of our high-quality wave functions in computing the reduced single-particle density matrix. This contribution establishes neural network models as flexible and high-precision Ansätze for periodic electronic systems, an important step towards applications to crystalline solids.

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Section: Related Workmentioning

confidence: 99%

Neural network ansatz for periodic wave functions and the homogeneous electron gas

et al. 2023

View full text Add to dashboard Cite

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“…Research into neural network Ansätze has covered Boltzmann machines and feedforward neural networks over a wide range of systems [23,[32][33][34], including more recent Slater determinant Ansätze [35,36]. Other more recent examples incorporate physics based structure [3], or large and deep networks [2,24,26] on molecular sys-tems.…”

Section: Related Workmentioning

confidence: 99%

Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

Wilson¹,

Moroni²,

Holzmann³

et al. 2022

Preprint

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We design a neural network Ansatz for variationally finding the ground-state wave function of the Homogeneous Electron Gas, a fundamental model in the physics of extended systems of interacting fermions. We study the spin-polarised and paramagnetic phases with 7, 14 and 19 electrons over a broad range of densities from rs = 1 to rs = 100, obtaining similar or higher accuracy compared to a state-of-the-art iterative backflow baseline even in the challenging regime of very strong correlation. Our work extends previous applications of neural network Ansätze to molecular systems with methods for handling periodic boundary conditions, and makes two notable changes to improve performance: splitting the pairwise streams by spin alignment and generating backflow coordinates for the orbitals from the network. This contribution establishes neural network models as flexible and high precision Ansätze for periodic electronic systems, an important step towards applications to crystalline solids.

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“…However, their DeepErwin model still requires separate models for each geometry, does not account for symmetries and achieves lower accuracy, as we show in Section 4. Other efforts have aimed at accelerating Ansätze by replacing costly determinant operations, but this comes at a significant loss of accuracy (Acevedo et al, 2020).…”

Section: Related Workmentioning

confidence: 99%

Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions

Gao¹,

Günnemann²

2021

Preprint

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Solving the Schrödinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modelling wave functions of many-electron systems. Together with the variational Monte-Carlo (VMC) framework, this led to solutions on par with the best known classical methods. Still, these neural methods require tremendous amounts of computational resources as one has to train a separate model for each molecular geometry. In this work, we combine a Graph Neural Network (GNN) with a neural wave function to simultaneously solve the Schrödinger equation for multiple geometries via VMC. This enables us to model continuous subsets of the potential energy surface with a single training pass. Compared to existing state-of-the-art networks, our Potential Energy Surface Network (PESNet) speeds up training for multiple geometries by up to 40 times while matching or surpassing their accuracy. This may open the path to accurate and orders of magnitude cheaper quantum mechanical calculations.

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Vandermonde Wave Function Ansatz for Improved Variational Monte Carlo

Cited by 10 publications

References 6 publications

Neural network ansatz for periodic wave functions and the homogeneous electron gas

Neural network ansatz for periodic wave functions and the homogeneous electron gas

Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas

Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions

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