Generative Neural Network for Simulating Radio Emission from Extensive Air Showers

Andreas Haungs; Pranav Sampathkumar; Ralph Engel; Tim Huege

REVIEW 3 major objections 6 minor 24 references

Generative Neural Network for Simulating Radio Emission from Extensive Air Showers

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A neural network trained on CoREAS showers can generate radio pulses and reconstruct Xmax with resolution close to full Monte Carlo.

desk verdict Promising neural surrogate for CoREAS radio pulses whose headline validation may be inflated by a per-run rather than per-shower train/test split. read the letter →

arxiv 2507.07713 v1 pith:SHKK62Z7 submitted 2025-07-10 astro-ph.HE astro-ph.IM

Pranav Sampathkumar , Tim Huege , Andreas Haungs , Ralph Engel This is my paper · ORCID

classification astro-ph.HEastro-ph.IM

keywords radioemissionfromextensiveairshowersneuralnetworksurrogateXmaxreconstructionCoREASAERAcosmicraysfluence

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that a fully connected neural network can replace per-event CORSIKA/CoREAS Monte Carlo simulations of radio emission from extensive air showers, at least inside the AERA training phase space. The network takes eleven physical inputs—shower maximum depth, electromagnetic energy, geomagnetic angle, atmospheric density and height at shower maximum, primary energy, arrival direction, and antenna position in the shower plane—and produces 1 ns radio pulses in two polarisations at 240 antenna positions. Pulse fluences agree with CoREAS to within about 10 percent for strong signals, and an $X_\mathrm{max}$ reconstruction built on the network's pulses has bias and resolution close to the same reconstruction run on full CoREAS simulations ($37$–$40\ \mathrm{g\,cm^{-2}}$ versus $31$–$32\ \mathrm{g\,cm^{-2}}$ at 5–10 percent noise). The reason to care is speed: CoREAS simulations are the dominant computational bottleneck in radio cosmic-ray analysis, while network inference takes only milliseconds per antenna and training takes about a week on a desktop CPU. The authors present this as a proof of concept limited to the phase space covered by the training library.

What carries the argument

The carrying mechanism is a fully connected neural network with 11 inputs, 8 hidden layers, about 4 million parameters, and 512 output nodes: 256 time bins at 1 ns resolution for each of the two polarisations. The network is trained directly on CoREAS pulses with an L1 loss, with the weaker $\vec{v}\times(\vec{v}\times\vec{B})$ polarisation weighted more heavily so that both polarisations are learned, and ADAM with weight decay is used for minimisation. Because the network outputs the pulse waveform itself at any antenna position in the shower plane, pulse shape information is retained rather than only integral fluence, which matters because pulse shape carries information about shower development.

What would settle it

Run the trained network on real AERA events whose $X_\mathrm{max}$ is independently known from fluorescence measurements and compare the reconstructed $X_\mathrm{max}$ values: if resolution or bias is substantially worse than the $37$–$40\ \mathrm{g\,cm^{-2}}$ seen on simulated CoREAS events, the paper's claim of comparable resolution on real data fails.

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Extended reading notes

Core claim

The paper's central claim is that radio pulses of extensive air showers can be generated by a trained neural network rather than by summing radiation from individual particle tracks, and that the generated pulses carry enough physical fidelity for $X_\mathrm{max}$ reconstruction. Trained on roughly 58,000 CoREAS simulations of AERA events (2158 shower configurations with 27 iterations each), the network reproduces 30–80 MHz radio pulses in both polarisations, with fluences that mostly match CoREAS within 10 percent and high pulse-wise correlation for strong signals. Running the same fluence-based $\chi^2$ reconstruction against both simulation types, the network gives $X_\mathrm{max}$ resolutions of $37.5$–$39.6\ \mathrm{g\,cm^{-2}}$ at 5–10 percent noise, compared with $30.7$–$31.6\ \mathrm{g\,cm^{-2}}$ for CoREAS, with comparable bias behaviour. The paper concludes that neural-network simulation is a viable tool for radio air-shower analyses and can be fine-tuned to other experiments and frequency bands.

Load-bearing premise

The demonstration assumes CoREAS Monte Carlo output is the true radio signal, since the network is trained on CoREAS pulses and benchmarked against CoREAS reconstructions; if CoREAS's emission model is biased for AERA conditions, the comparable resolution may not carry over to measured events.

Editorial extensions

If this is right

Radio pulse simulation drops from per-event Monte Carlo runs to milliseconds per antenna, removing the main computational bottleneck in iterating over noisy radio measurements.
$X_\mathrm{max}$ reconstruction on network pulses matches the resolution of full CoREAS-based reconstruction within the AERA training phase space, enabling fast analyses of many simulated event iterations.
Because the network is small (about 4 million parameters, 19 MB footprint), it could run on FPGAs for near-instant pulse generation and triggering.
The network is differentiable, so it can be combined with gradient-based inference frameworks such as Information Field Theory.
Adding inputs such as the full longitudinal shower profile could extend the same setup to reconstructing the longitudinal development of air showers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If CoREAS's radio-emission model is biased under real AERA atmospheric conditions, the demonstrated comparable resolution may not transfer to measured events; the direct test is applying the network to real data with independently known $X_\mathrm{max}$ values.
Because the training library follows AERA's measured phase-space distribution, the model is most reliable for typical events, while rare geometries and showers with $X_\mathrm{max}$ above $1000\ \mathrm{g\,cm^{-2}}$ need resampling or dedicated training sets.
A waveform-generating model may support observables beyond fluence-based $X_\mathrm{max}$, such as pulse timing, width, or asymmetry, since the network outputs full pulses rather than summary statistics.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the paper does something real and useful—trains a fully connected network to generate 30–80 MHz radio pulses for AERA-like geometries, and benchmarks it for Xmax reconstruction. The idea is not brand new (they cite a LOFAR model), but this is the first demonstration on AERA with a reconstruction benchmark, and the writing is clear and honest about phase-space limits.

What I like: the network takes 11 physically meaningful inputs and outputs 512 pulse bins directly. The held-out evaluation, as described, shows fluence agreement within about 10% and pulse correlations above 0.9 for strong signals. The Xmax reconstruction comparison is a fair way to test downstream usability, and they correctly note the 'comparable resolution' caveat: at 5–10% noise, NN resolution is 37–40 g/cm² versus 31–32 for CoREAS—about 25% worse, which is still in the ballpark. They also state the low-Xmax bias is from the parabola-fitting method, not the network, and flag poor performance beyond 1000 g/cm².

The soft spot: the train/test split. Section 2 says '80% of the simulations are used for training and the remaining 20% for testing.' The library has 2158 shower parameter sets, each with 27 iterations. If the split is done on individual runs, then for each test run, 26 other iterations with the identical input vector (same Xmax, energy, zenith, azimuth, antenna positions) sit in the training set. The network has seen that exact input during training and can memorize the conditional mean pulse. The test then measures reproduction of known showers, not generalization to new geometries. This would inflate the pulse correlations, fluence errors, and Xmax resolution. The paper never states that the split is grouped by parameter set, and no code or weights are released to check. This is the load-bearing issue for the abstract's claim.

Other gaps are minor in comparison: no statistical uncertainties on the bias/resolution numbers, and the validation is entirely internal to CoREAS. The authors acknowledge the latter implicitly by calling it a proof of concept and mentioning fine-tuning for LOFAR.

Verdict: the idea deserves a serious referee. The split ambiguity must be resolved—either re-run with a grouped split or clearly report it. If the grouped split gives similar numbers, this becomes a solid proof of concept. For now I would not cite it in my own work until that is fixed.

Referee Report

3 major / 6 minor

Summary. This paper presents a fully connected neural network trained on ~58k CoREAS simulations (2158 shower parameter sets times 27 iterations) to predict 30-80 MHz radio pulses at 240 star-shaped antenna positions for AERA-like geometries. The authors evaluate the surrogate on a held-out 20% of the simulations, comparing pulse shapes, energy fluence, pulse correlations, and a fluence-based Xmax reconstruction against per-event CoREAS simulations. They report fluence agreement within roughly 10% for strong pulses and Xmax resolutions of about 37-40 g/cm2 for the network versus 31-32 g/cm2 for CoREAS at 5-10% noise, concluding that the neural network can serve as a fast surrogate for radio-emission simulation in this phase space.

Significance. If the evaluation is performed on showers whose full parameter sets were excluded from training, the paper is a useful proof of concept: a compact fully connected regressor can reproduce CoREAS pulse shapes and support a downstream Xmax reconstruction at a resolution close to, albeit somewhat worse than, full Monte Carlo, with much faster inference. The authors are appropriately explicit about the limited phase space, the AERA-specific atmosphere and frequency band, and the degradation beyond Xmax = 1000 g/cm2. The main risk is that the reported test performance may not measure generalization to unseen shower parameters, because the paper does not state that the train/test split was grouped by the 2158 underlying parameter sets.

major comments (3)

[Section 2] The data split is not defined at the correct level. The library consists of 2158 shower parameter sets, each with 27 iterations, but the text says only that '80% of the simulations are used for training and the remaining 20% are used for testing.' If the split is made per CoREAS run, a typical test run will have 26 other iterations of the identical parameter set (same Xmax, energy, zenith, azimuth, and GDAS atmosphere) in the training sample, and because all of these quantities are explicit network inputs, the model has already been trained on the exact input vector. The pulse correlations in Figure 5 and the Xmax resolution comparison in Figure 7 and Table 1 would then measure reproduction of known parameter points rather than generalization to new showers. Please state explicitly that the split was performed on the 2158 parameter sets (or otherwise demonstrate test independence), and if it was not, repeat the evaluation with a grouped split.
[Section 4.4 / Table 1] Table 1 reports total bias and resolution as single numbers with no statistical uncertainties, and Figure 7 shows no confidence bands. The sampling is not described beyond 'N=2000 simulations,' and it is not stated how these events relate to the training and test sets. The table shows network resolutions of 39.6 and 37.5 g/cm2 versus CoREAS resolutions of 31.6 and 30.7 g/cm2 at 5% and 10% noise, i.e., about 22-25% worse. The abstract's phrase 'comparable resolution' needs a quantitative justification and an uncertainty estimate; as written, the reader cannot tell whether these differences are statistically significant.
[Sections 3 and 4] The network is deterministic: for a fixed input vector it always returns the same pulse, whereas the 27 CoREAS iterations at fixed shower parameters are stochastic realizations. The paper does not state whether the surrogate is intended to reproduce only the conditional mean pulse or also the event-by-event fluctuation distribution. This matters for the Xmax benchmark, because chi2 templates generated by the network cannot include shower-to-shower fluctuations that are present in CoREAS templates, and it also bears on the interpretation of the pulse-level correlations in Section 4.2. Please discuss this limitation and its effect on the reported resolution.

minor comments (6)

[Eq. (1)] Please define P_ant and P_sim; the S^2 factor in Eq. (1) is inconsistent with the statement that S accounts for multiplicative deviations between fluence measurements and simulations.
[Section 4.3] The noise model is not fully specified: the width of the Gaussian multiplicative noise is not given, and the additive noise is quoted as '1 muV/m^2' although fluences are in eV/m^2; please state the units and all noise parameters.
[Section 2] Please report the criterion and fraction of weak pulses removed as dominated by thinning artifacts; this affects the training distribution and the comparability of the network output with full CoREAS pulses.
[Figure 5] The vertical axis label 'N.Coorelation bw Pulses' contains typos; 'bw' should be 'between' and 'Coorelation' should be 'Correlation'.
[Section 4.1] The pulse comparison in Figure 3 is qualitative; please state explicitly whether the events shown in Figures 3-5 are drawn from the held-out test set.
[Section 3] The model is called 'generative,' but it is a deterministic function without a latent stochastic source; consider using 'surrogate' or 'emulator' in the title and text to avoid overstating the generative aspect.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the network is a CoREAS emulator evaluated on held-out CoREAS pulses; internal validation against the training simulator is a benchmark limitation, not a circular step.

full rationale

The paper claims that a neural network can simulate radio pulses and be used for Xmax reconstruction with resolution comparable to CoREAS. This is a surrogate-model claim, not a first-principles derivation. The network is trained on CoREAS pulses and tested on held-out CoREAS pulses; measuring fidelity against the same simulator that generated the training data is the standard and appropriate benchmark for an emulator, not a circular reduction. The Xmax reconstruction treats Xmax as an unknown scanning parameter and uses the network as a forward simulator in a chi-square template fit; because Xmax is an input to the network but is not supplied as truth during reconstruction, the procedure is a genuine inversion rather than a definitional identity. No load-bearing self-citation chain is present: the CoREAS citation defines the target simulator, and prior neural-network work is background. The only substantive concern is the ambiguity in the train/test split: the library has 2158 shower parameter sets with 27 iterations each, and the text says only that '80% of the simulations are used for training and the remaining 20% are used for testing.' If the split is at the level of individual runs rather than grouped by parameter set, test performance could be inflated by memorization. However, the paper does not state the split strategy, so under the hard rules this remains an unverified risk rather than an exhibited circular step. No quoted equation or described step makes an output equal to an input by construction, so the circularity score is low.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a fitted neural surrogate with about 4 million parameters, not on a physical derivation. All physical content comes from CoREAS; the paper adds no new entities. The main axioms are the faithfulness of CoREAS and the representativeness of the training library.

free parameters (4)

Neural network weights (~4 million) = Trained on the CoREAS AERA library
All pulse predictions are determined by these fitted weights; the surrogate has no physical constraints beyond the training data.
Loss weighting for v*v*B polarization = Not specified numerically
Chosen by hand to emphasize the weaker polarization; affects how both polarizations are learned (Section 3).
Input scaling nominal values = Not specified
Inputs are scaled to [-1,1] by nominal values chosen by the authors (Section 3).
Reconstruction noise model parameters = 5% and 10% multiplicative Gaussian noise, 1 uV/m^2 additive noise
Assumed for the Xmax benchmark; controls absolute resolution values, though the NN-vs-CoREAS comparison shares the same model.

assumptions (4)

domain assumption CoREAS radio-emission simulations are an accurate ground truth for AERA radio pulses
Used throughout Section 2 and Section 4.3; all training and validation are against CoREAS.
domain assumption The AERA simulation library's phase-space distribution is representative of events the network will see
Section 2 and Figure 1; the paper concedes rare events are under-represented and performance collapses beyond Xmax = 1000 g/cm^2.
ad hoc to paper Weak pulses dominated by thinning artifacts can be removed without losing physical information
Section 2 states 'the weak pulses, which are dominated by thinning artifacts during simulations, are removed.' This cut shapes the training target.
ad hoc to paper A fully connected network with 11 scalar inputs can represent the position- and geometry-dependent pulse shape
The entire model rests on this representational assumption; the paper validates it only on held-out star-grid points.

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Cite this review

Pith. "Pith review of Generative Neural Network for Simulating Radio Emission from Extensive Air Showers." pith.science (2026). https://pith.science/paper/SHKK62Z7

@misc{pith2026250707713,
  author       = {Pith},
  title        = {Pith review of: Generative Neural Network for Simulating Radio Emission from Extensive Air Showers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SHKK62Z7}},
  note         = {Machine review of arXiv:2507.07713}
}

abstract

Cosmic ray shower detection using large radio arrays has gained significant traction in recent years. With massive improvements in signal modelling and microscopic simulations, the analysis of incoming events is still severely limited by the simulation cost of radio emission to interpret the data. In this work, we show that a neural network can be used for simulating such radio pulses. We also demonstrate how such a neural network can be used for $X_\mathrm{max}$ reconstruction, while retaining comparable resolution to using full Monte-Carlo CORSIKA/CoREAS simulations for radio emission.

Figures

Figures reproduced from arXiv: 2507.07713 by the authors.

**Figure 1.** Shown are the distributions of 𝑋max, zenith angle 𝜃, and primary energy 𝐸0 for the full CORSIKA/CoREAS simulations. These show the phase space distribution of the training data and show us the regions the network is trained on. It is expected that the network works well in this phase-space region. 3. Neural Network Model Neural networks have been gaining substantial interest as an alternative simulation tool for ph… view at source ↗

**Figure 2.** Neural network schematic for generating radio pulses: The 11 inputs are described in Section 3, and the 512 outputs are the 256 time bins in the 2 polarisations. The network produces a pulse, given an antenna position and shower parameters. The model has about 4M parameters, and has a memory footprint of 19MB. 4. Performance 4.1 Pulses The neural network can directly produce centered pulses in the trained time resol… view at source ↗

**Figure 3.** Comparison of generated radio pulses between a CoREAS simulation and neural network-based simulation for both polarizations at antennas at various distances from the shower core (R). This is a simulation with 𝜃 = 43.56◦ and primary energy of 3 × 108 GeV with an 𝑋max of 703 g cm−2 . We see the agreement is quite good for strong pulses. A more quantitative comparison between the pulses is shown in [PITH_FULL_IMAGE:fi… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Comparison of fluence maps between a CoREAS simulation and neural network-based simulation for both polarizations. This is a simulation with 𝜃 = 54.1 ◦ and primary energy of 2.94 × 109 GeV with an 𝑋max of 733 g cm−2 . The pulses are simulated at the indicated antenna p…

**Figure 5.** Figure 5: The relative fluence error and the normalized correlation between the pulses simulated using CoREAS and Neural Network for 240 antennas in a star shaped grid for a typical shower are given here. We can see that the agreement is quite high for high fluence pulses, which…

**Figure 6.** Figure 6: We show the 𝑋max reconstruction for two events using a fluence based 𝜒 2 method. The same points which are used for the traditional reconstruction, are also sampled using a neural network and a parabola is fit. This highlights that the network has a correlation between…

**Figure 7.** Figure 7: In this Figure, on the left, you see the 𝑋max reconstruction procedure’s bias and resolution for the (N=2000) simulations done using CoREAS and the neural network compared for 5% Gaussian Noise. On the right we see the same for 10% Gaussian Noise. As expected, there is…

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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