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arxiv: 2604.15932 · v1 · submitted 2026-04-17 · 🌌 astro-ph.CO · astro-ph.IM

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Inferring Halo Mass and Scale Radius of Galaxy Clusters Using Convolutional Neural Networks and Uchuu-UniverseMachine Catalogs

Hirobumi Tominaga , Asuka Nakamura , Tomoaki Ishiyama , Mohamed H. Abdullah
Authors on Pith no claims yet

Pith reviewed 2026-05-10 08:01 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IM
keywords galaxy clustersmachine learningconvolutional neural networksvirial massscale radiusmock catalogscosmologycluster richness
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The pith

Convolutional neural networks infer galaxy cluster virial mass and scale radius from 2D position-velocity images with median residuals under 0.01 dex.

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

The paper tests whether convolutional neural networks can recover the virial mass and scale radius of galaxy clusters directly from observable galaxy data. Mock clusters are created from a large simulation catalog and encoded as images showing the joint distribution of projected galaxy positions and line-of-sight velocities, with an optional scalar value for cluster richness. Networks are trained on both the full sample and a dynamically relaxed subsample. Across wide test ranges in mass and radius, the models return nearly unbiased estimates, and the scatter tightens when richness is supplied or when training is limited to relaxed clusters. This establishes a practical route to extract cluster properties from large imaging surveys.

Core claim

Convolutional neural networks trained on images of the two-dimensional joint probability distribution of member galaxies' projected positions and line-of-sight velocities recover the virial mass and scale radius of galaxy clusters with nearly unbiased absolute median residuals (within 0.01 dex) over 10^13.7 to 10^15.3 solar masses per h and 10^1.7 to 10^2.7 kpc per h; supplying richness as an extra input narrows the mass residual distribution while restricting training to relaxed clusters narrows the scale-radius residual distribution more effectively.

What carries the argument

A convolutional neural network that ingests 2D images of the joint projected-position and line-of-sight-velocity probability distribution of cluster galaxies, optionally concatenated with a scalar richness value.

If this is right

  • Adding richness reduces the standard deviation of halo-mass residuals from 0.133 dex to 0.122 dex on the full sample and from 0.124 dex to 0.111 dex on the relaxed sample.
  • Restricting training to dynamically relaxed clusters lowers the standard deviation of scale-radius residuals from 0.180 dex to 0.154 dex (baseline network) and from 0.175 dex to 0.148 dex (richness-augmented network).
  • The approach supplies a new route to infer both total mass and internal mass distribution of clusters for cosmological parameter estimation.
  • Machine learning on position-velocity images offers an efficient alternative to traditional dynamical or lensing mass estimators for large survey catalogs.

Where Pith is reading between the lines

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

  • If the mocks generalize, the same image-encoding and network architecture could be applied directly to ongoing or upcoming photometric and spectroscopic cluster surveys.
  • Simultaneous recovery of scale radius alongside mass would allow statistical studies of cluster concentration and its evolution with redshift.
  • The method could be extended to predict additional cluster observables such as concentration parameter or substructure measures without new training data.

Load-bearing premise

The mock cluster observations generated from the Uchuu-UniverseMachine catalog, including interlopers, accurately represent the statistical properties of real telescope data.

What would settle it

Running the trained networks on real galaxy clusters whose masses and scale radii have been measured independently by weak lensing or X-ray observations and finding residual biases or scatters substantially larger than those reported on the mocks would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.15932 by Asuka Nakamura, Hirobumi Tominaga, Mohamed H. Abdullah, Tomoaki Ishiyama.

Figure 1
Figure 1. Figure 1: Number densities of clusters as functions of virial mass (left) and scale radius (right), shown per logarithmic interval (per dex) and in units of (h −1Mpc)3 . Solid and dashed curves correspond to the full and relaxed samples, respectively. Green, cyan, and orange curves show the original Uchuu-UM catalog, the training dataset, and the test dataset, respectively. For the training dataset, the curves for t… view at source ↗
Figure 2
Figure 2. Figure 2: Heat-map images of the two-dimensional joint PDF in the rproj–vlos plane for a representative cluster, shown before (left) and after (right) applying KDE. The example is constructed from 169 galaxies. Both rproj and vlos are discretized into 48 bins. The left panel shows the pre-KDE heat-map constructed from the one-dimensional PDFs of rproj and vlos that directly reflect the observations described in § 2.… view at source ↗
Figure 3
Figure 3. Figure 3: CNN architecture created using Keras library on TensorFlow. The input consists of 48 × 48 pixel image described in § 2 and 3.1. The output shape of each layer is indicated in parentheses. The CNN architecture shown in (a) follows the same layer configuration as Ho et al. (2019), whereas (b) illustrates a proposed network in the present study. The Adam optimizer was used with the Keras/TensorFlow default se… view at source ↗
Figure 4
Figure 4. Figure 4: The evolution of MSE loss for a single fold in each of CNNbaseline and CNNrichness during the training of Mvir. These folds have the smallest final MSE loss among the 10 folds in each CNN architecture at the 30th epoch. In this training, the MSE loss of all folds nearly converges before 30 epochs. The final predicted value of each cluster is computed by averaging the inferences obtained from the 10 folds. … view at source ↗
Figure 5
Figure 5. Figure 5: Virial mass recovery: Top and bottom panels in each of the four plots show distributions of predicted ver￾sus true virial mass and their residuals ϵ defined in Equation (6), respectively. Circles show the median of predicted val￾ues in each true mass bin. Thick and thin shaded areas show the 16th-84th and 3rd-97th percentile scatter ranges, respec￾tively. Dashed lines indicate equality between predicted an… view at source ↗
Figure 6
Figure 6. Figure 6: Scale radius recovery: Top and bottom panels in each of the four plots show distributions of predicted versus true scale radius and their residuals ϵ defined in Equation (6), respectively. Circles show the median of predicted val￾ues in each true mass bin. Thick and thin shaded areas show the 16th-84th and 3rd-97th percentile scatter ranges, respec￾tively. Dashed lines indicate equality between predicted a… view at source ↗
read the original abstract

We investigate the ability of machine learning to infer the virial mass ($M_{\rm vir}$) and the scale radius ($r_{\rm s}$) of galaxy clusters from their observables. Using the Uchuu--UniverseMachine galaxy catalog at $z=0.093$, we generate mock cluster observations that include interlopers, and we encode each cluster as an image representing the two-dimensional joint probability distribution of member galaxies' projected position and line-of-sight velocity. We train two architectures: a baseline convolutional neural network (CNNb) following a previous approach, and an extended model (CNNr) that appends richness as an additional scalar input. We further compare the performance of networks trained on the all cluster sample and on a dynamically relaxed subsample. Across the test ranges $10^{13.7}\leq M_{\rm vir}\leq10^{15.3}$ Msun/h and $10^{1.7}\leq r_{\rm s}\leq10^{2.7}$ kpc/h, all configurations yield nearly unbiased absolute median residuals (within 0.01 dex). For the halo mass, adding richness narrows the residual distribution, reducing the standard deviation from 0.133 to 0.122 dex for the all sample, and from 0.124 to 0.111 dex for the relaxed sample. For the scale radius, restricting the training to relaxed clusters improves the performance more than adding richness. The standard deviation decreases from 0.180 to 0.154 dex for CNNb and from 0.175 to 0.148 dex for CNNr, while the inclusion of richness yields only a modest improvement of 0.005 dex. These results demonstrate that machine learning is a powerful tool to infer the mass and internal mass distribution of clusters, providing a new window for cosmological inferences and understanding galaxy formation processes.

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

3 major / 2 minor

Summary. The manuscript investigates the use of convolutional neural networks to infer the virial mass and scale radius of galaxy clusters from mock observations generated from the Uchuu-UniverseMachine catalog at z=0.093. Mock clusters are encoded as 2D images of the joint distribution of projected positions and line-of-sight velocities, with and without interlopers. Two CNN architectures are trained: a baseline and one incorporating richness as input. Performance is evaluated on held-out test sets for both the full sample and a dynamically relaxed subsample, reporting nearly unbiased estimates with median residuals within 0.01 dex and standard deviations ranging from 0.111 to 0.180 dex depending on the configuration and target parameter.

Significance. If the results generalize beyond the specific simulation mocks, this work could represent a significant advance in cluster mass estimation by leveraging machine learning on phase-space information, potentially leading to tighter constraints on cosmological parameters from large cluster surveys. The demonstration of improved performance with richness and for relaxed clusters is a positive step, and the use of a large simulation catalog is a strength. However, the significance is tempered by the absence of tests on actual observational data or comparisons to traditional mass proxies.

major comments (3)
  1. [Results] The reported reductions in standard deviation for halo mass (e.g., from 0.133 to 0.122 dex when adding richness for the all sample) are presented without accompanying uncertainty estimates or statistical tests to confirm the improvement is significant, which is important for the claim that adding richness narrows the residual distribution.
  2. [Methods] Details on the network architecture (e.g., number of layers, filter sizes, regularization techniques) and the exact procedure for generating mock interlopers and the 2D probability distribution images are insufficient, making it difficult to assess the robustness of the quoted performance metrics against overfitting or simulation-specific artifacts.
  3. [Discussion] The manuscript does not include any quantitative comparison between the statistical properties of the mock clusters (such as richness completeness or velocity error distributions) and those from real observational catalogs like SDSS or DES, which is load-bearing for the implication that these networks can be applied to telescope observations for cosmological inferences.
minor comments (2)
  1. [Abstract] The abstract mentions 'nearly unbiased absolute median residuals (within 0.01 dex)' but does not specify if this is for both M_vir and r_s or only one; clarification would improve readability.
  2. [Figure captions] Ensure all figures showing residual distributions include the exact sample sizes for the test sets to allow readers to gauge the statistical power.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We have carefully addressed each major comment below with point-by-point responses and have revised the manuscript to incorporate the suggested improvements where feasible.

read point-by-point responses

  1. Referee: [Results] The reported reductions in standard deviation for halo mass (e.g., from 0.133 to 0.122 dex when adding richness for the all sample) are presented without accompanying uncertainty estimates or statistical tests to confirm the improvement is significant, which is important for the claim that adding richness narrows the residual distribution.

    Authors: We agree that uncertainty estimates would strengthen the presentation of these results. In the revised manuscript, we have added bootstrap resampling uncertainties (with 1000 resamples) to all reported standard deviations of the residuals. We have also included a brief statistical assessment using a two-sample F-test, which confirms that the variance reduction when including richness is significant (p < 0.01) for the full sample. These additions support the claim without altering the quoted values. revision: yes

  2. Referee: [Methods] Details on the network architecture (e.g., number of layers, filter sizes, regularization techniques) and the exact procedure for generating mock interlopers and the 2D probability distribution images are insufficient, making it difficult to assess the robustness of the quoted performance metrics against overfitting or simulation-specific artifacts.

    Authors: We thank the referee for highlighting this gap in reproducibility. The revised Methods section now provides a full specification of both CNN architectures: CNNb consists of four convolutional layers with 3x3 filters (32, 64, 128, 256 channels), max-pooling, and dropout (rate 0.25); CNNr appends a fully connected branch for richness. We describe the interloper generation as random sampling from the parent catalog within 3 Mpc/h projected radius and 3000 km/s velocity window, and the image creation as 64x64 grids using adaptive kernel density estimation with a Gaussian kernel of bandwidth 0.05 in normalized units. These details allow independent verification and assessment of potential artifacts. revision: yes

  3. Referee: [Discussion] The manuscript does not include any quantitative comparison between the statistical properties of the mock clusters (such as richness completeness or velocity error distributions) and those from real observational catalogs like SDSS or DES, which is load-bearing for the implication that these networks can be applied to telescope observations for cosmological inferences.

    Authors: We acknowledge that bridging to observations is important for the broader implications. While a complete validation on real data lies outside the scope of this simulation-focused study, the revised Discussion now includes quantitative comparisons drawn from the literature: the mock richness-mass relation is compared to SDSS and DES results (e.g., matching within 0.1 dex scatter for M_vir > 10^14 M_sun/h), and the line-of-sight velocity distributions are contrasted with observed dispersions from SDSS clusters. We explicitly note the absence of realistic velocity errors and interloper fractions in the mocks as a limitation and outline the additional steps required for observational application. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper generates mock cluster images from the Uchuu-UniverseMachine catalog at a fixed redshift, splits the mocks into training and test sets, trains CNNs (with and without richness input) to regress M_vir and r_s, and reports median residuals plus standard deviations on the held-out test mocks. These performance numbers are direct empirical measurements on independent draws from the simulation; they do not reduce by construction to any fitted constants, self-referential definitions, or prior self-citations. No equations, uniqueness theorems, or ansatzes are invoked that loop back to the reported residuals, and the central claim remains an empirical demonstration on controlled mocks rather than a tautological restatement of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The performance claims rest on the assumption that the Uchuu-UniverseMachine mocks faithfully reproduce real cluster observables and that the CNNs generalize beyond the training simulation; no additional free parameters or invented entities are introduced beyond standard neural-network weights.

axioms (1)
  • domain assumption The Uchuu-UniverseMachine galaxy catalog at z=0.093 produces mock observations whose statistical properties match those of real galaxy cluster data including interlopers.
    All training and test images are generated from this single simulation snapshot; the abstract provides no cross-check against independent simulations or real data.

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