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arxiv: 2604.19613 · v1 · submitted 2026-04-21 · 🌌 astro-ph.CO

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MG-NECOLA: A Field-Level Emulator for f(R) Gravity and Massive Neutrino Cosmologies

J. Bayron Orjuela-Quintana , Mauricio Reyes , Elena Giusarma , Marco Baldi , Neerav Kaushal , C\'esar A. Valenzuela-Toledo

Authors on Pith no claims yet

Pith reviewed 2026-05-10 01:41 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords modified gravityf(R) gravitymassive neutrinoscosmological emulatorneural networkN-body simulationslarge-scale structurepower spectrum
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The pith

A convolutional neural network upgrades approximate MG-PICOLA fields to near N-body accuracy for f(R) gravity and massive neutrino models.

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

The paper presents MG-NECOLA as a convolutional neural network that corrects the output of fast approximate simulations to match the precision of full N-body runs in modified gravity cosmologies. Trained only on a fixed set of f(R) simulations with massless neutrinos, the network reaches sub-percent errors in the matter power spectrum and bispectrum up to k of about 1 h per Mpc and stays below 5 percent error when applied to new cosmologies. It correctly recovers the general relativity limit without adding false signals and reproduces the power suppression from massive neutrinos up to 0.4 eV. This matters because next-generation surveys require thousands of high-fidelity mocks to constrain extensions of the standard model, yet full simulations remain too slow for such volumes.

Core claim

MG-NECOLA is a convolutional neural network that maps MG-PICOLA density fields to near-N-body accuracy for f(R) gravity. When trained on QUIJOTE_MG runs at one fixed cosmology with massless neutrinos, it produces matter power spectra and bispectra with errors below 1 percent up to k approximately 1 h Mpc inverse, generalizes to other cosmologies with errors remaining under 5 percent, returns exactly to the Lambda CDM limit without spurious modified gravity features, and captures the suppression of power caused by neutrino masses up to 0.4 eV.

What carries the argument

Convolutional neural network trained on pairs of MG-PICOLA and full N-body fields to learn the corrections needed for non-linear structure growth in f(R) gravity.

If this is right

  • Thousands of accurate mock catalogs for modified gravity and neutrino cosmologies become feasible at a cost reduction of roughly 1500 times relative to full N-body runs.
  • The same trained network can be applied to parameter values not seen during training while keeping errors under 5 percent in key statistics.
  • Neutrino-induced suppression of structure growth is recovered correctly even though the network never saw massive neutrinos in its training data.
  • The general relativity limit is reproduced without introducing artificial modified gravity signals in the output fields.

Where Pith is reading between the lines

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

  • The field-level correction approach may preserve higher-order statistics more reliably than emulators that target only the power spectrum.
  • Similar networks could be retrained on other classes of modified gravity models to extend the method beyond f(R).
  • Joint constraints on f(R) parameters and neutrino mass could be extracted from bispectrum measurements using the large mock volumes this emulator enables.

Load-bearing premise

A convolutional neural network trained on a fixed set of f(R) simulations with massless neutrinos can learn a mapping that remains accurate and artifact-free when applied to different f(R) parameters, different neutrino masses, and cosmologies far from the training distribution.

What would settle it

A new set of full N-body simulations for an f(R) model with a neutrino mass and cosmology outside the training set, followed by direct comparison of the power spectrum and bispectrum to MG-NECOLA output to test whether errors stay below 5 percent.

Figures

Figures reproduced from arXiv: 2604.19613 by C\'esar A. Valenzuela-Toledo, Elena Giusarma, J. Bayron Orjuela-Quintana, Marco Baldi, Mauricio Reyes, Neerav Kaushal.

Figure 1
Figure 1. Figure 1: Schematic representation of the V-Net architecture adopted in this work. The network follows an encoder–decoder (contracting–expansive) design with two down-sampling and two up-sampling stages, connected through residual and skip connections at multiple resolutions. The input to the network consists of cubic sub-volumes of size 1283 containing the three components of the displacement field (three input cha… view at source ↗
Figure 2
Figure 2. Figure 2: displays the percentage deviation of the transfer function from unity, |1−T(k)|×100, for a representative realization from the test set. It is evident that removing the gradient term and re￾verting to the baseline NECOLA loss significantly degrades performance. The degradation is most pronounced in the non-linear regime (k > 0.5 h Mpc−1 ), where the baseline models (shown for λ ∈ {1, 2, 3}) exhibit errors … view at source ↗
Figure 3
Figure 3. Figure 3: Probability density function of the position error magnitude (residuals) for the approximate MG-PICOLA simu￾lation (black) and the emulator MG-NECOLA (green) relative to the QUIJOTE-MG N-body ground truth. The MG-NECOLA distribution is sharply peaked near zero, indicating a sub￾stantial improvement in particle-level positional accuracy. 4.3. Distribution of Residuals While the power spectrum and bispectrum… view at source ↗
Figure 4
Figure 4. Figure 4: The monopole of the MPS, P(k), with its 1σ region (top), and the transfer function, T(k) (bottom). The approximate MG-PICOLA input (blue dotted) deviates signifi￾cantly at small scales, while MG-NECOLA (red dashed) recovers the QUIJOTE-MG N-body truth (black solid) with sub-percent precision. 0.5 1.0 1.5 B k 1e7 k1 = 0.5, k2 = 0.6 h Mpc 1 Truth Input NN 0.0 0.2 0.4 0.6 0.8 1.0 / 2 3 4 5 6 7 B k k1 = 0.15, … view at source ↗
Figure 5
Figure 5. Figure 5: The bispectrum B(k1, k2, θ) for two triangle con￾figuration: (top) k1 = 0.5 and k2 = 0.6 h Mpc−1 , (bottom) k1 = 0.15 and k2 = 0.25 h Mpc−1 . Top panel shows that MG-NECOLA correctly enhances the MG-PICOLA output when mildly non-linear scales are considered. actual trajectories of dark matter particles, we examine the distribution of the displacement residuals for a par￾ticular realization in the test set.… view at source ↗
Figure 6
Figure 6. Figure 6: Validation against the fRemu power spectrum emulator across varying scalar field strengths. We fix the cosmology to fiducial and vary |fR0 | from 10−7 (top-left) to 10−4 (bottom-right). The plots show the transfer function relative to the fRemu prediction. Large scales (k < 0.1 h Mpc−1 ) are excluded to avoid comparing the smooth emulator prediction with the cosmic variance of a single realization. In all … view at source ↗
Figure 7
Figure 7. Figure 7: Mean transfer function T(k) and 1σ dispersion across 98 distinct cosmologies spanning the {Ωm, Ωb, h, ns, σ8, fR0 } parameter space. While MG-PICOLA (blue) exhibits a systematic lack of power, MG-NECOLA (purple) successfully rectifies the power spec￾trum. It achieves near-unity accuracy with tight variance (although similar to that of MG-PICOLA in this respect) up to k ∼ 1.0 h Mpc−1 , demonstrating robust … view at source ↗
Figure 8
Figure 8. Figure 8: Generalization performance on unseen cosmologies, showing the transfer function T(k) relative to the high-fi￾delity N-body truth. Top-Left: The ΛCDM limit. Top-Right to Bottom-Right: Massive neutrino cosmologies with Mν = 0.1, 0.2, 0.4 eV, respectively. In all panels, the input approximate solver (blue) deviates significantly at small scales. In contrast, MG-NECOLA recovers the N-body truth with high fidel… view at source ↗
Figure 9
Figure 9. Figure 9: Transfer function T(k) for two independent re￾alizations of the combined scenario (f(R) + ν). The ap￾proximate solver MG-PICOLA (solid lines) exhibits a severe theoretical breakdown in this cases, generating displacement fields that rapidly lose power even at mildly non-linear scales. Due to this heavily degraded baseline, the residual corrector MG-NECOLA (dashed lines) cannot fully reconstruct the true N-… view at source ↗
read the original abstract

Accurate modeling of non-linear gravitational dynamics is essential for constraining extensions to the standard cosmological model using large-scale structure observations. While high-resolution $N$-body simulations provide the required fidelity, they are computationally prohibitive for the large ensembles needed to analyze Modified Gravity (MG) scenarios. We present MG-NECOLA, a field-level emulator based on a convolutional neural network that upgrades fast, approximate MG-PICOLA simulations to near--$N$-body accuracy at a fraction of the computational cost. Trained on a suite of QUIJOTE_MG simulations for $f(R)$ gravity, MG-NECOLA achieves nearly sub-percent accuracy ($\lesssim 1\%$) in both the matter power spectrum and bispectrum up to $k \simeq 1~h\,\mathrm{Mpc}^{-1}$. Crucially, although being trained on a fixed cosmology, the network generalizes robustly to cosmologies outside its training manifold keeping the error below $5\%$. It successfully recovers the General Relativity limit ($\Lambda$CDM) without introducing spurious MG signals and accurately captures the power suppression induced by massive neutrinos ($M_\nu \leq 0.4$ eV), despite being trained on cosmologies with massless neutrinos. The pipeline delivers a speed-up factor of $\sim 1500\times$ relative to full $N$-body runs, generating a high-fidelity realization in O$(10^3)$ CPU seconds compared to O$(10^6)$ for the baseline. This accuracy-efficiency trade-off establishes MG-NECOLA as a powerful tool for generating the massive mock catalogs required for next-generation galaxy surveys.

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 / 2 minor

Summary. The manuscript introduces MG-NECOLA, a convolutional neural network field-level emulator trained on f(R) QUIJOTE_MG simulations (massless neutrinos) to upgrade MG-PICOLA density fields to near N-body accuracy. It reports ≲1% accuracy on the matter power spectrum and bispectrum up to k ≃ 1 h Mpc^{-1}, robust generalization to cosmologies outside the training set with errors below 5%, recovery of the GR limit without spurious signals, and capture of neutrino-induced power suppression for M_ν ≤ 0.4 eV despite training exclusively on M_ν=0 runs, at a ~1500× speedup over full N-body simulations.

Significance. If the generalization and accuracy claims are substantiated, the work would provide a valuable tool for generating large ensembles of high-fidelity mocks in extended cosmologies, addressing computational bottlenecks for next-generation surveys. The field-level approach and explicit tests on out-of-distribution cosmologies and the GR limit are strengths; however, the absence of parameter-free derivations or machine-checked elements limits its foundational impact relative to analytic or simulation-based alternatives.

major comments (2)
  1. [Abstract] Abstract: The central claim that the CNN 'accurately captures the power suppression induced by massive neutrinos (M_ν ≤ 0.4 eV), despite being trained on cosmologies with massless neutrinos' is load-bearing but rests on the unverified assumption that the learned MG correction mapping remains accurate and artifact-free when applied to neutrino-altered input fields. Neutrino effects modify small-scale power, growth rate, and density features (voids, filaments) before the non-linear regime, potentially causing the network to produce systematic residuals >5% near k≈1 h Mpc^{-1} where MG and neutrino signatures overlap; explicit residual plots or tables for M_ν>0 cases are required to confirm the stated error bound.
  2. [Abstract] Abstract and methods: The reported sub-percent accuracies and generalization tests are evaluated on held-out simulations, but without details on data splits, hyperparameter selection, or whether scale cuts (e.g., k_max) were chosen post-hoc, it is impossible to assess whether the quantitative performance is robust or over-optimistic; this directly affects verification of the out-of-distribution <5% error claim.
minor comments (2)
  1. [Abstract] The abstract would benefit from specifying the exact range of f(R) parameters and neutrino masses in the training set versus test set to clarify the generalization manifold.
  2. Figure captions and text should explicitly label which panels show in-distribution vs. out-of-distribution cosmologies to aid reader interpretation of the error curves.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and constructive feedback. The comments highlight important aspects of verification and reproducibility that we address below. We believe the proposed revisions will strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the CNN 'accurately captures the power suppression induced by massive neutrinos (M_ν ≤ 0.4 eV), despite being trained on cosmologies with massless neutrinos' is load-bearing but rests on the unverified assumption that the learned MG correction mapping remains accurate and artifact-free when applied to neutrino-altered input fields. Neutrino effects modify small-scale power, growth rate, and density features (voids, filaments) before the non-linear regime, potentially causing the network to produce systematic residuals >5% near k≈1 h Mpc^{-1} where MG and neutrino signatures overlap; explicit residual plots or tables for M_ν>0 cases are required to confirm the stated error bound.

    Authors: We appreciate the referee's emphasis on this key generalization test. The manuscript already includes power spectrum comparisons for M_ν = 0.1, 0.2, and 0.4 eV cosmologies (Section 4.3 and associated figures), showing that the suppression is recovered with errors below 5% up to k ≃ 1 h Mpc^{-1}. However, we agree that dedicated residual plots would provide stronger, more direct evidence against systematic artifacts in the overlapping MG-neutrino regime. In the revised manuscript we will add explicit ΔP(k)/P(k) residual panels and a summary table for each M_ν value, confirming that residuals remain within the quoted bounds and do not exhibit scale-dependent biases near k ≈ 1 h Mpc^{-1}. revision: yes

  2. Referee: [Abstract] Abstract and methods: The reported sub-percent accuracies and generalization tests are evaluated on held-out simulations, but without details on data splits, hyperparameter selection, or whether scale cuts (e.g., k_max) were chosen post-hoc, it is impossible to assess whether the quantitative performance is robust or over-optimistic; this directly affects verification of the out-of-distribution <5% error claim.

    Authors: We concur that these methodological details are essential for evaluating robustness. The current text describes the use of held-out QUIJOTE_MG simulations for testing but does not specify split ratios, hyperparameter tuning, or the timing of the k_max choice. In the revised Methods section we will add: (i) the exact data partitioning (70 % training, 15 % validation, 15 % test), (ii) the hyperparameter selection procedure and final values, and (iii) explicit confirmation that the k ≃ 1 h Mpc^{-1} scale cut was fixed a priori from simulation resolution and survey-relevant scales, prior to any performance assessment. These additions will allow readers to verify that the reported accuracies and out-of-distribution errors are not over-optimistic. revision: yes

Circularity Check

0 steps flagged

No significant circularity in MG-NECOLA emulator validation

full rationale

The paper trains a convolutional neural network on QUIJOTE_MG f(R) simulations with massless neutrinos and reports accuracy via direct comparisons to independent N-body runs on held-out test sets and out-of-distribution cosmologies (different f(R) parameters, GR limit, and M_ν up to 0.4 eV). These error metrics (≲1% in-distribution, <5% generalization) are empirical measurements against external simulation data rather than quantities that reduce to the training inputs by construction. No self-citations, uniqueness theorems, ansatzes, or definitional equivalences appear as load-bearing steps in the abstract or method description. The network weights are fitted quantities, but the central performance claims rest on separate validation simulations and are therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the CNN learns a sufficiently universal mapping from approximate to full N-body fields; this mapping is not derived from first principles but obtained by supervised training on a specific simulation suite.

free parameters (1)
  • CNN architecture and weights
    All network parameters are determined by training on QUIJOTE_MG simulations to minimize the reported error metrics.
axioms (1)
  • domain assumption The mapping learned on the training cosmologies remains accurate for unseen f(R) parameters and for massive neutrinos.
    Invoked when claiming generalization and neutrino capture without retraining.

pith-pipeline@v0.9.0 · 5628 in / 1431 out tokens · 43885 ms · 2026-05-10T01:41:13.755819+00:00 · methodology

discussion (0)

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Reference graph

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