Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Wilson, Max; Gao, Nicholas; Wudarski, Filip; Rieffel, Eleanor; Tubman, Norm M.

doi:10.48550/arxiv.2103.12570

Cited by 13 publications

(32 citation statements)

References 28 publications

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“…The diagram is representative but not exact, it does not contain all operations, for an exact description see Section III. mance on molecular systems [2][3][4][24][25][26].…”

Section: Permutation Equivariant Layersmentioning

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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“…The diagram is representative but not exact, it does not contain all operations, for an exact description see Section III. mance on molecular systems [2][3][4][24][25][26].…”

Section: Permutation Equivariant Layersmentioning

confidence: 99%

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

Wilson¹,

Moroni²,

Holzmann³

et al. 2022

Preprint

Self Cite

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“…Using a deep neural network-based ansatz for variational Monte Carlo (VMC) has recently emerged as a novel approach for highly accurate ab-initio solutions to the multi-electron Schrödinger equation [1][2][3][4][5]. It has been observed that such methods can exceed gold-standard quantum-chemistry methods like CCSD(T) [6] in accuracy, with a computational cost per step scaling only with O(N 4 ) in the number of electrons [4].…”

Section: Introductionmentioning

confidence: 99%

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks

Scherbela¹,

Reisenhofer²,

Gerard³

et al. 2021

Preprint

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Accurate numerical solutions for the Schrödinger equation are of utmost importance in quantum chemistry. However, the computational cost of current high-accuracy methods scales poorly with the number of interacting particles. Combining Monte Carlo methods with unsupervised training of neural networks has recently been proposed as a promising approach to overcome the curse of dimensionality in this setting and to obtain accurate wavefunctions for individual molecules at a moderately scaling computational cost. These methods currently do not exploit the regularity exhibited by wavefunctions with respect to their molecular geometries. Inspired by recent successful applications of deep transfer learning in machine translation and computer vision tasks, we attempt to leverage this regularity by introducing a weight-sharing constraint when optimizing neural network-based models for different molecular geometries. That is, we restrict the optimization process such that up to 95 percent of weights in a neural network model are in fact equal across varying molecular geometries. We find that this technique can accelerate optimization when considering sets of nuclear geometries of the same molecule by an order of magnitude and that it opens a promising route towards pre-trained neural network wavefunctions that yield high accuracy even across different molecules.

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“…It is worth mentioning a variety of related works to put the present contribution into a broader perspective. First, there have been various wavefunction ansatzes for ground-state VMC calculation of fermions, from the traditional Slater-Jastrow [19], backflow [20][21][22][23] to more recent attempts based on neural networks [24][25][26][27][28][29][30][31]. However, unitary transformations are not considered in these ansatzes, since only a single wavefunction, instead of a whole basis, is needed in this situation.…”

Section: Introductionmentioning

confidence: 99%

Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

Xie,

Zhang,

Wang

2021

Preprint

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We present a variational density matrix approach to the thermal properties of interacting fermions in the continuum. The variational density matrix is parametrized by a permutation equivariant many-body unitary transformation together with a discrete probabilistic model. The unitary transformation is implemented as a quantum counterpart of neural canonical transformation, which incorporates correlation effects via a flow of fermion coordinates. As the first application, we study electrons in a two-dimensional quantum dot with an interaction-induced crossover from Fermi liquid to Wigner molecule. The present approach provides accurate results in the low-temperature regime, where conventional quantum Monte Carlo methods face severe difficulties due to the fermion sign problem. The approach is general and flexible for further extensions, thus holds the promise to deliver new physical results on strongly correlated fermions in the context of ultracold quantum gases, condensed matter, and warm dense matter physics.

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Simulations of state-of-the-art fermionic neural network wave functions with diffusion Monte Carlo

Cited by 13 publications

References 28 publications

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

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

Solving the electronic Schrödinger equation for multiple nuclear geometries with weight-sharing deep neural networks

Ab-initio study of interacting fermions at finite temperature with neural canonical transformation

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