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REVIEW 4 major objections 5 minor 48 references

Prediction of Individual Halo Concentrations Across Cosmic Time Using Neural Networks

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A neural network fed a halo's full mass accretion history predicts its concentration from redshift 0 to 2 with about one-third lower error than analytic models on a separate simulation.

desk verdict A useful, honest ML emulator for individual halo concentrations from MAHs, but the claimed RMSE advantage over Zhao/Giocoli is probably inflated by an uncalibrated comparison to a different concentration estimator. read the letter →

arxiv 2501.16618 v1 pith:6IUNPNRF submitted 2025-01-28 astro-ph.CO

Tianchi Zhang , Tianxiang Mao , Wenxiao Xu , Guan Li This is my paper · ORCID
classification astro-ph.CO
keywords haloconcentrationmassaccretionhistoryneuralnetworkN-bodysimulationdarkmatterhaloesNFWprofilecosmologicalemulator
topics Dark Matter
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

The paper sets out to show that a dark matter halo's concentration—the ratio $c = r_{\rm vir}/r_s$ of its virial radius to its NFW scale radius—can be predicted from its main-branch mass accretion history alone, without fitting the density profile. The authors train a feedforward neural network on roughly 7000 accretion histories from one cosmological N-body simulation and test it on a different simulation with a different initial-condition realization. At $z=0$ the network's root-mean-square error in $\log_{10} c$ is $0.0845$, compared with $0.128$ for the analytic models of Zhao et al. and Giocoli et al., and the advantage persists at $z=0.5$, $1$, and $2$. If this holds, the network is a fast emulator that turns a merger tree into a concentration estimate at any requested redshift.

What carries the argument

The machinery is a five-hidden-layer feedforward neural network with 256, 128, 64, 32, and 16 nodes per layer and 124 input neurons: 123 main-branch progenitor masses spaced along the history and the target redshift encoded as $\log(1/(1+z))$. It is trained on 618,000 input–target pairs covering 103 redshifts per halo, using ReLU activations, the Adam optimizer, and a mean-squared-error loss in $\log c$. The baselines are the Zhao et al. model, which uses only the time when the main progenitor first reaches 4% of its current mass, and the Giocoli et al. model, which adds the half-mass time; the paper attributes the network's advantage to using the entire history instead of one or two summary numbers.

What would settle it

Take haloes with nearly identical main-branch mass accretion histories but different large-scale environments, for instance one member of a close pair versus an isolated halo, and compare their fitted NFW concentrations; if the scatter between matched pairs is substantially larger than the network's RMSE of about 0.08 in $\log_{10} c$, the mapping is incomplete. Alternatively, add a second input encoding local density or tidal field and check whether the validation RMSE drops clearly below 0.0845.

Watch

Extended reading notes

Core claim

The central discovery is that the full main-branch mass accretion history, encoded as 123 snapshot masses plus the target redshift, carries enough information to predict an individual halo's NFW concentration more accurately than the two-parameter analytic models that compress the history into one or two formation times. Trained on about 7000 haloes from SimA and evaluated on 1480 haloes from a different realization SimB, the network achieves RMSE $0.0845$ in $\log_{10} c$ at $z=0$, against $0.1282$ for the Zhao et al. model and $0.1281$ for the Giocoli et al. model, and it remains lower at every tested redshift between $z=2$ and $z=0$. The predictions also interpolate continuously to snapshots not in the training set, indicating that the network learns a smooth mapping from history to concentration.

Load-bearing premise

The result rests on the assumption that a halo's concentration at a given redshift is fully determined by its main-branch mass accretion history, so that any scatter from environment, subhalo mergers, or the details of the NFW fit is small enough to be ignored.

Editorial extensions

If this is right

  • For any halo with a merger tree, the trained network returns a concentration estimate without fitting a density profile, so large-volume simulations can be post-processed rapidly.
  • Predictions are continuous in target redshift, so concentrations can be obtained at a redshift for which no snapshot was stored.
  • The accuracy on a simulation with different particle resolution and initial conditions suggests the learned mapping from mass accretion history to concentration is not overfit to one box.
  • The same architecture can be retrained for other halo definitions or to predict additional structural properties from the same mass accretion history input.

Reading between the lines

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

  • The comparison implies that the full accretion history carries information beyond one or two formation epochs; a natural next test is whether the network's residuals correlate with environment or large-scale density, which would reveal what the mass accretion history alone misses.
  • If the mapping is as deterministic as the RMSE suggests, most of the scatter in the concentration–mass relation is driven by diversity in accretion histories rather than independent assembly noise; this could be checked by feeding the same network a smoothed or noise-corrupted history and measuring how much the error degrades.
  • Because the paper fixes one set of cosmological parameters, the method could be extended to a grid of cosmologies to turn the network into a tool for cosmological inference from halo structure.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper trains a fully connected neural network to predict the NFW concentration c(z) of individual dark matter haloes from their main-branch mass accretion history (MAH) and a target redshift. The network is trained on 7000 MAHs from a 1024^3 N-body simulation (SimA), with 123 snapshot masses plus the target redshift as inputs, and is tested on 1480 MAHs from an independent 512^3 simulation (SimB). The headline result is that the network achieves RMSE 0.0845 at z=0 on SimB, compared with 0.1282 for the Zhao et al. (2009) model and 0.1281 for the Giocoli et al. (2012) model, and that the network's RMSE is lower at every tested redshift between z=2 and z=0. The paper also shows that the model reproduces the mean c-M relation and that it interpolates between training snapshots.

Significance. If the headline comparisons hold under a properly calibrated and causally consistent setup, the paper would provide a fast and accurate emulator for individual halo concentrations from merger-tree information, which would be practically useful for generating mock catalogs and for studies where per-halo concentrations are needed. The use of a held-out simulation with a different initial realization and a different mass resolution is a genuine strength, as is the explicit comparison against two established analytic models. However, the significance is moderated by two concerns that directly affect the central quantitative claim: the comparison with the analytic models may mix a systematic concentration-definition offset with true predictive scatter, and the network may be using information from epochs later than the target redshift. These issues are addressable but require additional experiments.

major comments (4)
  1. [Section 3, Figure 4 (comparison with Eqs. 6 and 7)] The comparison between the neural network and the Zhao et al. and Giocoli et al. models is not apples-to-apples. The network is trained and evaluated on concentrations measured by the authors' own NFW least-squares fit (Section 2.2, Eq. 3, with 20 bins between 0.05 rvir and rvir), whereas Eqs. (6) and (7) are universal formulas calibrated against concentration measurements that may use a different halo definition, fitting range, or fitting procedure. Because the network's training labels come from the same pipeline it is asked to predict, it can absorb any systematic offset of that pipeline, while the analytic models cannot; the reported RMSE difference then conflates learning a specific concentration estimator with predicting halo concentration better. The paper never reports the mean residual (bias) of the Zhao/Giocoli predictions, only RMSE, so the systematic component cannot be separated from scatter. I ask the authors to recalibrate the baseline formulas to the same concentration definition on SimA (e.g., by fitting a constant offset or refitting their parameters) and to report bias and scatter separately, or otherwise demonstrate that the RMSE advantage survives an estimator-calibration correction.
  2. [Section 2.3, Figure 1 and Section 3] The input layer contains the full 123-snapshot MAH from z=4.6 to z=0 for every target redshift in the range [0,2]. For a target redshift z=2, this means the network sees the halo masses at all later snapshots down to z=0, i.e., information from epochs after the time at which the concentration is being predicted. This look-ahead gives the network information that is not available in a physical prediction at that epoch and that is also not available to the Zhao/Giocoli formation-time variables t0.04 and t0.5, making the comparison unfair and the wording "predict concentration at a given redshift" misleading. The authors should either truncate the MAH input at the target redshift and retrain/retest, or explicitly state that the model is an emulator that uses the full simulation output to z=0 and justify why the comparison with the analytic models remains informative. The RMSE after truncation is a necessary check for the paper's central claim.
  3. [Section 2.3 (Train/Validation split)] The description of the train/validation split is ambiguous and potentially leaky. The text says that after shuffling the MAHs, the first 618,000 datasets form the TrainDataset and the remaining 103,000 form the ValidationDataset. Because each MAH contributes 103 datasets (one per target redshift), a random row-wise shuffle can place the same halo in both the training and validation sets at different redshifts. This would make the validation RMSE of 0.0868 optimistic and would affect model selection. The authors should split by halo (e.g., train on 90% of the MAHs and validate on the remaining 10%) before expanding into per-redshift datasets. This does not invalidate the SimB test, but it is important for the internal validation and for the reported generalization statement.
  4. [Section 3, Figure 5] The RMSE values at z=0 (0.0845 vs. 0.1282 and 0.1281) are quoted as if the difference is automatically significant, but no uncertainties or significance tests are provided. The error bars in Figure 5 are described as the 16th and 84th percentiles, but the resampling unit is not stated (haloes? bootstrap replicates? scatter across mass bins?). The authors should provide bootstrap confidence intervals over haloes for the RMSE at each redshift and, ideally, a paired test of the RMSE difference, to support the word "significantly" used in the abstract and conclusions.
minor comments (5)
  1. [Section 2.3] The sentence "The neural network model is trained 100 times with a learning rate of 0.001" is ambiguous: it likely means 100 epochs, not 100 independent training runs. Please clarify.
  2. [Section 3, Figure 2] The residual panel says the median error of the model is compared with the median error from the simulation; the text should specify that the residual is the ratio of predicted to simulated median concentrations, as the axis labels suggest.
  3. [Section 4 and Data Availability] The paper states that simulation data will be shared on reasonable request, but no mention is made of releasing the trained network or the code. Providing the trained model would make the claimed emulator directly usable by the community.
  4. [Throughout] There are several typographical and grammatical issues, including "the our model", "universe is age", "thecsim=cpred", and "The scatter points are distributed around the diagonal but exhibit significant spread". These should be corrected in a careful copyedit.
  5. [Section 2.2] The sample selection is restricted to main branches of z=0 haloes with Nvir>7000 (SimA) or Nvir>2000 (SimB), so the high-redshift predictions are for progenitors of massive z=0 haloes rather than for a representative population of haloes at those redshifts. This limitation should be stated explicitly when the model is described as predicting concentrations "at a given redshift".

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the model is trained on SimA labels, validated and tested on a separate SimB sample, and compared against external analytic formulas applied to the same test set.

full rationale

The paper's derivation chain is not circular. Concentration labels are obtained by a fixed NFW least-squares fit (Eq. 3 with c = rvir/rs, Eq. 4) over 20 logarithmic bins, and the network inputs are 123 main-branch masses plus the target redshift; no target concentration is fed into the network as an input. The model is trained on 618,000 SimA samples, selected by validation on 103,000 held-out SimA samples, and then evaluated once on the 152,440 TestDataset samples drawn from a different initial-condition realization (SimB), so the quoted RMSE values (0.0868 validation, 0.0845 test at z = 0) are genuine out-of-sample generalization numbers. The baselines (Zhao et al., Eq. 6, and Giocoli et al., Eq. 7) are external analytic formulas applied to the same test MAHs without fitting their parameters here; no network output is used to build those baselines, and no baseline parameter is fitted to the test set. The only caveat is benchmark fairness rather than circularity: the network is trained on the same concentration estimator it is asked to reproduce, whereas Zhao/Giocoli were calibrated on possibly different profile-fitting conventions, so part of the RMSE gap may reflect estimator-specific bias instead of a better physical c-MAH mapping. The self-citations (Zhang et al. for optimal softening length and for CCVT pre-initial conditions) are numerical setup choices, not load-bearing evidence for the predictive claim. The paper also candidly states limitations (fixed cosmology, narrow mass range), which are scope restrictions rather than hidden circular assumptions. No step in the claimed derivation reduces by construction to its own input.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical entities; its free parameters are the network weights and hand-chosen analysis thresholds. The main assumptions are the NFW profile model, the sufficiency of the HBT+ main-branch MAH, and transfer within the same simulation family.

free parameters (3)
  • Neural network weights and biases = not disclosed (architecture implies about 44k trainable parameters)
    Trained on 618,000 SimA examples; the final fitted weights define the model and are not released.
  • Network architecture and training hyperparameters = 5 hidden layers (256, 128, 64, 32, 16), ReLU, Adam, LR 0.001, batch size 256, 100 epochs
    Chosen by hand without ablation; reported RMSE depends on these choices.
  • Halo and profile-fit selection thresholds = Nvir > 7000 (SimA), Nvir > 2000 (SimB), > 500 particles for fits; 20 bins from 0.05 rvir to rvir
    These choices set the mass range and the ground-truth c values; the authors acknowledge the mass range is narrow.
assumptions (3)
  • domain assumption Dark matter halo density profiles follow the NFW form (Eq. 3) over the fitted radial range at all epochs studied.
    The target concentration is obtained by NFW least-squares fits; any profile deviations propagate into the labels the network learns.
  • domain assumption The main-branch MAH from FOF plus HBT+ merger trees contains all information needed to predict concentration; inputs include the full MAH to z = 0 even when predicting at earlier z.
    Figure 1 feeds the full MAH (z = 4.6 to z = 0) for every target z, so the network is not forced to use only causal past information; the sufficiency of MAH is assumed.
  • domain assumption The relation learned in SimA transfers to SimB because both use GADGET-2, identical cosmology, and identical box size, differing only in resolution and random seed.
    This is the basis for the headline generalization test; no cross-code or cross-cosmology check is performed.

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Cite this review

Pith. "Pith review of Prediction of Individual Halo Concentrations Across Cosmic Time Using Neural Networks." pith.science (2026). https://pith.science/paper/6IUNPNRF

@misc{pith2026250116618,
  author       = {Pith},
  title        = {Pith review of: Prediction of Individual Halo Concentrations Across Cosmic Time Using Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6IUNPNRF}},
  note         = {Machine review of arXiv:2501.16618}
}
read the original abstract

The concentration of dark matter haloes is closely linked to their mass accretion history. We utilize the halo mass accretion histories from large cosmological N-body simulations as inputs for our neural networks, which we train to predict the concentration of individual haloes at a given redshift. The trained model performs effectively in other cosmological simulations, achieving the root mean square error between the actual and predicted concentrations that significantly lower than that of the model by Zhao et al. and Giocoli et al. at any redshift. This model serves as a valuable tool for rapidly predicting halo concentrations at specified redshifts in large cosmological simulations.

Figures

Figures reproduced from arXiv: 2501.16618 by the authors.

Figure 1
Figure 1. The schematic of our neural network is presented here. Red squares represent the input layer neurons, which take the MAH and the desired z as input parameters. The blue circles indicate the neurons in the hidden layers; there are five layers in total, with the number of neurons in each layer denoted by Nnode. The red circle represents the single neuron in the output layer, which outputs the halo concentration at z. … view at source ↗
Figure 2
Figure 2. The halo concentration–mass relation at z = 0 is derived from fitting the NFW profile (black) and utilizing a neural network model (red). The scatter points in the background indicate individual haloes, whereas the larger points connected by lines represent the median values. Error bars denote the 16th and 84th percentiles. The small panel in the upper right displays the residuals between the predicted results of ou… view at source ↗
Figure 3
Figure 3. A comparison of the measured concentrations with those predicted by our model in SimA and SimB at z = 0. Blue points represent the ValidationDataset from SimA, while red points denote the TestDataset from SimB. The contours enclose 10%, 50%, and 90% of the haloes, providing a visual representation of concentration distribution. The solid black lines indicate the csim=cpred in each panel, highlighting the accuracy of… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: The median relationship between the RMSE of the actual and predicted concentrations as a function of redshift. Black, blue, and red lines show results of neural network, Zhao, and Giocoli models, respectively. Error bars indicate the 16th and 84th percentiles. The cons…
Figure 6
Figure 6. Figure 6: Similarly to [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 21 canonical work pages

  1. [1]

    Dark matter and cosmic structure

    Frenk, C.S.; White, S.D.M. Dark matter and cosmic structure. Ann. Der Phys. 2012, 524, 507–534. https://doi.org/10.1002/andp. 201200212

    doi:10.1002/andp 2012

  2. [2]

    Large-scale dark matter simulations

    Angulo, R.E.; Hahn, O. Large-scale dark matter simulations. Living Rev. Comput. Astrophys. 2022, 8, 1. https://doi.org/10.1007/ s41115-021-00013-z

    work page 2022

  3. [3]

    Dark matter halo concentrations: a short review

    Okoli, C. Dark matter halo concentrations: A short review. arXiv 2017, arXiv:1711.05277. arXiv:astro-ph.CO/1711.05277

    work page Pith review arXiv 2017

  4. [4]

    Is the dark-matter halo spin a predictor of galaxy spin and size? Mon

    Jiang, F.; Dekel, A.; Kneller, O.; Lapiner, S.; Ceverino, D.; Primack, J.R.; Faber, S.M.; Macciò, A.V .; Dutton, A.A.; Genel, S.; et al. Is the dark-matter halo spin a predictor of galaxy spin and size? Mon. Not. R. Astron. Soc. 2019, 488, 4801–4815. https://doi.org/10.1093/mnras/stz1952

    doi:10.1093/mnras/stz1952 2019

  5. [5]

    The formation of galactic discs

    Mo, H.J.; Mao, S.; White, S.D.M. The formation of galactic discs. Mon. Not. R. Astron. Soc. 1998, 295, 319–336. https: //doi.org/10.1046/j.1365-8711.1998.01227.x

    work page arXiv 1998

  6. [6]

    The galaxy size to halo spin relation of disc galaxies in cosmological hydrodynamical simulations

    Yang, H.; Gao, L.; Frenk, C.S.; Grand, R.J.J.; Guo, Q.; Liao, S.; Shao, S. The galaxy size to halo spin relation of disc galaxies in cosmological hydrodynamical simulations. Mon. Not. R. Astron. Soc. 2023, 518, 5253–5259. https://doi.org/10.1093/mnras/ stac3335

    doi:10.1093/mnras/ 2023

  7. [7]

    The unusually high dark matter concentration of the galaxy group NGC 1600

    Runge, J.; Walker, S.A.; Mirakhor, M.S. The unusually high dark matter concentration of the galaxy group NGC 1600. Mon. Not. R. Astron. Soc. 2022, 509, 2647–2653. https://doi.org/10.1093/mnras/stab3139

    work page doi:10.1093/mnras/stab3139 2022

  8. [8]

    An unexpected high concentration for the dark substructure in the gravitational lens SDSSJ0946+1006

    Minor, Q.; Gad-Nasr, S.; Kaplinghat, M.; Vegetti, S. An unexpected high concentration for the dark substructure in the gravitational lens SDSSJ0946+1006. Mon. Not. R. Astron. Soc. 2021, 507, 1662–1683. https://doi.org/10.1093/mnras/stab2247. Universe 2025, 1, 0 11 of 12

    doi:10.1093/mnras/stab2247 2021

Show all 48 references
  1. [9]

    The overconcentrated dark halo in the strong lens SDSS J0946+1006 is a subhalo: Evidence for self interacting dark matter? arXiv 2024, arXiv:astro-ph.CO/2411.08565

    Enzi, W.J.R.; Krawczyk, C.M.; Ballard, D.J.; Collett, T.E. The overconcentrated dark halo in the strong lens SDSS J0946+1006 is a subhalo: Evidence for self interacting dark matter? arXiv 2024, arXiv:astro-ph.CO/2411.08565

    2024 arXiv

  2. [10]

    Concentration, spin and shape of dark matter haloes as a function of the cosmological model: WMAP1, WMAP3 and WMAP5 results

    Macciò, A.V .; Dutton, A.A.; van den Bosch, F.C. Concentration, spin and shape of dark matter haloes as a function of the cosmological model: WMAP1, WMAP3 and WMAP5 results. Mon. Not. R. Astron. Soc. 2008, 391, 1940–1954. https: //doi.org/10.1111/j.1365-2966.2008.14029.x

    2008

  3. [11]

    The mass-concentration- redshift relation of cold dark matter haloes

    Ludlow, A.D.; Navarro, J.F.; Angulo, R.E.; Boylan-Kolchin, M.; Springel, V .; Frenk, C.; White, S.D.M. The mass-concentration- redshift relation of cold dark matter haloes. Mon. Not. R. Astron. Soc. 2014, 441, 378–388. https://doi.org/10.1093/mnras/stu483

    2014 doi

  4. [12]

    The statistics ofΛ CDM halo concentrations

    Neto, A.F.; Gao, L.; Bett, P .; Cole, S.; Navarro, J.F.; Frenk, C.S.; White, S.D.M.; Springel, V .; Jenkins, A. The statistics ofΛ CDM halo concentrations. Mon. Not. R. Astron. Soc. 2007, 381, 1450–1462. https://doi.org/10.1111/j.1365-2966.2007.12381.x

    2007

  5. [13]

    The redshift dependence of the structure of massive Λ cold dark matter haloes

    Gao, L.; Navarro, J.F.; Cole, S.; Frenk, C.S.; White, S.D.M.; Springel, V .; Jenkins, A.; Neto, A.F. The redshift dependence of the structure of massive Λ cold dark matter haloes. Mon. Not. R. Astron. Soc. 2008, 387, 536–544. https://doi.org/10.1111/j.1365-296 6.2008.13277.x

    2008 arXiv

  6. [14]

    Dark Matter Halos in the Standard Cosmological Model: Results from the Bolshoi Simulation

    Klypin, A.A.; Trujillo-Gomez, S.; Primack, J. Dark Matter Halos in the Standard Cosmological Model: Results from the Bolshoi Simulation. Astrophys. J. 2011, 740, 102. https://doi.org/10.1088/0004-637X/740/2/102

    2011 doi

  7. [15]

    Dark Matter Halo Profiles of Massive Clusters: Theory versus Observations

    Bhattacharya, S.; Habib, S.; Heitmann, K.; Vikhlinin, A. Dark Matter Halo Profiles of Massive Clusters: Theory versus Observations. Astrophys. J. 2013, 766, 32. https://doi.org/10.1088/0004-637X/766/1/32

    2013 doi

  8. [16]

    Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles

    Dutton, A.A.; Macciò, A.V . Cold dark matter haloes in the Planck era: evolution of structural parameters for Einasto and NFW profiles. Mon. Not. R. Astron. Soc. 2014, 441, 3359–3374. https://doi.org/10.1093/mnras/stu742

    2014 doi

  9. [17]

    Halo Profiles and the Concentration-Mass Relation for a ΛCDM Universe

    Child, H.L.; Habib, S.; Heitmann, K.; Frontiere, N.; Finkel, H.; Pope, A.; Morozov, V . Halo Profiles and the Concentration-Mass Relation for a ΛCDM Universe. Astrophys. J. 2018, 859, 55. https://doi.org/10.3847/1538-4357/aabf95

    2018 doi

  10. [18]

    An Accurate Physical Model for Halo Concentrations

    Diemer, B.; Joyce, M. An Accurate Physical Model for Halo Concentrations. Astrophys. J. 2019, 871, 168. https://doi.org/10.3847/ 1538-4357/aafad6

    2019

  11. [19]

    The Uchuu simulations: Data Release 1 and dark matter halo concentrations

    Ishiyama, T.; Prada, F.; Klypin, A.A.; Sinha, M.; Metcalf, R.B.; Jullo, E.; Altieri, B.; Cora, S.A.; Croton, D.; de la Torre, S.; et al. The Uchuu simulations: Data Release 1 and dark matter halo concentrations. Mon. Not. R. Astron. Soc. 2021, 506, 4210–4231. https://doi.org/1...

    2021 doi

  12. [20]

    Profiles of dark haloes: evolution, scatter and environment

    Bullock, J.S.; Kolatt, T.S.; Sigad, Y.; Somerville, R.S.; Kravtsov, A.V .; Klypin, A.A.; Primack, J.R.; Dekel, A. Profiles of dark haloes: evolution, scatter and environment. Mon. Not. R. Astron. Soc. 2001, 321, 559–575. https://doi.org/10.1046/j.1365-8711.2001.040 68.x

    2001

  13. [21]

    Concentrations of Dark Halos from Their Assembly Histories

    Wechsler, R.H.; Bullock, J.S.; Primack, J.R.; Kravtsov, A.V .; Dekel, A. Concentrations of Dark Halos from Their Assembly Histories. Astrophys. J. 2002, 568, 52–70. https://doi.org/10.1086/338765

    2002 doi

  14. [22]

    Mass and Redshift Dependence of Dark Halo Structure.Astrophys

    Zhao, D.H.; Jing, Y.P .; Mo, H.J.; Börner, G. Mass and Redshift Dependence of Dark Halo Structure.Astrophys. J. 2003, 597, L9–L12. https://doi.org/10.1086/379734

    2003 doi

  15. [23]

    Accurate Universal Models for the Mass Accretion Histories and Concentrations of Dark Matter Halos

    Zhao, D.H.; Jing, Y.P .; Mo, H.J.; Börner, G. Accurate Universal Models for the Mass Accretion Histories and Concentrations of Dark Matter Halos. Astrophys. J. 2009, 707, 354–369. https://doi.org/10.1088/0004-637X/707/1/354

    2009 doi

  16. [24]

    Formation times, mass growth histories and concentrations of dark matter haloes

    Giocoli, C.; Tormen, G.; Sheth, R.K. Formation times, mass growth histories and concentrations of dark matter haloes. Mon. Not. R. Astron. Soc. 2012, 422, 185–198. https://doi.org/10.1111/j.1365-2966.2012.20594.x

    2012

  17. [25]

    Surveying the reach and maturity of machine learning and artificial intelligence in astronomy

    Fluke, C.J.; Jacobs, C. Surveying the reach and maturity of machine learning and artificial intelligence in astronomy. WIREs Data Min. Knowl. Discov. 2020, 10, e1349. https://doi.org/10.1002/widm.1349

    2020 doi

  18. [26]

    Astronomical big data processing using machine learning: A comprehensive review

    Sen, S.; Agarwal, S.; Chakraborty, P .; Singh, K.P . Astronomical big data processing using machine learning: A comprehensive review. Exp. Astron. 2022, 53, 1–43. https://doi.org/10.1007/s10686-021-09827-4

    2022 doi

  19. [27]

    Classifying the large-scale structure of the universe with deep neural networks

    Aragon-Calvo, M.A. Classifying the large-scale structure of the universe with deep neural networks. Mon. Not. R. Astron. Soc. 2019, 484, 5771–5784. https://doi.org/10.1093/mnras/stz393

    2019 doi

  20. [28]

    HIKER: a halo-finding method based on kernel-shift algorithm

    Sun, S.; Liao, S.; Guo, Q.; Wang, Q.; Gao, L. HIKER: a halo-finding method based on kernel-shift algorithm. arXiv 2019, arXiv:1909.13301, arXiv:astro-ph.CO/1909.13301

    2019 arXiv

  21. [29]

    HInet: Generating Neutral Hydrogen from Dark Matter with Neural Networks

    Wadekar, D.; Villaescusa-Navarro, F.; Ho, S.; Perreault-Levasseur, L. HInet: Generating Neutral Hydrogen from Dark Matter with Neural Networks. Astrophys. J. 2021, 916, 42. https://doi.org/10.3847/1538-4357/ac033a

    2021 doi

  22. [30]

    Baryon acoustic oscillations reconstruction using convolutional neural networks

    Mao, T.X.; Wang, J.; Li, B.; Cai, Y.C.; Falck, B.; Neyrinck, M.; Szalay, A. Baryon acoustic oscillations reconstruction using convolutional neural networks. Mon. Not. R. Astron. Soc. 2021, 501, 1499–1510. https://doi.org/10.1093/mnras/staa3741

    2021 doi

  23. [31]

    First Light and Reionisation Epoch Simulations (FLARES) XVII: Learning the galaxy-halo connection at high redshifts

    Maltz, M.G.A.; Thomas, P .A.; Lovell, C.C.; Roper, W.J.; Vijayan, A.P .; Irodotou, D.; Liao, S.; Seeyave, L.T.C.; Wilkins, S.M. First Light and Reionisation Epoch Simulations (FLARES) XVII: Learning the galaxy-halo connection at high redshifts. arXiv 2024, arXiv:2410.24082. ht...

    2024 doi arXiv

  24. [32]

    The cosmological simulation code GADGET-2.Mon

    Springel, V . The cosmological simulation code GADGET-2.Mon. Not. R. Astron. Soc. 2005, 364, 1105–1134. https://doi.org/10.1 111/j.1365-2966.2005.09655.x

    2005

  25. [33]

    Baryonic Features in the Matter Transfer Function

    Eisenstein, D.J.; Hu, W. Baryonic Features in the Matter Transfer Function. Astrophys. J. 1998, 496, 605–614. https://doi.org/10.1 086/305424. Universe 2025, 1, 0 12 of 12

    1998

  26. [34]

    An alternative method to generate pre-initial conditions for cosmological N-body simulations

    Liao, S. An alternative method to generate pre-initial conditions for cosmological N-body simulations. Mon. Not. R. Astron. Soc. 2018, 481, 3750–3760. https://doi.org/10.1093/mnras/sty2523

    2018 doi

  27. [35]

    Numerical convergence of pre-initial conditions on dark matter halo properties

    Zhang, T.; Liao, S.; Li, M.; Zhang, J. Numerical convergence of pre-initial conditions on dark matter halo properties. Mon. Not. R. Astron. Soc. 2021, 507, 6161–6176. https://doi.org/10.1093/mnras/stab2543

    2021 doi

  28. [36]

    The optimal gravitational softening length for cosmological N-body simulations

    Zhang, T.; Liao, S.; Li, M.; Gao, L. The optimal gravitational softening length for cosmological N-body simulations. Mon. Not. R. Astron. Soc. 2019, 487, 1227–1232. https://doi.org/10.1093/mnras/stz1370

    2019 doi

  29. [37]

    The evolution of large-scale structure in a universe dominated by cold dark matter

    Davis, M.; Efstathiou, G.; Frenk, C.S.; White, S.D.M. The evolution of large-scale structure in a universe dominated by cold dark matter. Astrophys. J. 1985, 292, 371–394. https://doi.org/10.1086/163168

    1985 doi

  30. [38]

    HBT+: an improved code for finding subhaloes and building merger trees in cosmological simulations

    Han, J.; Cole, S.; Frenk, C.S.; Benitez-Llambay, A.; Helly, J. HBT+: an improved code for finding subhaloes and building merger trees in cosmological simulations. Mon. Not. R. Astron. Soc. 2018, 474, 604–617. https://doi.org/10.1093/mnras/stx2792

    2018 doi

  31. [39]

    Statistical Properties of X-Ray Clusters: Analytic and Numerical Comparisons

    Bryan, G.L.; Norman, M.L. Statistical Properties of X-Ray Clusters: Analytic and Numerical Comparisons. Astrophys. J. 1998, 495, 80–99. https://doi.org/10.1086/305262

    1998 doi

  32. [40]

    The Structure of Cold Dark Matter Halos

    Navarro, J.F.; Frenk, C.S.; White, S.D.M. The Structure of Cold Dark Matter Halos. Astrophys. J. 1996, 462, 563. https: //doi.org/10.1086/177173

    1996 doi

  33. [41]

    A Universal Density Profile from Hierarchical Clustering

    Navarro, J.F.; Frenk, C.S.; White, S.D.M. A Universal Density Profile from Hierarchical Clustering. Astrophys. J. 1997, 490, 493–508. https://doi.org/10.1086/304888

    1997 doi

  34. [42]

    Pytorch: An imperative style, high-performance deep learning library

    Paszke, A.; Gross, S.; Massa, F.; Lerer, A.; Bradbury, J.; Chanan, G.; Killeen, T.; Lin, Z.; Gimelshein, N.; Antiga, L.; et al. Pytorch: An imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst. 2019, 32

    2019

  35. [43]

    Rectified linear units improve restricted boltzmann machines

    Nair, V .; Hinton, G.E. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th International Conference on Machine Learning (ICML-10), Haifa, Israel, 21–24 June 2010; pp. 807–814

    2010

  36. [44]

    Learning representations by back-propagating errors

    Rumelhart, D.E.; Hinton, G.E.; Williams, R.J. Learning representations by back-propagating errors. Nature 1986, 323, 533–536

    1986

  37. [45]

    Adam: A method for stochastic optimization

    Kingma, D.P . Adam: A method for stochastic optimization. arXiv 2014, arXiv:1412.6980

    2014 arXiv

  38. [46]

    Universal structure of dark matter haloes over a mass range of 20 orders of magnitude

    Wang, J.; Bose, S.; Frenk, C.S.; Gao, L.; Jenkins, A.; Springel, V .; White, S.D.M. Universal structure of dark matter haloes over a mass range of 20 orders of magnitude. Nature 2020, 585, 39–42. https://doi.org/10.1038/s41586-020-2642-9

    2020 doi

  39. [47]

    The abundance of dark matter haloes down to Earth mass

    Zheng, H.; Bose, S.; Frenk, C.S.; Gao, L.; Jenkins, A.; Liao, S.; Liu, Y.; Wang, J. The abundance of dark matter haloes down to Earth mass. Mon. Not. R. Astron. Soc. 2024, 528, 7300–7309. https://doi.org/10.1093/mnras/stae289

    2024 doi

  40. [48]

    The mass accretion history of dark matter haloes down to Earth mass

    Liu, Y.; Gao, L.; Bose, S.; Frenk, C.S.; Jenkins, A.; Springel, V .; Wang, J.; White, S.D.M.; Zheng, H. The mass accretion history of dark matter haloes down to Earth mass. Mon. Not. R. Astron. Soc. 2024, 527, 11740–11750. https://doi.org/10.1093/mnras/stae003. Disclaimer/Publ...

    2024 doi

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