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arxiv: 2511.03636 · v2 · submitted 2025-11-05 · 🌌 astro-ph.CO · cs.LG· physics.comp-ph

Quantifying Weighted Morphological Content of Large-Scale Structures via Simulation-Based Inference

M. H. Jalali Kanafi , S. M. S. Movahed This is my paper

Pith reviewed 2026-05-18 01:07 UTC · model grok-4.3

classification 🌌 astro-ph.CO cs.LGphysics.comp-ph
keywords large-scale structureMinkowski functionalsconditional moments of derivativessimulation-based inferencecosmological parametershalo power spectrumredshift spacemorphological statistics
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The pith

Weighted morphological statistics from large-scale structures yield up to 45 percent tighter constraints on sigma_8 and Omega_m than the halo power spectrum in mass-selected samples.

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

This paper compares higher-order morphological summary statistics, specifically Minkowski Functionals and Conditional Moments of Derivatives, against the standard redshift-space power spectrum for extracting cosmological information from simulated halo catalogs. Using simulation-based inference with neural posterior estimation, it shows that the weighted morphological measures capture nonlinear and anisotropic features more effectively than the power spectrum at matched scales. The joint estimator improves constraints over Minkowski Functionals alone by roughly 27 percent for sigma_8, and in mass-selected halo samples it outperforms the power spectrum by 45 percent for sigma_8 and 43 percent for Omega_m. This approach matters because it offers a way to extract more information from the same data volume without relying on perturbative models valid only at large scales.

Core claim

The central claim is that at matched effective scales of k_max approximately 0.16 h per Mpc, the combination of Minkowski Functionals and Conditional Moments of Derivatives outperforms the power spectrum multipoles by 45 percent plus or minus 20 percent for sigma_8 and 43 percent plus or minus 10 percent for Omega_m in the mass-selected halo configuration at redshift 0.5, as determined through simulation-based forecasting with neural posterior estimation on Big Sobol Sequence halo catalogs.

What carries the argument

The Conditional Moments of Derivatives (CMD), a class of weighted morphological measures that quantify the moments of derivatives of the smoothed density field conditioned on its value, providing sensitivity to anisotropic and nonlinear features in redshift space.

Load-bearing premise

The neural posterior estimation framework accurately recovers unbiased posteriors for the chosen summary statistics without architecture-dependent biases or insufficient training coverage of the parameter space.

What would settle it

Applying the same neural posterior estimation pipeline to an independent set of mock halo catalogs or to actual survey data and finding that the morphological estimator no longer produces tighter constraints or yields parameter values inconsistent with the power spectrum results.

Figures

Figures reproduced from arXiv: 2511.03636 by M. H. Jalali Kanafi, S. M. S. Movahed.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic overview of the simulation-based forecasts pipeline used in this work. Starting from broad priors on [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Distribution of halo number densities across BSQ sim [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic representation of the neural posterior es [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Normalized rank distributions for the five ΛCDM parameters [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The standard deviation of estimated [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Forecast uncertainties, std( [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of the cosmological constraints ob [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: In the next step, we go beyond the single fiducial cosmology and perform forecasts across a continuous range of parameter values, aiming to assess how the constraining capability of different summary statistics [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Forecast uncertainties of Ω [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Forecast precision dependence on the smoothing scale for two morphological descriptors: [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
read the original abstract

We perform a simulation-based forecasting analysis to compare the cosmological constraining power of higher-order summary statistics of the large-scale structure, the Minkowski Functionals (MFs) and a class weighted morphological measure known as the Conditional Moments of Derivatives (CMD), with that of the redshift-space halo power spectrum multipoles (PS), with a particular focus on their sensitivity to nonlinear and anisotropic features in redshift space. Our analysis relies on halo catalogs from the Big Sobol Sequence simulations at redshift $z=0.5$, employing a likelihood-free inference framework implemented via neural posterior estimation. At the fiducial Quijote cosmology and for a Gaussian smoothing scale of $R=15\,h^{-1}\mathrm{Mpc}$, CMD provide systematically tighter constraints than MFs. Combining MFs and CMD into a joint estimator improves the precision by $27\%^{+9\%}_{-5\%}$ for $\sigma_8$ and $26\%^{+7\%}_{-5\%}$ for $\Omega_{\mathrm{m}}$ relative to MFs alone, highlighting the complementary anisotropy-sensitive information captured by the CMD in contrast to the scalar morphological content encapsulated by the MFs. We compare the combined statistic MFs+CMD with the PS at matched effective scales ($k_{\max}\simeq0.16\,h\,\mathrm{Mpc^{-1}}$) under three halo-selection conditions: all halos, fixed number density, and mass-selected ($M>3\times10^{13}\,h^{-1}M_\odot$). In the mass-selected configuration, the (weighted) morphological estimator outperforms the power spectrum by $45\%^{+20\%}_{-9\%}$ for $\sigma_8$ and $43\%^{+10\%}_{-7\%}$ for $\Omega_{\mathrm{m}}$. We also extend the simulation-based forecast analysis across a continuous range of cosmological parameters and multiple smoothing scales for morphological measures.

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

1 major / 2 minor

Summary. The manuscript performs a simulation-based forecasting analysis using neural posterior estimation (NPE) on halo catalogs from the Big Sobol Sequence simulations at z=0.5 to compare the cosmological constraining power of Minkowski Functionals (MFs) and Conditional Moments of Derivatives (CMD) against redshift-space halo power spectrum multipoles (PS). At the fiducial Quijote cosmology and Gaussian smoothing R=15 h^{-1}Mpc, it reports that CMD outperform MFs, that the joint MFs+CMD estimator improves precision by 27% for σ8 and 26% for Ωm over MFs alone, and that in the mass-selected sample (M>3×10^{13} h^{-1}M_⊙) the combined morphological estimator outperforms the PS by 45%^{+20%}_{-9%} for σ8 and 43%^{+10%}_{-7%} for Ωm at matched effective scales k_max ≃ 0.16 h Mpc^{-1}. The analysis is extended across continuous cosmological parameters and multiple smoothing scales.

Significance. If the NPE posteriors are demonstrated to be unbiased and well-calibrated, the results would indicate that weighted morphological statistics capture complementary nonlinear and anisotropic information in redshift space, offering a more informative summary than the power spectrum for mass-selected tracers. The simulation-based approach and extension to continuous parameters provide a useful forecasting framework for future surveys.

major comments (1)
  1. The central claims of percentage improvements (e.g., 45%^{+20%}_{-9%} tighter σ8 constraints from MFs+CMD versus PS in the mass-selected configuration) rest on the assumption that NPE recovers unbiased, well-calibrated posteriors for both the higher-dimensional morphological summaries and the lower-dimensional PS. No explicit coverage tests, rank statistics on held-out mocks, or architecture/training ablation results are described to rule out differential variance underestimation or calibration failures between the statistics.
minor comments (2)
  1. Clarify the precise definition of the 'weighted' morphological estimator and how CMD are combined with MFs in the joint analysis.
  2. Provide additional justification or sensitivity tests for the choice of Gaussian smoothing scale R=15 h^{-1}Mpc and the k_max matching procedure between morphological measures and the power spectrum.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We appreciate the emphasis placed on rigorously validating the neural posterior estimation (NPE) results, which is essential for supporting the reported improvements in cosmological constraints. We address the major comment below.

read point-by-point responses

  1. Referee: The central claims of percentage improvements (e.g., 45%^{+20%}_{-9%} tighter σ8 constraints from MFs+CMD versus PS in the mass-selected configuration) rest on the assumption that NPE recovers unbiased, well-calibrated posteriors for both the higher-dimensional morphological summaries and the lower-dimensional PS. No explicit coverage tests, rank statistics on held-out mocks, or architecture/training ablation results are described to rule out differential variance underestimation or calibration failures between the statistics.

    Authors: We agree that explicit demonstration of NPE calibration and lack of bias is necessary to substantiate the percentage improvements in precision. While our analysis uses standard NPE implementations on the Big Sobol Sequence simulations and internal validation was performed during development, these checks were not documented in the original manuscript. In the revised version, we will add coverage probability tests and rank statistics on held-out mock catalogs for both the MFs+CMD and PS estimators. We will also include architecture and training ablation results to confirm that posterior widths are robust and show no differential underestimation between the higher-dimensional morphological summaries and the lower-dimensional PS. These additions will directly address the referee's concern and strengthen the reliability of the comparative results. revision: yes

Circularity Check

0 steps flagged

No circularity: forward simulation-based forecast derives constraints from external suites

full rationale

The analysis is a pure forecasting exercise that generates mock halo catalogs from the Big Sobol Sequence at fixed fiducial cosmology, computes summary statistics (MFs, CMD, PS multipoles), trains neural posterior estimators on those mocks, and reports posterior-width ratios as measures of relative information content. All quoted percentage improvements (e.g., 45% for σ8 in the mass-selected case) are obtained by direct numerical comparison of the resulting posterior standard deviations on the same simulation ensemble; no parameter is fitted to external data and then re-used as a prediction, no summary statistic is defined in terms of the target cosmological parameters, and no uniqueness theorem or ansatz is imported via self-citation to force the result. The derivation chain therefore remains self-contained against the external simulation benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The forecast rests on the accuracy of the chosen N-body simulations and the neural density estimator; no new physical entities are postulated.

free parameters (2)
  • Gaussian smoothing scale R
    Fixed at 15 h^{-1} Mpc for the fiducial comparison; chosen by hand rather than derived.
  • k_max matching scale
    Set to ≃0.16 h Mpc^{-1} to equate effective scales between morphological and power-spectrum estimators.
axioms (1)
  • domain assumption Big Sobol Sequence halo catalogs at z=0.5 faithfully reproduce nonlinear and redshift-space anisotropic features of the large-scale structure for the Quijote cosmology.
    Central to all reported constraints; invoked when generating the training data for neural posterior estimation.

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