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arxiv: 2606.12998 · v1 · pith:CLDNDSZSnew · submitted 2026-06-11 · ⚛️ nucl-th

Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation

Mao Li , Yilong Yang , Pengwei Zhao This is my paper

Pith reviewed 2026-06-27 05:39 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords pionless effective field theoryvariational Monte Carloeigenvector continuationnuclear ground stateslight nucleilow-energy constantssensitivity analysisemulation
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The pith

Leading-order pionless effective field theory cannot simultaneously match the ground-state energies of carbon-12 and oxygen-16.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds an emulator that pairs a neural-network variational Monte Carlo method called FeynmanNet with eigenvector continuation. This tool lets researchers evaluate ground-state energies and radii for many different values of the low-energy constants in a leading-order pionless Hamiltonian at very low cost while keeping errors below half a percent. The emulator is then used to scan the three low-energy constants across a wide range and to compute properties of oxygen and carbon isotopes. A global sensitivity study shows that the two-body constant in the triplet S-wave channel drives most of the variation in binding energies, radii, and separation energies. The scan also reveals that no single set of constants can bring both the carbon-12 and oxygen-16 experimental binding energies into agreement at the same time.

Core claim

Varying the three low-energy constants inside the leading-order pionless Hamiltonian produces a family of calculated ground-state energies for helium-4, carbon-12, and oxygen-16 whose correlations show that the experimental values for carbon-12 and oxygen-16 lie outside any single point in that family. The analysis therefore concludes that additional physics beyond the leading-order two-body terms is required to describe these light nuclei.

What carries the argument

The combination of FeynmanNet neural-network variational Monte Carlo with eigenvector continuation, which supplies fast, accurate ground-state energies for new low-energy constant values.

If this is right

  • The two-body low-energy constant in the triplet S-wave channel is the dominant driver of ground-state energies, charge radii, and separation energies across the studied nuclei.
  • Global sensitivity analysis and uncertainty quantification become feasible for variational Monte Carlo calculations on light and medium-mass nuclei.
  • The binding energies of helium-4, carbon-12, and oxygen-16 are strongly correlated once the low-energy constants are allowed to vary.
  • The leading-order pionless Hamiltonian requires additional terms to describe the ground states of carbon-12 and oxygen-16 simultaneously.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Extending the emulator to include three-nucleon forces or next-to-leading-order terms could test whether those additions remove the incompatibility between the two nuclei.
  • The same workflow could be applied to other observables such as electromagnetic moments or excitation spectra to map which quantities are most sensitive to missing physics.
  • If the incompatibility persists at higher orders, it would point to a deeper limitation in the pionless formulation rather than a simple parameter-tuning issue.

Load-bearing premise

Eigenvector continuation reproduces the full FeynmanNet ground-state energies for new low-energy constant values to within 0.5 percent.

What would settle it

A full FeynmanNet calculation performed at a low-energy constant point where the emulator predicts both carbon-12 and oxygen-16 binding energies within a few hundred keV of experiment, if it instead yields an error larger than 0.5 percent or shows that the two nuclei still cannot be fit together.

Figures

Figures reproduced from arXiv: 2606.12998 by Mao Li, Pengwei Zhao, Yilong Yang.

Figure 1
Figure 1. Figure 1: FIG. 1: Distribution of the selected EC samples in the three-dimensio [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Comparison of the EC emulation for [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The eigenvalues of the norm matrix with [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The differences ∆ [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Main-effect and total-effect Sobol indices for the (a) grou [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The ground-state energies of [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
read the original abstract

An efficient emulator for \emph{ab initio} calculations of nuclear ground-state properties is developed by integrating the neural-network variational Monte Carlo framework, FeynmanNet, with the eigenvector continuation. It enables the calculation of observables for different Hamiltonians with minimal computational cost, while delivering ground-state energies with errors below $0.5\%$ compared to the full FeynmanNet results. With this emulator, the ground-state energies and charge radii of ${}^{16}\mathrm{O}$, ${}^{15}\mathrm{O}$, ${}^{14}\mathrm{O}$, ${}^{15}\mathrm{N}$, and ${}^{14}\mathrm{C}$ are computed using a nuclear Hamiltonian derived from the leading-order pionless effective field theory, with a large number of different values of low-energy constants (LECs). Then, we perform a global sensitivity analysis of the ground-state energies, charge radii, separation energies of selected nuclei for the three LECs in the Hamiltonian, to identify how each LEC contributes to the variances of these observables. It shows that the two-body LEC in the $^3S_1$ channel is the most influential LEC governing these nuclear bulk properties. Finally, the correlations among the ground-state energies of $^4$He, $^{12}$C, and $^{16}$O are investigated by varying the LECs in the Hamiltonian. The analysis reveals that the experimental ground-state energies of $^{12}$C and $^{16}$O cannot be reproduced simultaneously by varying the LECs in the leading-order pionless Hamiltonian. This suggests that additional ingredients in the leading-order Hamiltonian are required to improve its description of light nuclei. The present work establishes an efficient framework for global sensitivity analysis and uncertainty quantification in the quantum Monte Carlo calculations for light and medium-mass nuclei.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper develops an emulator integrating neural-network variational Monte Carlo (FeynmanNet) with eigenvector continuation to efficiently compute ground-state energies and charge radii of light nuclei for varying low-energy constants (LECs) in a leading-order pionless EFT Hamiltonian. It performs global sensitivity analysis showing the two-body LEC in the ^3S_1 channel is most influential, and concludes that experimental energies of ^{12}C and ^{16}O cannot be simultaneously reproduced by varying the three LECs, implying additional Hamiltonian ingredients are needed.

Significance. If the central numerical claims hold, the work provides an efficient framework for exploring LEC dependence and uncertainty quantification in ab initio nuclear calculations, while highlighting a concrete limitation of LO pionless EFT for A=12-16 nuclei. The combination of NN-VMC with eigenvector continuation is a methodological strength for reducing computational cost in parameter scans.

major comments (2)
  1. [Abstract] Abstract (emulator performance paragraph): the claim of errors below 0.5% relative to full FeynmanNet results is load-bearing for the conclusion that no LEC values simultaneously fit the experimental energies of ^{12}C and ^{16}O, yet the manuscript supplies no error bars, convergence diagnostics, validation dataset size, or checks for systematic bias in the ^{12}C–^{16}O energy difference; without these, the sampled points cannot be shown to rule out simultaneous reproduction.
  2. [Correlations among ground-state energies] Correlations section (final paragraph): the statement that experimental energies of ^{12}C and ^{16}O cannot be reproduced simultaneously rests on the emulator faithfully tracking the full variational energies across the sampled LEC space, but no quantitative test is given for whether emulator error correlates with the energy difference or exceeds the ~0.5% threshold in the relevant region.
minor comments (1)
  1. [Global sensitivity analysis] The global sensitivity analysis results would benefit from explicit reporting of the variance decomposition fractions or Sobol indices for each LEC and observable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and will make revisions to strengthen the presentation of the emulator validation and its implications for the conclusions.

read point-by-point responses

  1. Referee: [Abstract] Abstract (emulator performance paragraph): the claim of errors below 0.5% relative to full FeynmanNet results is load-bearing for the conclusion that no LEC values simultaneously fit the experimental energies of ^{12}C and ^{16}O, yet the manuscript supplies no error bars, convergence diagnostics, validation dataset size, or checks for systematic bias in the ^{12}C–^{16}O energy difference; without these, the sampled points cannot be shown to rule out simultaneous reproduction.

    Authors: We agree that additional documentation of the validation process is needed to fully support the 0.5% error claim and its bearing on the conclusion. The error bound was determined from direct comparisons on a held-out set of LEC combinations, but these details were omitted for brevity. In the revised manuscript, we will expand the abstract if space allows and add a new paragraph in the results section providing the validation dataset size, convergence checks, and explicit verification that the emulator error on the ^{12}C–^{16}O difference does not permit simultaneous fits within the sampled space. This will include quantitative measures to rule out systematic bias affecting the key conclusion. revision: yes

  2. Referee: [Correlations among ground-state energies] Correlations section (final paragraph): the statement that experimental energies of ^{12}C and ^{16}O cannot be reproduced simultaneously rests on the emulator faithfully tracking the full variational energies across the sampled LEC space, but no quantitative test is given for whether emulator error correlates with the energy difference or exceeds the ~0.5% threshold in the relevant region.

    Authors: The correlations analysis relies on the emulator's accuracy across the LEC space, with the reported bound applying globally. However, we recognize the value of a targeted test for the energy difference in the physically relevant region. We will add such an analysis to the correlations section, including a quantitative assessment of emulator errors on the difference and confirmation that it remains below the threshold needed to alter the conclusion. This revision will directly address the concern about potential correlation of errors with the difference. revision: yes

Circularity Check

0 steps flagged

No circularity: emulator validated externally and LEC scan is direct sampling

full rationale

The paper builds an eigenvector-continuation emulator on top of FeynmanNet VMC, explicitly validates it by comparing emulator energies to independent full FeynmanNet runs (errors <0.5%), then uses the validated emulator to sample LEC space and compare resulting energies/radii directly to experimental values for 12C and 16O. No equation or claim reduces to a fitted quantity by construction, no self-citation is load-bearing for the central incompatibility result, and no ansatz or uniqueness theorem is smuggled in. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the variational Monte Carlo framework being able to produce accurate ground states, the validity of the leading-order pionless EFT Hamiltonian, and the accuracy of eigenvector continuation for interpolation in LEC space. No new entities are postulated.

free parameters (1)
  • Three low-energy constants (LECs) in the pionless EFT Hamiltonian
    Varied across ranges to perform sensitivity analysis and correlation studies; their specific values are not fixed but scanned.
axioms (2)
  • standard math Variational principle in quantum Monte Carlo yields upper bounds to ground-state energies
    Invoked implicitly by the FeynmanNet VMC method.
  • domain assumption Eigenvector continuation provides accurate extrapolation for observables when the Hamiltonian varies smoothly with LECs
    Core assumption enabling the emulator; stated in the abstract description of the method.

pith-pipeline@v0.9.1-grok · 5851 in / 1416 out tokens · 21430 ms · 2026-06-27T05:39:06.300751+00:00 · methodology

discussion (0)

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