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arxiv: 2606.00219 · v1 · pith:VHWL5OW6new · submitted 2026-05-29 · 🌌 astro-ph.CO · astro-ph.GA· cs.LG

21cmEMUv3: a hybrid diffusion-LSTM emulator of 21cmFAST summary observables

Daniela Breitman , Andrei Mesinger , Steven G. Murray , Ivan Nikolic , Roberto Trotta This is my paper

Pith reviewed 2026-06-28 20:50 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GAcs.LG
keywords 21cm power spectrumcosmic dawnepoch of reionizationemulatordiffusion modelLSTMHERAX-ray luminosity
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The pith

A hybrid diffusion-LSTM emulator reproduces seven 21cm summary observables at sub-percent median accuracy

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

The paper introduces 21cmEMUv3, an emulator trained on 21cmFASTv3 simulations that include both atomically and molecularly cooling galaxies. It uses score-based diffusion to model the cylindrical 21cm power spectrum at high resolution across redshifts 6 to 30, while LSTM networks handle the spherical power spectrum, neutral fraction, spin temperature, global signal, UV luminosity functions, and Thomson optical depth. All seven summaries reach sub-percent median accuracy as functions of sigma_8 and ten astrophysical parameters. The emulator is applied to reinterpret HERA upper limits on the 21cm power spectrum, incorporating priors on star formation in low-mass galaxies drawn from hydrodynamical simulations. This produces a 95 percent lower bound on the soft-band X-ray luminosity per unit star formation rate.

Core claim

21cmEMUv3 produces the cylindrical 21cm power spectrum via score-based diffusion and the remaining six summaries via LSTM networks, all achieving sub-percent median accuracy; the inferred soft-band X-ray luminosity per unit star formation rate excludes values below 10^{39.2} erg s^{-1} M^{-1}_sun yr at 95 percent confidence when reinterpreting HERA 21cm PS upper limits with hydro-informed priors on molecularly cooling galaxies.

What carries the argument

Hybrid emulator using score-based diffusion for the cylindrical 21cm power spectrum and LSTM networks for the other six summary observables

Load-bearing premise

The 21cmFASTv3 simulations with both atomically and molecularly cooling galaxies provide a sufficiently accurate representation of the underlying physics to serve as training data and to inform priors for inference on star formation in low-mass galaxies.

What would settle it

Direct comparison of emulator predictions against an independent set of 21cmFASTv3 runs withheld from training, or independent observational evidence that the soft-band X-ray luminosity per star formation rate lies below 10^{39.2} erg s^{-1} M^{-1}_sun yr

Figures

Figures reproduced from arXiv: 2606.00219 by Andrei Mesinger, Daniela Breitman, Ivan Nikolic, Roberto Trotta, Steven G. Murray.

Figure 1
Figure 1. Figure 1: Diagram of the architecture of 21cmEMUv3. The input consists of a total of eleven parameters: 𝜎8 and ten astrophysical parameters, three of which affect pop III galaxies. 21cmEMUv3 consists of two networks: timeseries LSTM network on the left and the score-base diffusion network for the 2D 21-cm PS on the right. The network on the left emulates the globally-averaged 21-cm signal, spin temperature, and neut… view at source ↗
Figure 2
Figure 2. Figure 2: Top row: a cylindrical 21-cm PS realisation from the test set (left) and the corresponding [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: True (solid) and emulated (dashed) outputs from [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Left plot: Prior on the SHMR from L24 (Lazare et al. 2024) (grey). Prior used in this work that is similar to L24 but not [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left plot: In yellow, we show the SHMR for the Renaissance hydrodynamic simulations (Xu et al. 2016). We use these to [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Left panel: Mock SKA observation of the 21-cm 1D PS at wavemode [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original abstract

We are witnessing a surge in observations of the cosmic dawn (CD) and epoch of reionisation (EoR), driving an increasing demand for fast and robust theoretical interpretation frameworks. In response, machine learning (ML), and emulation in particular, has emerged as a powerful approach to accelerate and enhance inference pipelines. In this work, we present 21cmEMUv3, an emulator trained on 21cmFASTv3 simulations that model both atomically and molecularly cooling galaxies. 21cmEMUv3 is conditioned on $\sigma_8$ and ten astrophysical parameters to produce seven summary observables: (i) the cylindrical 21cm power spectrum (PS), emulated for the first time at such high resolution and accuracy across a wide redshift range of $z \sim$ 6--30; (ii) the spherically-averaged 21cm PS; (iii) the mean neutral fraction of the intergalactic medium (IGM); (iv) the mean 21cm spin temperature; (v) the global 21cm signal; (vi) the ultraviolet (UV) luminosity functions (LFs); and (vii) the Thomson scattering optical depth. Notably, the cylindrical 21cm PS is emulated via score-based diffusion, while the remaining six summaries are emulated via long-short term memory (LSTM) networks, all achieving sub-percent median accuracy. We use the emulator to reinterpret current 21cm PS upper limits from HERA, for the first time using state-of-the-art hydrodynamical simulations to inform priors on star formation inside molecularly cooling galaxies. We find that our inferred soft-band X-ray luminosity per unit star formation rate is consistent with extrapolations of high-mass X-ray binaries to the low-metallicity regimes expected in the first galaxies, excluding values below $10^{39.2}$ erg s$^{-1}M^{-1}_\odot \rm{yr}$ at $95\%$ confidence. Finally, we produce forecasts for the detection of the cosmic 21cm PS with the Square Kilometre Array for different array configurations. The 21cmEMU package is publicly available.

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 21cmEMUv3, a hybrid emulator trained on 21cmFASTv3 simulations including both atomically and molecularly cooling galaxies. Conditioned on σ₈ and ten astrophysical parameters, it emulates the cylindrical 21cm power spectrum via score-based diffusion and six other summaries (spherically-averaged PS, IGM neutral fraction, spin temperature, global 21cm signal, UV LFs, Thomson optical depth) via LSTM networks, all at sub-percent median accuracy over z~6-30. The emulator is used to reinterpret HERA 21cm PS upper limits with hydrodynamical-simulation-informed priors on star formation in molecularly cooling galaxies, excluding soft-band X-ray luminosity per unit SFR below 10^{39.2} erg s^{-1} M_⊙^{-1} yr^{-1} at 95% confidence, and provides SKA forecasts. The 21cmEMU package is released publicly.

Significance. If the sub-percent accuracies hold under detailed scrutiny and the 21cmFASTv3 training set is representative, this work supplies a practical, publicly available tool that accelerates parameter inference for cosmic dawn and reionization. The hybrid diffusion-LSTM architecture for high-resolution cylindrical PS emulation is a technical contribution, and the hydro-informed priors yield a concrete, falsifiable constraint on early X-ray emission that aligns with HMXB extrapolations. Public code release supports reproducibility.

major comments (2)
  1. [Validation section (results on emulator accuracy)] Validation section (results on emulator accuracy): the sub-percent median accuracy claim for the diffusion model on the cylindrical PS and the LSTM models on the other six summaries is load-bearing for both the emulator utility and the downstream HERA inference; the manuscript must supply quantitative error distributions (median, 68/95 percentiles) broken down by redshift, k-mode, and astrophysical parameter values, plus direct residual plots against the 21cmFASTv3 training set.
  2. [Inference section (HERA reinterpretation and priors)] Inference section (HERA reinterpretation and priors): the 95% exclusion on soft-band X-ray luminosity per SFR depends on the hydro-informed priors for molecularly cooling galaxies; the paper should demonstrate consistency between 21cmFASTv3 outputs (UV LF normalization, 21cm PS shape at relevant halo masses) and the hydrodynamical simulations used for the priors, or quantify the impact of any systematic offset on the reported bound.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'sub-percent median accuracy' would be strengthened by quoting the actual median fractional error (e.g., 0.3%) and the redshift/k range over which it applies.
  2. [Notation] Notation: ensure the X-ray luminosity unit is written uniformly as erg s^{-1} M_⊙^{-1} yr^{-1} throughout text, tables, and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive report. We address each major comment below and will revise the manuscript accordingly to improve clarity and robustness.

read point-by-point responses

  1. Referee: Validation section (results on emulator accuracy): the sub-percent median accuracy claim for the diffusion model on the cylindrical PS and the LSTM models on the other six summaries is load-bearing for both the emulator utility and the downstream HERA inference; the manuscript must supply quantitative error distributions (median, 68/95 percentiles) broken down by redshift, k-mode, and astrophysical parameter values, plus direct residual plots against the 21cmFASTv3 training set.

    Authors: We agree that more granular validation metrics are necessary to substantiate the sub-percent accuracy claims. In the revised manuscript we will expand the validation section with tables and figures reporting median, 68th, and 95th percentile errors for each observable, stratified by redshift, k-mode (where applicable), and across the astrophysical parameter space. Direct residual plots comparing emulator predictions to the 21cmFASTv3 test set will also be included for representative parameter combinations. revision: yes

  2. Referee: Inference section (HERA reinterpretation and priors): the 95% exclusion on soft-band X-ray luminosity per SFR depends on the hydro-informed priors for molecularly cooling galaxies; the paper should demonstrate consistency between 21cmFASTv3 outputs (UV LF normalization, 21cm PS shape at relevant halo masses) and the hydrodynamical simulations used for the priors, or quantify the impact of any systematic offset on the reported bound.

    Authors: We will add a dedicated subsection in the revised manuscript that directly compares 21cmFASTv3 UV luminosity function normalizations and 21cm power spectrum shapes at halo masses relevant to molecularly cooling galaxies against the hydrodynamical simulations used to inform the priors. Should any systematic offsets appear, we will perform additional inference runs to quantify their effect on the reported 95% exclusion limit on soft-band X-ray luminosity per unit SFR. revision: yes

Circularity Check

0 steps flagged

No significant circularity; emulator and inference rely on independent external simulations

full rationale

The paper trains 21cmEMUv3 on 21cmFASTv3 simulations (with diffusion for cylindrical PS and LSTM for other summaries) and reinterprets HERA limits using priors from separate hydrodynamical simulations on molecularly cooling galaxies. The sub-percent accuracy is measured against those training simulations, and the X-ray luminosity bound is obtained via the emulator with external priors. No step reduces by construction to a fitted parameter or self-citation chain; the derivation is self-contained against the stated external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The accuracy and inference claims rest on the fidelity of 21cmFASTv3 simulations and the generalization performance of the trained neural networks; the ten astrophysical parameters and sigma_8 are varied inputs rather than outputs of the derivation.

free parameters (2)
  • sigma_8 and ten astrophysical parameters
    These are the conditioning inputs varied across the training simulations.
  • neural network weights in diffusion and LSTM models
    These are fitted during training to reproduce the simulation outputs.
axioms (1)
  • domain assumption 21cmFASTv3 simulations accurately model the physics of atomically and molecularly cooling galaxies
    The emulator is trained directly on outputs from these simulations.

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