https://doi.org/10.1140/epjp/s13360-024-04983-w
Regular Article
Machine learning the deuteron: new architectures and uncertainty quantification
1
Departament de Física Quàntica i Astrofísica, Universitat de Barcelona (UB), c. Martí i Franquès 1, 08028, Barcelona, Spain
2
Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB), c. Martí i Franquès 1, 08028, Barcelona, Spain
3
Department of Physics, University of Surrey, GU2 7XH, Guildford, UK
Received:
23
October
2023
Accepted:
7
February
2024
Published online:
25
February
2024
We solve the ground state of the deuteron using a variational neural network ansatz for the wavefunction 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 per cent 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-connected 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 errors associated to the model oscillations around the real minimum are larger than the stochastic initilization uncertainties.
The original online version of this article was revised: In this article the caption to Fig. 1 in subplots (b), (c) and (d) was inadvertently omitted. The following should be appended to the captions: “Note that the first layer includes a bias.” In Sect. 3.2, paragraph 1, the sentence 4 instead of: “[…] is better than that associated to the S state” should have read “[…] is better than that associated to the D state”. In Sect. 3.2, paragraph 2, the sentence 5 instead of: “[…] the D-state fidelity is much lower for small Nhid 80, approaching…” should have read “[…] the D-state fidelity is much lower for small Nhid, approaching…”.
A correction to this article is available online at https://doi.org/10.1140/epjp/s13360-024-05193-0.
Copyright comment corrected publication 2024
© The Author(s) 2024. corrected publication 2024
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