Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions

Gnech, Alex; Adams, C.; Brawand, Nicholas; Carleo, Giuseppe; Lovato, Alessandro; Rocco, Noemi

doi:10.1007/s00601-021-01706-0

Cited by 25 publications

(22 citation statements)

References 53 publications

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“…A promising avenue to be pursued in the future includes tackling the electroweak responses of medium mass nuclei, including 16 O and 40 Ar within AFDMC. In this regard, an importart role is expected to be played by artificial neural-network representations of the AFDMC wave function [387,388]. Preliminary AFDMC calculations of the density response functions of 4 He are in excellent agreement FIG.…”

Section: Continuum Quantum Monte Carlo Approachesmentioning

confidence: 82%

Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators

Alvarez¹,

Ankowski²,

Bacca³

et al. 2022

Preprint

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Section: Continuum Quantum Monte Carlo Approachesmentioning

confidence: 82%

Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators

Alvarez¹,

Ankowski²,

Bacca³

et al. 2022

Preprint

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“…[27] for a detailed uncertainty-quantification analysis. Subsequently, an anti-symmetric coordinate-space ansatz defined through the product between a permutation-invariant ANNs Jastrow and a Slater determinant of single-particle orbitals has been utilized in a variational Monte Carlo (VMC) method to solve leading-order pionless-EFT Hamiltonians of A ≤ 6 nuclei [28,29]. Detailed comparisons against Green's function Monte Carlo and the hypershperical harmonics approaches have validated the expressivity of this ANN Slater-Jastrow (ANN-SJ) ansatz, but also highlighted its shortcomings, essentially due to the incorrect nodal surface of the Slater determinant.…”

Section: Introductionmentioning

confidence: 99%

“…We couple the "hidden nucleons" wave function with the VMC method developed in Refs. [28,29] to compute the ground-state energies of 3 H, 3 He, 4 He, and 16 O nuclei starting from the pionless-EFT Hamiltonian of Ref. [31].…”

Section: Introductionmentioning

confidence: 99%

Hidden-nucleons neural-network quantum states for the nuclear many-body problem

Lovato,

Adams,

Carleo

et al. 2022

Preprint

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We generalize the hidden-fermion family of neural network quantum states to encompass both continuous and discrete degrees of freedom and solve the nuclear many-body Schrödinger equation in a systematically improvable fashion. We demonstrate that adding hidden nucleons to the original Hilbert space considerably augments the expressivity of the neural-network architecture compared to the Slater-Jastrow ansatz. The benefits of explicitly encoding in the wave function point symmetries such as parity and time-reversal are also discussed. Leveraging on improved optimization methods and sampling techniques, the hidden-nucleon ansatz achieves an accuracy comparable to the numerically-exact hyperspherical harmonic method in light nuclei and to the auxiliary field diffusion Monte Carlo in 16 O. Thanks to its polynomial scaling with the number of nucleons, this method opens the way to highly-accurate quantum Monte Carlo studies of medium-mass nuclei.

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“…Nuclear physics is no exception, and the number of machine learning (ML) tools is increasing steadily [3,4,5,6,7,8,9]. An interesting and relatively recent use of ANNs is the solution of quantum mechanical problems, including in the many-body domain [10,11]. These methods use ANNs as an ansatz for the many-body wave function, and employ ready-made ML tools to minimise the energy of the system [12,13].…”

Section: Introductionmentioning

confidence: 99%

Machine learning the deuteron: new architectures and uncertainty quantification

Sarmiento¹,

Keeble²,

Rios³

2022

Preprint

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We solve the ground state of the deuteron using a variational neural network ansatz for the wave function in momentum space. This ansatz provides a flexible representation of both the S and the D states, with relative errors in the energy which are within fractions of a percent of a full diagonalisation benchmark. We extend the previous work on this area in two directions. First, we study new architectures by adding more layers to the network and by exploring different connections between the states. Second, we provide a better estimate of the numerical uncertainty by taking into account the final oscillations at the end of the minimisation process. Overall, we find that the best performing architecture is the simple one-layer, state-independent network. Two-layer networks show indications of overfitting, in regions that are not probed by the fixed momentum basis where calculations are performed. In all cases, the error associated to the model oscillations around the real minimum is larger than the stochastic initialisation uncertainties. The conclusions that we draw can be generalised to other quantum mechanics settings.

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Nuclei with Up to $$\varvec{A=6}$$ Nucleons with Artificial Neural Network Wave Functions

Cited by 25 publications

References 53 publications

Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators

Theoretical tools for neutrino scattering: interplay between lattice QCD, EFTs, nuclear physics, phenomenology, and neutrino event generators

Hidden-nucleons neural-network quantum states for the nuclear many-body problem

Machine learning the deuteron: new architectures and uncertainty quantification

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