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arxiv: 2411.14748 · v2 · submitted 2024-11-22 · 🌌 astro-ph.CO · astro-ph.IM· cs.LG

Cosmological Analysis with Calibrated Neural Quantile Estimation and Approximate Simulators

He Jia This is my paper

Pith reviewed 2026-05-23 16:40 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IMcs.LG
keywords simulation-based inferenceneural quantile estimationcosmological parameterslarge-scale structureapproximate simulationsdark matter density mapsparticle-mesh simulations
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0 comments X

The pith

Calibrated neural quantile estimation produces unbiased cosmological posteriors from mostly approximate simulations.

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

The paper introduces calibrated Neural Quantile Estimation, an SBI technique that trains a neural model on a large set of inexpensive approximate simulations and then adjusts it with a small set of high-fidelity simulations. This procedure is claimed to guarantee an unbiased posterior for cosmological parameters no matter how inaccurate the approximate simulations are, while recovering near-optimal constraints when the approximations are decent. The approach is shown on field-level inference of parameters from two-dimensional projected dark matter density maps, reaching scales up to k_max ~1.5 h/Mpc at z=0. A reader would care because high-fidelity simulations remain the main computational bottleneck for analyzing upcoming large-scale structure surveys.

Core claim

Calibrated NQE trains on roughly 10,000 Particle-Mesh simulations that include a transfer-function correction, then calibrates the resulting neural quantile estimator with roughly 100 Particle-Particle simulations. The calibrated estimator yields posteriors that match those obtained by training directly on 10,000 expensive PP simulations, while the method is asserted to remain unbiased even when the PM runs are imperfect.

What carries the argument

Calibrated Neural Quantile Estimation, which trains primarily on approximate simulators and corrects the resulting estimator with a small high-fidelity calibration set to enforce unbiased simulation-based inference.

If this is right

  • Posteriors from the calibrated estimator closely match those from direct training on 10,000 expensive PP simulations.
  • Field-level cosmological parameters can be recovered from 2D dark matter density maps up to k_max ~1.5 h/Mpc at z=0.
  • The method supplies a scalable route to precise inference on large volumes and small scales without requiring every simulation to be high-fidelity.

Where Pith is reading between the lines

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

  • The same calibration step could be applied to other simulation-based inference tasks that mix cheap and expensive simulators.
  • Extending the method to three-dimensional fields or to galaxy clustering observables would test whether the calibration cost remains low when the data dimensionality increases.
  • If the required number of high-fidelity runs stays near 100, the approach could support repeated analyses over different survey masks or redshift bins at modest extra cost.

Load-bearing premise

A few hundred high-fidelity simulations suffice to remove every bias introduced by the much larger set of approximate simulations and by the transfer-function correction applied to them.

What would settle it

A side-by-side test in which the posterior obtained after calibration differs measurably from the posterior obtained by training the same estimator on a large number of high-fidelity simulations would show the unbiasedness claim is false.

Figures

Figures reproduced from arXiv: 2411.14748 by He Jia.

Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of power spectrum ratios and cross [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Flowchart of the proposed method, which first ap [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Posterior comparison for [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Empirical coverage of different estimators with CNN as data compressor. Uncalibrated estimators may exhibit bias [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of the constraining power across different methods, as measured by the inverse volume of the 1- [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Validation loss for Ω [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Similar to Fig. 4, but comparing estimators calibrated using only quantile shifting (Shift Only) and only importance [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. A toy example illustrating the limitations of IS-only [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
read the original abstract

A major challenge in extracting information from current and upcoming surveys of cosmological Large-Scale Structure (LSS) is the limited availability of computationally expensive high-fidelity simulations. We introduce calibrated Neural Quantile Estimation (NQE), a new Simulation-Based Inference (SBI) method that leverages a large number of approximate simulations for training and a small number of high-fidelity simulations for calibration. This approach guarantees an unbiased posterior regardless of approximate simulation accuracy, while achieving near-optimal constraining power when the approximate simulations are reasonably accurate. As a proof of concept, we demonstrate that cosmological parameters can be inferred at field level from projected 2-dim dark matter density maps up to $k_{\rm max}\sim1.5\,h$/Mpc at $z=0$ by training on $\sim10^4$ Particle-Mesh (PM) simulations with transfer function correction and calibrating with $\sim10^2$ Particle-Particle (PP) simulations. The calibrated posteriors closely match those obtained by directly training on $\sim10^4$ expensive PP simulations, but at a fraction of the computational cost. Our method offers a practical and scalable framework for SBI of cosmological LSS, enabling precise inference across vast volumes and down to small scales.

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

2 major / 2 minor

Summary. The manuscript introduces Calibrated Neural Quantile Estimation (NQE), an SBI method that trains a neural quantile estimator on a large ensemble of approximate PM simulations (~10^4) with transfer-function correction and calibrates it using a small set of high-fidelity PP simulations (~10^2). It claims this produces unbiased posteriors for cosmological parameters inferred at field level from projected 2D dark matter density maps up to k_max ~1.5 h/Mpc at z=0, with constraining power matching direct training on expensive PP simulations at far lower cost.

Significance. If the unbiased-posterior guarantee holds, the method would substantially lower the computational barrier to field-level LSS inference, enabling analyses over larger volumes and to smaller scales with mostly inexpensive simulations. The reported match between calibrated and direct-PP posteriors is a concrete positive result that supports practicality.

major comments (2)
  1. [Calibration procedure] The central guarantee of an unbiased posterior independent of PM accuracy rests entirely on the calibration step. With only ~100 PP realizations in the high-dimensional space of 2D density maps at k_max~1.5 h/Mpc, it is unclear whether the calibration can remove all systematic differences between the PM+TF ensemble and the true PP distribution without residual coverage errors or added variance. This needs explicit validation (e.g., posterior coverage tests or bias quantification) in the relevant section describing the calibration procedure.
  2. [Transfer function correction] The transfer-function correction applied to the PM runs is an additional modeling choice whose residuals must lie within the span of what the small calibration set can correct. The manuscript should demonstrate that any uncorrected TF residuals do not propagate into the final posterior or provide a quantitative bound on their effect.
minor comments (2)
  1. [Abstract and results] Clarify the precise definition of 'near-optimal constraining power' and provide quantitative metrics (e.g., figure-of-merit ratios) comparing calibrated NQE to direct PP training.
  2. [Figures] Ensure all posterior comparison figures include uncertainty estimates on the calibrated versus direct-PP contours.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Calibration procedure] The central guarantee of an unbiased posterior independent of PM accuracy rests entirely on the calibration step. With only ~100 PP realizations in the high-dimensional space of 2D density maps at k_max~1.5 h/Mpc, it is unclear whether the calibration can remove all systematic differences between the PM+TF ensemble and the true PP distribution without residual coverage errors or added variance. This needs explicit validation (e.g., posterior coverage tests or bias quantification) in the relevant section describing the calibration procedure.

    Authors: We agree that explicit validation strengthens the claim. The manuscript already provides empirical support via the close match between calibrated NQE posteriors and those from direct training on ~10^4 PP simulations. To directly address coverage and potential residual errors, we will add posterior coverage tests and bias quantification (using held-out PP realizations) in the section describing the calibration procedure. revision: yes

  2. Referee: [Transfer function correction] The transfer-function correction applied to the PM runs is an additional modeling choice whose residuals must lie within the span of what the small calibration set can correct. The manuscript should demonstrate that any uncorrected TF residuals do not propagate into the final posterior or provide a quantitative bound on their effect.

    Authors: The TF correction aligns the PM power spectrum with PP before training. We will add a quantitative assessment of post-correction residuals and show (via comparison of posteriors with and without TF correction, or by bounding their effect) that any remaining differences fall within the span corrected by the calibration set. revision: yes

Circularity Check

0 steps flagged

No significant circularity; unbiasedness is a stated design property of the calibration procedure

full rationale

The paper presents calibrated NQE as a method that trains on approximate PM simulations and calibrates with a small set of PP simulations to guarantee unbiased posteriors by construction of the calibration step. No equations, self-citations, or fitting procedures in the abstract or described claims reduce the central guarantee to a tautology or to the same data used for training. The comparison to direct PP training is presented as external validation rather than a self-referential loop. This is a standard methodological contribution with no load-bearing self-definition or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard SBI assumptions plus the unproven effectiveness of the specific calibration step; no free parameters or new physical entities are introduced in the abstract.

axioms (1)
  • domain assumption Simulation-based inference frameworks can map summary statistics or fields to posterior distributions over cosmological parameters.
    Standard premise in the field of cosmological data analysis.
invented entities (1)
  • Calibrated Neural Quantile Estimation no independent evidence
    purpose: To produce unbiased posteriors when training data come from approximate simulators
    New method name and procedure introduced in the paper; no independent evidence supplied in the abstract.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Machine Learning Techniques for Astrophysics and Cosmology: Simulation-Based Inference

    astro-ph.CO 2026-05 unverdicted novelty 2.0

    Simulation-based inference uses neural networks trained on simulations to enable parameter inference in cosmology and astrophysics where traditional likelihood calculations are intractable.

Reference graph

Works this paper leans on

51 extracted references · 51 canonical work pages · cited by 1 Pith paper · 7 internal anchors

  1. [1]

    or model misspecification (e.g., PM and PM+TF), calibration yields unbiased posteriors in all cases, as evi- denced by the diagonal empirical coverage curves. Fig. 3 also shows that while all calibrated estimators are unbiased, their constraining power varies: the poste- rior contours from calibrated PM+TF are comparable to those from calibrated PP 10K bu...

    work page

  2. [2]

    The number of simulations needed for calibration therefore also depends on the number of independent ob- servational data points that can be produced per simula- tion. Nonetheless, we expect that approximately O(102) simulations should be sufficient for calibration in most scenarios, except when θ is high-dimensional with com- plex correlations between di...

    work page

  3. [3]

    Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument

    B. Abareshi et al. , Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument, AJ 164, 207 (2022), arXiv:2205.10939 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  4. [4]

    Euclid Collaboration, Euclid. I. Overview of the Eu- clid mission, arXiv e-prints , arXiv:2405.13491 (2024), arXiv:2405.13491 [astro-ph.CO]

    work page arXiv 2024

  5. [5]

    LSST: from Science Drivers to Reference Design and Anticipated Data Products

    ˇZ. Ivezi´ cet al., LSST: From Science Drivers to Reference 6 Design and Anticipated Data Products, ApJ 873, 111 (2019), arXiv:0805.2366 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [6]

    D. Spergel et al., Wide-Field InfrarRed Survey Telescope- Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 Report, arXiv e-prints , arXiv:1503.03757 (2015), arXiv:1503.03757 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  7. [7]

    Cranmer, J

    K. Cranmer, J. Brehmer, and G. Louppe, The frontier of Simulation-Based Inference, Proceedings of the National Academy of Sciences 117, 30055 (2020)

    work page 2020

  8. [8]

    Lueckmann, J

    J.-M. Lueckmann, J. Boelts, D. Greenberg, P. Goncalves, and J. Macke, Benchmarking Simulation-Based Infer- ence, in Proceedings of the 24th International Conference on Artificial Intelligence and Statistics , Proceedings of Machine Learning Research, Vol. 130 (2021) pp. 343–351

    work page 2021

  9. [9]

    Papamakarios and I

    G. Papamakarios and I. Murray, Fast ε-free inference of simulation models with bayesian conditional density esti- mation, Advances in Neural Information Processing Sys- tems 29 (2016)

    work page 2016

  10. [10]

    Lueckmann, P

    J.-M. Lueckmann, P. J. Goncalves, G. Bassetto, K. ¨Ocal, M. Nonnenmacher, and J. H. Macke, Flexible statisti- cal inference for mechanistic models of neural dynamics, Advances in Neural Information Processing Systems 30 (2017)

    work page 2017

  11. [11]

    Greenberg, M

    D. Greenberg, M. Nonnenmacher, and J. Macke, Auto- matic posterior transformation for likelihood-free infer- ence, in Proceedings of the 36th International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 97 (2019) pp. 2404–2414

    work page 2019

  12. [12]

    Papamakarios, D

    G. Papamakarios, D. Sterratt, and I. Murray, Sequen- tial neural likelihood: Fast likelihood-free inference with autoregressive flows, in Proceedings of the 22nd Interna- tional Conference on Artificial Intelligence and Statis- tics, Proceedings of Machine Learning Research, Vol. 89 (2019) pp. 837–848

    work page 2019

  13. [13]

    Lueckmann, G

    J.-M. Lueckmann, G. Bassetto, T. Karaletsos, and J. H. Macke, Likelihood-free inference with emulator networks, in Proceedings of the 1st Symposium on Advances in Ap- proximate Bayesian Inference , Proceedings of Machine Learning Research, Vol. 96 (2019) pp. 32–53

    work page 2019

  14. [14]

    Hermans, V

    J. Hermans, V. Begy, and G. Louppe, Likelihood-free MCMC with amortized approximate ratio estimators, in Proceedings of the 37th International Conference on Ma- chine Learning , Proceedings of Machine Learning Re- search, Vol. 119 (2020) pp. 4239–4248

    work page 2020

  15. [15]

    Jia, Simulation-Based Inference with Quantile Regres- sion, in Proceedings of the 41st International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol

    H. Jia, Simulation-Based Inference with Quantile Regres- sion, in Proceedings of the 41st International Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 235 (2024) pp. 21731–21752

    work page 2024

  16. [16]

    LeCun, B

    Y. LeCun, B. Boser, J. Denker, D. Henderson, R. Howard, W. Hubbard, and L. Jackel, Handwrit- ten digit recognition with a back-propagation network, Advances in Neural Information Processing Systems 2 (1989)

    work page 1989

  17. [17]

    K. He, X. Zhang, S. Ren, and J. Sun, Deep residual learn- ing for image recognition, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2016)

    work page 2016

  18. [18]

    Springel, R

    V. Springel, R. Pakmor, O. Zier, and M. Reinecke, Simu- lating cosmic structure formation with the GADGET- 4 code, MNRAS 506, 2871 (2021), arXiv:2010.03567 [astro-ph.IM]

    work page arXiv 2021

  19. [19]

    L. H. Garrison, D. J. Eisenstein, D. Ferrer, N. A. Mak- simova, and P. A. Pinto, The ABACUS cosmological N- body code, MNRAS 508, 575 (2021), arXiv:2110.11392 [astro-ph.CO]

    work page arXiv 2021

  20. [20]

    G. L. Bryan, M. L. Norman, B. W. O’Shea, T. Abel, J. H. Wise, M. J. Turk, D. R. Reynolds, D. C. Collins, P. Wang, S. W. Skillman, et al. , ENZO: An Adaptive Mesh Refinement Code for Astrophysics, ApJS 211, 19 (2014), arXiv:1307.2265 [astro-ph.IM]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  21. [21]

    Weinberger, V

    R. Weinberger, V. Springel, and R. Pakmor, The AREPO Public Code Release, ApJS 248, 32 (2020), arXiv:1909.04667 [astro-ph.IM]

    work page arXiv 2020

  22. [22]

    J. M. Stone, P. D. Mullen, D. Fielding, P. Grete, M. Guo, P. Kempski, E. R. Most, C. J. White, and G. N. Wong, AthenaK: A Performance-Portable Version of the Athena++ AMR Framework, arXiv e-prints , arXiv:2409.16053 (2024), arXiv:2409.16053 [astro-ph.IM]

    work page arXiv 2024

  23. [23]

    FastPM: a new scheme for fast simulations of dark matter and halos

    Y. Feng, M.-Y. Chu, U. Seljak, and P. McDon- ald, FASTPM: a new scheme for fast simulations of dark matter and haloes, MNRAS 463, 2273 (2016), arXiv:1603.00476 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  24. [24]

    Y. Li, L. Lu, C. Modi, D. Jamieson, Y. Zhang, Y. Feng, W. Zhou, N. Pok Kwan, F. Lanusse, and L. Greengard, pmwd: A Differentiable Cosmological Particle-Mesh N- body Library, arXiv e-prints , arXiv:2211.09958 (2022), arXiv:2211.09958 [astro-ph.IM]

    work page arXiv 2022

  25. [25]

    Rampf, F

    C. Rampf, F. List, and O. Hahn, BullFrog: Multi-step perturbation theory as a time integrator for cosmologi- cal simulations, arXiv e-prints , arXiv:2409.19049 (2024), arXiv:2409.19049 [astro-ph.CO]

    work page arXiv 2024

  26. [26]

    B. Dai, Y. Feng, and U. Seljak, A gradient based method for modeling baryons and matter in halos of fast simula- tions, J. Cosmology Astropart. Phys. 2018, 009 (2018), arXiv:1804.00671 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  27. [27]

    S. He, Y. Li, Y. Feng, S. Ho, S. Ravanbakhsh, W. Chen, and B. P´ oczos, Learning to predict the cosmologi- cal structure formation, Proceedings of the National Academy of Science 116, 13825 (2019), arXiv:1811.06533 [astro-ph.CO]

    work page arXiv 2019

  28. [28]

    Payot, P

    N. Payot, P. Lemos, L. Perreault-Levasseur, C. Cuesta- Lazaro, C. Modi, and Y. Hezaveh, Learning an Effective Evolution Equation for Particle-Mesh Simulations Across Cosmologies, arXiv e-prints , arXiv:2311.18017 (2023), arXiv:2311.18017 [astro-ph.CO]

    work page arXiv 2023

  29. [29]

    Sharma, B

    D. Sharma, B. Dai, F. Villaescusa-Navarro, and U. Sel- jak, A field-level emulator for modeling baryonic ef- fects across hydrodynamic simulations, arXiv e-prints , arXiv:2401.15891 (2024), arXiv:2401.15891 [astro- ph.CO]

    work page arXiv 2024

  30. [30]

    Jamieson, Y

    D. Jamieson, Y. Li, F. Villaescusa-Navarro, S. Ho, and D. N. Spergel, Field-level Emulation of Cosmic Structure Formation with Cosmology and Redshift De- pendence, arXiv e-prints , arXiv:2408.07699 (2024), arXiv:2408.07699 [astro-ph.CO]

    work page arXiv 2024

  31. [31]

    Lemos, L

    P. Lemos, L. Parker, C. Hahn, S. Ho, M. Eickenberg, J. Hou, E. Massara, C. Modi, A. M. Dizgah, B. R.-S. Blancard, D. Spergel, and SimBIG Collaboration, Field- level simulation-based inference of galaxy clustering with convolutional neural networks, Phys. Rev. D109, 083536 (2024)

    work page 2024

  32. [32]

    Power Spectrum Super-Sample Covariance

    M. Takada and W. Hu, Power spectrum super- sample covariance, Phys. Rev. D 87, 123504 (2013), arXiv:1302.6994 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  33. [33]

    A. E. Bayer, J. Liu, R. Terasawa, A. Barreira, Y. Zhong, and Y. Feng, Super-sample covariance of the 7 power spectrum, bispectrum, halos, voids, and their cross covariances, Phys. Rev. D 108, 043521 (2023), arXiv:2210.15647 [astro-ph.CO]

    work page arXiv 2023

  34. [34]

    Modi and O

    C. Modi and O. H. E. Philcox, Hybrid SBI or How I Learned to Stop Worrying and Learn the Likelihood, arXiv e-prints , arXiv:2309.10270 (2023), arXiv:2309.10270 [astro-ph.CO]

    work page arXiv 2023

  35. [35]

    Cheng, Y.-S

    S. Cheng, Y.-S. Ting, B. M´ enard, and J. Bruna, A new approach to observational cosmology using the scattering transform, MNRAS 499, 5902 (2020), arXiv:2006.08561 [astro-ph.CO]

    work page arXiv 2020

  36. [36]

    Valogiannis and C

    G. Valogiannis and C. Dvorkin, Towards an optimal es- timation of cosmological parameters with the wavelet scattering transform, Phys. Rev. D 105, 103534 (2022), arXiv:2108.07821 [astro-ph.CO]

    work page arXiv 2022

  37. [37]

    K. Lin, B. Joachimi, and J. D. McEwen, Simulation- based inference with scattering representations: scatter- ing is all you need, arXiv e-prints , arXiv:2410.11883 (2024), arXiv:2410.11883 [cs.LG]

    work page arXiv 2024

  38. [38]

    https://github.com/h3jia/nqe

    work page

  39. [39]

    Rezende and S

    D. Rezende and S. Mohamed, Variational inference with normalizing flows, in Proceedings of the 32nd Interna- tional Conference on Machine Learning , Proceedings of Machine Learning Research, Vol. 37 (2015) pp. 1530– 1538

    work page 2015

  40. [40]

    Papamakarios, E

    G. Papamakarios, E. Nalisnick, D. J. Rezende, S. Mo- hamed, and B. Lakshminarayanan, Normalizing flows for probabilistic modeling and inference, Journal of Machine Learning Research 22, 1 (2021)

    work page 2021

  41. [41]

    Jia and B

    H. Jia and B. Dai, Effective Calibration Strategies for Neural Quantile Estimation, in prep

    work page

  42. [42]

    However, the shift step alone does ensure correct q-coverage for each 1-dim conditional posterior

    In this work, we adopt the standard definition of coverage based on the rank of posterior density, referred to as p- coverage in [13]. However, the shift step alone does ensure correct q-coverage for each 1-dim conditional posterior

    work page

  43. [43]

    Sharma, B

    D. Sharma, B. Dai, and U. Seljak, A comparative study of cosmological constraints from weak lensing using Convo- lutional Neural Networks, J. Cosmology Astropart. Phys. 2024, 010 (2024), arXiv:2403.03490 [astro-ph.CO]

    work page arXiv 2024

  44. [44]

    Lanzieri, J

    D. Lanzieri, J. Zeghal, T. L. Makinen, A. Boucaud, J.- L. Starck, and F. Lanusse, Optimal Neural Summari- sation for Full-Field Weak Lensing Cosmological Im- plicit Inference, arXiv e-prints , arXiv:2407.10877 (2024), arXiv:2407.10877 [astro-ph.CO]

    work page arXiv 2024

  45. [45]

    T. L. Makinen, C. Sui, B. D. Wandelt, N. Porqueres, and A. Heavens, Hybrid Summary Statistics, arXiv e-prints , arXiv:2410.07548 (2024), arXiv:2410.07548 [stat.ML]

    work page arXiv 2024

  46. [46]

    Villaescusa-Navarro, C

    F. Villaescusa-Navarro, C. Hahn, E. Massara, A. Baner- jee, A. M. Delgado, D. K. Ramanah, T. Charnock, E. Giusarma, Y. Li, E. Allys, et al. , The Quijote Sim- ulations, ApJS 250, 2 (2020), arXiv:1909.05273 [astro- ph.CO]

    work page arXiv 2020

  47. [47]

    N. S. M. de Santi, H. Shao, F. Villaescusa-Navarro, L. R. Abramo, R. Teyssier, P. Villanueva-Domingo, Y. Ni, D. Angl´ es-Alc´ azar, S. Genel, E. Hern´ andez- Mart´ ınez, U. P. Steinwandel, C. C. Lovell, K. Dolag, T. Castro, and M. Vogelsberger, Robust Field-level Likelihood-free Inference with Galaxies, ApJ 952, 69 (2023), arXiv:2302.14101 [astro-ph.CO]

    work page arXiv 2023

  48. [48]

    Echeverri-Rojas, F

    N. Echeverri-Rojas, F. Villaescusa-Navarro, C. Chawak, Y. Ni, C. Hahn, E. Hern´ andez-Mart´ ınez, R. Teyssier, D. Angl´ es-Alc´ azar, K. Dolag, and T. Castro, Cosmology with One Galaxy? The ASTRID Model and Robustness, ApJ 954, 125 (2023), arXiv:2304.06084 [astro-ph.CO]

    work page arXiv 2023

  49. [49]

    Roncoli, A

    A. Roncoli, A. ´Ciprijanovi´ c, M. Voetberg, F. Villaescusa- Navarro, and B. Nord, Domain Adaptive Graph Neural Networks for Constraining Cosmological Pa- rameters Across Multiple Data Sets, arXiv e-prints , arXiv:2311.01588 (2023), arXiv:2311.01588 [astro- ph.CO]

    work page arXiv 2023

  50. [50]

    Lee, J.-h

    J.-Y. Lee, J.-h. Kim, M. Jung, B. K. Oh, Y. Jo, S. Park, J. Lee, Y.-S. Ting, and H. S. Hwang, Inferring Cosmolog- ical Parameters on SDSS via Domain-generalized Neu- ral Networks and Light-cone Simulations, ApJ 975, 38 (2024), arXiv:2409.02256 [astro-ph.CO]

    work page arXiv 2024

  51. [51]

    D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, in 3rd International Conference on Learn- ing Representations (2015). The Neural Quantile Estimation Algorithm NQE [13] infers model parameters θ from observa- tional data x by estimating approximately 20 individ- ual quantiles for each 1-dim conditional distribution p(θ(i) | x, θ(j<i)). ...

    work page 2015