Prospects for Deep-Learning-Based Mass Reconstruction of Ultra-High-Energy Cosmic Rays using Simulated Air-Shower Profiles

arxiv: 2508.13933 · v5 · submitted 2025-08-19 · 🌌 astro-ph.HE · astro-ph.IM

Prospects for Deep-Learning-Based Mass Reconstruction of Ultra-High-Energy Cosmic Rays using Simulated Air-Shower Profiles

Zhuoyi Wang , Eric Mayotte , Sonja Mayotte , Nathan Woo , Julia Burton-Heibges , Nicolas San Martin , Cailyn Smith This is my paper

Pith reviewed 2026-05-18 22:19 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.IM

keywords ultra-high-energy cosmic raysmass compositiondeep learningair-shower profilesfluorescence detectionconvolutional neural networkshadronic interaction models

0 comments p. Extension

The pith

A convolutional neural network predicts the mass of ultra-high-energy cosmic rays from their full longitudinal air-shower profiles.

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

The paper examines whether a deep-learning model can extract primary particle mass directly from the simulated longitudinal energy-deposit profile of extensive air showers. Current composition estimates for ultra-high-energy cosmic rays rely heavily on the depth of shower maximum and offer limited event-by-event resolution, limiting tests of source models and acceleration mechanisms. The authors train a convolutional network on profiles spanning nuclei from protons to iron nuclei and report low bias together with resolution that improves on simpler machine-learning baselines using only summary parameters. The network maintains performance when tested on an alternate hadronic interaction model and under varied noise levels, while an ablation study indicates that the complete profile carries composition information beyond the standard Gaisser-Hillas fit.

Core claim

We present the first study of a deep-learning neural-network approach to predict a primary's mass (ln A) directly from the longitudinal energy-deposit profile of simulated extensive air showers. After rescaling, our network achieves a maximum bias better than 0.4 in ln A with a resolution between 1.5 for protons and 1 for iron, corresponding to a proton-iron Merit Factor of 2.19 (AUC = 0.976). The CNN outperforms simpler ML models trained on profile-shape parameters (X_max, E_cal, R, and L) extracted from the same data and shows only mild degradation when cross-predicting on simulations made with the Sibyll-2.3d hadronic interaction model.

What carries the argument

A convolutional neural network that ingests the full longitudinal energy-deposit profile of a simulated air shower and regresses the primary mass ln A.

If this is right

The full longitudinal profile supplies composition-sensitive structure beyond what the Gaisser-Hillas parameterization captures.
Even simple machine-learning models operating on standard profile parameters already surpass several published benchmarks for mass sensitivity.
Performance remains usable when the network is tested on showers generated with a different hadronic interaction model.
The approach continues to function across a wide range of added noise levels representative of detector conditions.

Where Pith is reading between the lines

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

The method could be retrained or fine-tuned on real fluorescence data once sufficient labeled events become available.
Improved mass resolution per event would tighten constraints on the distribution of cosmic-ray sources and their acceleration spectra.
The same network architecture might be extended to incorporate additional observables such as arrival direction or muon content.

Load-bearing premise

The simulated longitudinal profiles generated with CONEX and EPOS-LHC faithfully reproduce the composition-sensitive features present in real ultra-high-energy cosmic ray air showers observed by fluorescence telescopes.

What would settle it

Apply the trained network to real fluorescence-telescope profiles recorded by an observatory and compare the resulting mass distribution against independent composition constraints obtained from other detectors or analysis techniques.

read the original abstract

Knowledge of the mass composition of ultra-high-energy cosmic rays is crucial to understanding their origins; however, current approaches have limited event-by-event resolution. With fluorescence telescope measurements of the longitudinal shower profile, there are opportunities to improve this situation by applying Machine Learning (ML) to leverage more information beyond $X_{max}$ alone. To our knowledge, we present the first study of a deep-learning neural-network approach to predict a primary's mass ($\ln{A}$) directly from the longitudinal energy-deposit profile of simulated extensive air showers. We train and validate our model on simulated showers, generated with CONEX and EPOS-LHC, covering nuclei from $A = 1$ to 61, sampled uniformly in $\ln{A}$. After rescaling, our network achieves a maximum bias better than 0.4 in $\ln{A}$ with a resolution between 1.5 for protons and 1 for iron, corresponding to a proton-iron Merit Factor of 2.19 (AUC = 0.976). We benchmark this against simpler ML models trained on profile-shape parameters ($X_{ max}$, $E_{cal}$, $R$, and $L$) extracted from the same data. We find that even simple models can substantially exceed published benchmarks for combinations of these observables, demonstrating that ML methods applied even to standard profile-shape parameters can significantly improve available mass sensitivity. The CNN outperforms this strong baseline, and this performance is only mildly degraded when cross-predicting on simulations made with the Sibyll-2.3d hadronic interaction model, showing robustness against model choice. The network also maintains its performance across a wide range of noise conditions. An ablation study further demonstrates that the full profile contains composition-sensitive structure not captured by the GH parameterization, while the strong performance of the CNN suggests this information should be resolvable in real events.

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.

Desk Editor's Note private letter to a colleague

The CNN improves on shape-parameter baselines for ln A on these simulations, but the gain rests on untested assumptions about how well the models match real shower profiles.

read the letter

The paper's core result is that a convolutional network trained on the full longitudinal energy deposit profile outperforms even a strong baseline using Xmax plus a few GH shape parameters, reaching a proton-iron merit factor of 2.19 on held-out CONEX+EPOS-LHC events. That is the main new thing: direct use of the unbinned profile rather than derived scalars, and they show the extra structure matters via an ablation. They also run a clean cross-check on Sibyll-2.3d and add realistic noise, which keeps the performance drop modest. Those checks are useful and done properly on the same simulated set. The numbers look internally consistent and the baselines are not straw men. Credit for that. The soft spot is exactly where the stress-test note points: all performance is simulation-only, and the claim that the extra information should be resolvable in real events assumes the hadronic models reproduce the mass-sensitive sub-structure at the level the network exploits. They only test two models; systematic differences in multiplicity or elasticity that affect the electromagnetic profile at 10-20% would move the learned features and could erase the reported edge. The noise and ablation tests do not close that gap. This is a simulation study with good internal controls, not yet a demonstration that the method works on telescope data. Readers working on UHECR composition or ML applications to air-shower profiles will find the comparison and robustness sections worth their time. It is coherent on its own terms and shows clear thinking about the problem, so it deserves a serious referee rather than a desk reject. I would send it out, with the expectation that reviewers will press on the simulation-to-data step.

Referee Report

2 major / 2 minor

Summary. The paper presents the first deep-learning study using a CNN to predict primary mass (ln A) directly from simulated longitudinal energy-deposit profiles of ultra-high-energy cosmic ray air showers. Trained and validated on CONEX+EPOS-LHC simulations spanning A=1 to 61 (uniform in ln A), the network achieves, after rescaling, a maximum bias better than 0.4 in ln A, resolutions of 1.5 (protons) to 1 (iron), a proton-iron merit factor of 2.19 (AUC=0.976), and outperforms a strong baseline using Gaisser-Hillas parameters (X_max, E_cal, R, L). Performance degrades only mildly on cross-prediction with Sibyll-2.3d profiles and remains stable under varied noise; an ablation study indicates additional composition-sensitive structure beyond the GH parameterization.

Significance. If transferable to real fluorescence-telescope data, the approach could meaningfully advance event-by-event mass composition resolution beyond current X_max-limited methods. The work is strengthened by clear quantitative metrics, direct comparison to a strong baseline on identical simulated data, explicit robustness tests against a second hadronic model and added noise, and the demonstration that even simple ML on standard profile parameters already exceeds published benchmarks. These elements provide a solid foundation for the stated prospects.

major comments (2)

[Abstract] Abstract: The forward-looking claim that 'the strong performance of the CNN suggests this information should be resolvable in real events' rests on the untested assumption that composition-sensitive sub-structure in the simulated profiles (beyond X_max, R, L) matches that present in actual air showers. Only two hadronic models are compared; systematic differences in multiplicity, elasticity, or electromagnetic development at the 10-20% level between models and nature could shift the learned features and erase the reported gain over the GH baseline.
[Results (cross-prediction subsection)] Cross-prediction results: While mild degradation is reported when applying the EPOS-LHC-trained network to Sibyll-2.3d profiles, the manuscript does not quantify the profile-level differences (e.g., in longitudinal development or fluctuation statistics) between the two models. This quantification is needed to evaluate whether the CNN is learning robust, model-independent features or model-specific artifacts.

minor comments (2)

[Methods] The rescaling procedure applied to the network output should be described in full (including how the scaling parameters are chosen and whether they are fixed or data-dependent) so that the reported bias and resolution values can be reproduced and compared unambiguously to the baseline.
[Figures] Figure captions and axis labels should explicitly state the units and normalization conventions used for the energy-deposit profiles to improve clarity for readers unfamiliar with CONEX output.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review, positive assessment of the work, and recommendation for minor revision. We address each major comment below and have incorporated revisions to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: The forward-looking claim that 'the strong performance of the CNN suggests this information should be resolvable in real events' rests on the untested assumption that composition-sensitive sub-structure in the simulated profiles (beyond X_max, R, L) matches that present in actual air showers. Only two hadronic models are compared; systematic differences in multiplicity, elasticity, or electromagnetic development at the 10-20% level between models and nature could shift the learned features and erase the reported gain over the GH baseline.

Authors: We agree that the original wording in the abstract was overly forward-looking given the simulation-only nature of the study. We have revised the abstract to remove the specific claim and instead state that the results 'demonstrate the potential of deep learning to extract additional composition information from profiles beyond standard parameterizations, motivating further studies with experimental data.' We have also added a dedicated paragraph in the conclusions section discussing the limitations of hadronic model comparisons and the possibility that unmodeled differences with nature could affect performance. This provides a more balanced presentation while retaining the core findings from the simulations. revision: yes
Referee: [Results (cross-prediction subsection)] Cross-prediction results: While mild degradation is reported when applying the EPOS-LHC-trained network to Sibyll-2.3d profiles, the manuscript does not quantify the profile-level differences (e.g., in longitudinal development or fluctuation statistics) between the two models. This quantification is needed to evaluate whether the CNN is learning robust, model-independent features or model-specific artifacts.

Authors: We thank the referee for highlighting this gap. In the revised manuscript we have added a new figure and accompanying text in the cross-prediction subsection that directly quantifies the differences between EPOS-LHC and Sibyll-2.3d. This includes comparisons of mean longitudinal profiles, X_max distributions, and profile fluctuation widths for proton and iron primaries. The observed differences are modest (a few g cm^{-2} in X_max and comparable in other moments), consistent with known variations between the models. The mild performance degradation of the CNN despite these differences supports that it captures at least partially robust features rather than purely model-specific artifacts. revision: yes

Circularity Check

0 steps flagged

No circularity: performance metrics derived from held-out simulation test set

full rationale

The paper trains a CNN on CONEX+EPOS-LHC simulated longitudinal profiles to predict ln A, then reports bias, resolution, merit factor (2.19), and AUC (0.976) on held-out simulated events from the same generator. These quantities are computed directly from network outputs versus true labels and do not reduce to any fitted parameters, self-citations, or ansatzes by construction. The benchmark against GH-parameter models and the cross-test on Sibyll-2.3d are independent evaluations. The derivation is a standard supervised ML pipeline with no load-bearing self-referential steps.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim depends on the fidelity of hadronic interaction models in the simulations and on the assumption that the network extracts genuine composition information rather than simulation-specific artifacts.

free parameters (2)

Rescaling applied to network output
Post-training adjustment to reduce bias in ln A predictions.
CNN architecture and training hyperparameters
Chosen to optimize performance on the validation set of simulated profiles.

axioms (1)

domain assumption Simulations generated with CONEX and EPOS-LHC (and cross-checked with Sibyll-2.3d) accurately capture the mass-dependent features of real air-shower profiles.
All training, validation, and robustness tests rest on these Monte Carlo models.

pith-pipeline@v0.9.0 · 5897 in / 1463 out tokens · 46208 ms · 2026-05-18T22:19:20.357054+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

we present the first study of a deep-learning neural-network approach to directly predict a primary’s mass (ln A) from the full longitudinal energy-deposit profile
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

merit factor … X_max … N_μ … GH parameterization

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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Reference graph

Works this paper leans on

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Depth of Maximum of Air-Shower Profiles at the Pierre Auger Observatory: Measurements at Energies above 10^17.8 eV

A. Aab, et al., Depth of Maximum of Air-Shower Profiles at the Pierre Auger Observatory: Measurements at Energies above 10 17.8 eV, Phys. Rev. D 90 (12) (2014) 122005. arXiv:1409.4809,doi:10.1103/PhysRevD.90.122005

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T. Pierog, I. Karpenko, J. M. Katzy, E. Yatsenko, K. Werner, Epos lhc: Test of collective hadronization with data measured at the cern large hadron collider, Phys. Rev. C 92 (2015) 034906.doi:10.1103/PhysRevC.92.034906. – 17 –

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work page doi:10.1088/1475-7516/2021/06/007 2021

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Comparison between methods for the determination of the primary cosmic ray mass composition from the longitudinal profile of atmospheric cascades

M. Ambrosio, C. Aramo, C. Donalek, D. D’Urso, A. D. Erlykin, F. Guarino, A. Insoiia, G. Longo, Comparison between methods for the determination of the primary cosmic ray mass composition from the longitudinal profile of atmospheric cascades, Astropart. Phys. 24 (2005) 355–371.arXiv:astro-ph/0507543,doi:10.1016/j.astropartphys.2005.07.008

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S. Andringa, R. Conceicao, M. Pimenta, Mass composition and cross-section from the shape of cosmic ray shower longitudinal profiles, Astropart. Phys. 34 (2011) 360–367. doi:10.1016/j.astropartphys.2010.10.002

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work page doi:10.1103/physrevlett.134.021001 2025

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work page internal anchor Pith review Pith/arXiv arXiv 2007

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First Results of Fast One-dimensional Hybrid Simulation of EAS Using CONEX

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Inferences on Mass Composition and Tests of Hadronic Interactions from 0.3 to 100 EeV using the water-Cherenkov Detectors of the Pierre Auger Observatory

A. Aab, et al., Inferences on mass composition and tests of hadronic interactions from 0.3 to 100 EeV using the water-Cherenkov detectors of the Pierre Auger Observatory, Phys. Rev. D 96 (12) (2017) 122003.arXiv:1710.07249,doi:10.1103/PhysRevD.96.122003

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