cloelib: A Flexible Python Library for Computing Cosmological Observables in the Euclid Era
Pith reviewed 2026-05-25 02:58 UTC · model grok-4.3
The pith
cloelib is a modular Python library that computes cosmological observables for Euclid by interfacing with Boltzmann solvers and using JAX automatic differentiation.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
cloelib defines consistent protocols for background evolution, perturbations, and non-linear structure formation. It interfaces with Boltzmann solvers and incorporates JAX-based automatic differentiation to enable gradient-based methods. The library supports photometric and spectroscopic large-scale structure probes as well as cross-correlations with the Cosmic Microwave Background and galaxy clusters. In its finalised form cloelib is intended to serve as the reference theory computation infrastructure for Euclid's first cosmological release.
What carries the argument
The modular architecture that interfaces with Boltzmann solvers and incorporates JAX-based automatic differentiation for gradient-based inference.
If this is right
- Supports gradient-based optimization methods in cosmological inference pipelines.
- Covers the full range of photometric, spectroscopic, CMB cross-correlation and cluster observables needed for Euclid.
- Bridges traditional numerical cosmology codes with modern optimization and machine learning inference techniques.
- Provides the reference theory computation layer for Euclid's first cosmological data release.
Where Pith is reading between the lines
- The differentiable interface could allow hybrid models that combine numerical solvers with neural network emulators for faster parameter scans.
- Similar modular protocols might be adapted for other upcoming surveys that require consistent observable predictions across multiple probes.
- Automatic differentiation opens the possibility of end-to-end gradient flow from theory parameters through to likelihood evaluations in joint analyses.
- The library's design may reduce duplication of effort by letting different analysis teams share the same underlying observable computations.
Load-bearing premise
The modular architecture will interface with Boltzmann solvers and support all required observables without major accuracy or performance shortfalls.
What would settle it
A direct numerical comparison of cloelib outputs against established Boltzmann codes for a set of Euclid-like observables that reveals discrepancies exceeding the required precision.
read the original abstract
cloelib is a Python library developed to compute cosmological observables within the Cosmology Likelihood for Observables in Euclid (CLOE) ecosystem (cloe-org). As cosmology enters a precision era driven by galaxy survey missions such as Euclid, there is a growing need for flexible, efficient, and differentiable software capable of supporting next-generation inference pipelines. cloelib addresses these demands through a modular architecture that interfaces seamlessly with established Boltzmann solvers whilst incorporating JAX-based automatic differentiation to enable gradient-based methods. The library defines consistent protocols for background evolution, perturbations, and non-linear structure formation, and supports a wide range of observables, including photometric and spectroscopic large-scale structure probes, as well as cross-correlations with the Cosmic Microwave Background and galaxy clusters. In its finalised form, cloelib is intended to serve as the reference theory computation infrastructure for Euclid's first cosmological release, bridging traditional numerical cosmology with modern optimisation techniques and emerging machine learning approaches to inference.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript describes cloelib, a Python library for computing cosmological observables in the Euclid context. It outlines a modular architecture with protocols for background evolution, perturbations, and non-linear structure formation; interfaces to Boltzmann solvers; and JAX-based automatic differentiation for gradient-based methods. The library supports photometric/spectroscopic large-scale structure, CMB cross-correlations, and cluster observables, with the intent to serve as reference infrastructure for Euclid's first cosmological release.
Significance. If the described features are realized, the library would offer a useful bridge between established numerical cosmology tools and modern differentiable/ML inference techniques, addressing needs in the Euclid precision era. The consistent protocol definitions and JAX integration are explicit strengths that enable the claimed flexibility.
major comments (1)
- Abstract: the assertion that the architecture 'interfaces seamlessly with established Boltzmann solvers' and supports the full range of observables 'without major accuracy or performance shortfalls' is presented without any benchmarks, validation tests, or error analysis. This is load-bearing for the central claim of serving as the reference infrastructure.
minor comments (2)
- The manuscript should include a diagram or explicit listing of the defined protocols to clarify the modular interfaces for readers.
- Consider adding references to prior differentiable cosmology libraries (e.g., those using JAX or similar) to better situate the contribution.
Simulated Author's Rebuttal
We thank the referee for their constructive review. The single major comment correctly identifies that the abstract makes strong claims about seamless interfacing and performance without supporting evidence in the current manuscript. We address this below and will revise accordingly.
read point-by-point responses
-
Referee: Abstract: the assertion that the architecture 'interfaces seamlessly with established Boltzmann solvers' and supports the full range of observables 'without major accuracy or performance shortfalls' is presented without any benchmarks, validation tests, or error analysis. This is load-bearing for the central claim of serving as the reference infrastructure.
Authors: We agree that the abstract's claims require supporting evidence to be credible, particularly given the manuscript's positioning as reference infrastructure. The current version contains no benchmarks or validation tests. In the revised manuscript we will add a new section (provisionally Section 5) presenting direct comparisons against CLASS and CAMB for background quantities, linear power spectra, and selected observables (photometric and spectroscopic clustering, CMB cross-correlations). This section will include relative error plots, convergence tests, and wall-clock timing benchmarks on representative hardware. The abstract will be revised to reference these results or to qualify the performance claims. These additions directly address the load-bearing concern. revision: yes
Circularity Check
No significant circularity: software description paper with no derivations or predictions
full rationale
The manuscript is a library description paper whose central claim is the design and intended scope of cloelib as modular infrastructure for Euclid observables. No equations, fitted parameters, predictions, or load-bearing derivations are presented that could reduce to inputs by construction. Self-citations to cloe-org are descriptive of the ecosystem rather than justificatory of a physical result. The argument is self-contained as a statement of architectural choices and supported observables, with no internal reduction to fitted quantities or self-referential uniqueness theorems.
Axiom & Free-Parameter Ledger
Reference graph
Works this paper leans on
-
[1]
doi:10.5281/zenodo.20054482 , url =
Moretti, Chiara , title =. doi:10.5281/zenodo.20054482 , url =
-
[2]
Charles R. Harris and K. Jarrod Millman and St. Array programming with. 2020 , journal =. doi:10.1038/s41586-020-2649-2 , publisher =
-
[3]
and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and
Virtanen, Pauli and Gommers, Ralf and Oliphant, Travis E. and Haberland, Matt and Reddy, Tyler and Cournapeau, David and Burovski, Evgeni and Peterson, Pearu and Weckesser, Warren and Bright, Jonathan and. Nature Methods , year =
-
[4]
Hunter, J. D. , Title =. Computing in Science & Engineering , Volume =
-
[5]
IOS Press , year = 2016, pages =
Jupyter Notebooks a publishing format for reproducible computational workflows. IOS Press , year = 2016, pages =. doi:10.3233/978-1-61499-649-1-87 , adsurl =
-
[6]
Building a Framework for Predictive Science
Michael M. McKerns and Leif Strand and Tim Sullivan and Alta Fang and Michael A. G. Aivazis , title =. arXiv preprint arXiv:1202.1056 , year =
work page internal anchor Pith review Pith/arXiv arXiv
-
[7]
Blinding multiprobe cosmological experiments. , keywords =. doi:10.1093/mnras/staa965 , archivePrefix =. 1911.05929 , primaryClass =
-
[8]
KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey
KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey. , keywords =. doi:10.1051/0004-6361/202554908 , archivePrefix =. 2503.19441 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/202554908
-
[9]
Dark Energy Survey Year 6 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing. arXiv e-prints , keywords =. doi:10.48550/arXiv.2601.14559 , archivePrefix =. 2601.14559 , primaryClass =
-
[10]
Hyper Suprime-Cam Year 3 results: Cosmology from galaxy clustering and weak lensing with HSC and SDSS using the emulator based halo model. , keywords =. doi:10.1103/PhysRevD.108.123517 , archivePrefix =. 2304.00704 , primaryClass =
-
[11]
Large Synoptic Survey Telescope: Dark Energy Science Collaboration
Large Synoptic Survey Telescope: Dark Energy Science Collaboration. arXiv e-prints , keywords =. doi:10.48550/arXiv.1211.0310 , archivePrefix =. 1211.0310 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1211.0310
-
[12]
The DES Science Verification Weak Lensing Shear Catalogues
The DES Science Verification weak lensing shear catalogues. , keywords =. doi:10.1093/mnras/stw990 , archivePrefix =. 1507.05603 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stw990
-
[13]
Blind Observers of the Sky. , keywords =. doi:10.1088/1475-7516/2020/09/052 , archivePrefix =. 2006.10857 , primaryClass =
-
[14]
Measurement of _ m , _ from a Blind Analysis of Type Ia Supernovae with CMAGIC: Using Color Information to Verify the Acceleration of the Universe. , keywords =. doi:10.1086/503533 , archivePrefix =. astro-ph/0602411 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/503533
-
[15]
A blinding solution for inference from astronomical data. , keywords =. doi:10.1093/mnras/staa043 , archivePrefix =. 1910.08533 , primaryClass =
-
[19]
S. D. P. Vitenti and M. Penna-Lima , year =. ascl , primaryclass =:1408.013 , adsurl =
-
[20]
Monthly Notices of the Royal Astronomical Society , volume =
Lange, Johannes U , title = ". Monthly Notices of the Royal Astronomical Society , volume =. 2023 , month =. doi:10.1093/mnras/stad2441 , url =
-
[21]
The Journal of Open Source Software , year = 2016, month = aug, volume = 1, eid =
ChainConsumer. The Journal of Open Source Software , year = 2016, month = aug, volume = 1, eid =. doi:10.21105/joss.00045 , adsurl =
-
[22]
Astropy: A Community Python Package for Astronomy
doi:10.1051/0004-6361/201322068 , Eid =. arXiv , Author =:1307.6212 , Journal =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201322068
-
[23]
The Astropy Project: Building an inclusive, open-science project and status of the v2.0 core package
The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package. , keywords =. doi:10.3847/1538-3881/aabc4f , archivePrefix =. 1801.02634 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-3881/aabc4f
-
[24]
The Astropy Project: Sustaining and Growing a Community-oriented Open-source Project and the Latest Major Release (v5.0) of the Core Package. , keywords =. doi:10.3847/1538-4357/ac7c74 , archivePrefix =. 2206.14220 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ac7c74
-
[25]
Armando Solé and jialin and Daniel Hay Guest and Yu Feng and Mark Kittisopikul , title =
Andrew Collette and Thomas Kluyver and Thomas A Caswell and James Tocknell and Jerome Kieffer and Aleksandar Jelenak and Anthony Scopatz and Darren Dale and Chen and Thomas VINCENT and Matt Einhorn and payno and juliagarriga and Pierlauro Sciarelli and Valentin Valls and Satrajit Ghosh and Ulrik Kofoed Pedersen and jakirkham and Martin Raspaud and Cyril D...
-
[27]
CMB power spectrum parameter degeneracies in the era of precision cosmology
CMB power spectrum parameter degeneracies in the era of precision cosmology. , keywords =. doi:10.1088/1475-7516/2012/04/027 , archivePrefix =. 1201.3654 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2012/04/027 2012
-
[29]
A unified pseudo-$C_\ell$ framework
A unified pseudo-C _ framework. , keywords =. doi:10.1093/mnras/stz093 , archivePrefix =. 1809.09603 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz093
-
[30]
Brand, Amy and Allen, Liz and Altman, Micah and Hlava, Marjorie and Scott, Jo , title =. Learned Publishing , volume =. doi:10.1087/20150211 , year =
-
[31]
The Open Journal of Astrophysics , keywords =
The catalog-to-cosmology framework for weak lensing and galaxy clustering for LSST. The Open Journal of Astrophysics , keywords =. doi:10.21105/astro.2212.09345 , archivePrefix =. 2212.09345 , primaryClass =
-
[32]
Overview of the Euclid mission
Euclid: I. Overview of the Euclid mission. Astronomy & Astrophysics , keywords =. doi:10.1051/0004-6361/202450810 , archivePrefix =. 2405.13491 , primaryClass =
-
[33]
The Astrophysical Journal , year = 2000, month = aug, volume = 538, number = 2, pages =
Efficient Computation of Cosmic Microwave Background Anisotropies in Closed Friedmann-Robertson-Walker Models. The Astrophysical Journal , year = 2000, month = aug, volume = 538, number = 2, pages =. doi:10.1086/309179 , archivePrefix =
-
[34]
Part II: Approximation schemes
The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes. Journal of Cosmology and Astroparticle Physics , year = 2011, month = jul, volume = 2011, number = 07, pages =. doi:10.1088/1475-7516/2011/07/034 , archivePrefix =
-
[35]
HMcode-2020: improved modelling of non-linear cosmological power spectra with baryonic feedback. Monthly Notices of the Royal Astronomical Society , year = 2021, month = mar, volume = 502, number = 1, pages =. doi:10.1093/mnras/stab082 , archivePrefix =
-
[36]
Modified gravity and massive neutrinos: constraints from the full shape analysis of BOSS galaxies and forecasts for Stage IV surveys. , keywords =. doi:10.1088/1475-7516/2023/12/025 , archivePrefix =. 2306.09275 , primaryClass =
-
[37]
COMET: Clustering observables modelled by emulated perturbation theory
Eggemeier, Alexander and Camacho-Quevedo, Benjamin and Pezzotta, Andrea and Crocce, Martin and Scoccimarro, Rom \'a n and S \'a nchez, Ariel G. COMET: Clustering observables modelled by emulated perturbation theory. Monthly Notices of the Royal Astronomical Society. 2022. doi:10.1093/mnras/stac3667. arXiv:2208.01070
-
[38]
Pezzotta, Andrea and Eggemeier, Alexander and Gambardella, Giosu \`e and Finkbeiner, Lukas and S \'a nchez, Ariel G. and Camacho Quevedo, Benjamin and Crocce, Martin and Lee, Nanoom and Parimbelli, Gabriele and Scoccimarro, Rom \'a n. Extending evolution mapping to massive neutrinos with COMET. Physical Review D. 2025. doi:10.1103/vy3h-p92n. arXiv:2503.16160
-
[39]
James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake
-
[40]
Spurio Mancini, Alessio and Piras, Davide and Alsing, Justin and Joachimi, Benjamin and Hobson, Michael P. CosmoPower: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys. Monthly Notices of the Royal Astronomical Society. 2022. doi:10.1093/mnras/stac064. arXiv:2106.03846
-
[42]
Capse.jl: efficient and auto-differentiable
Bonici, Marco and Bianchini, Federico and Ruiz-Zapatero, Jaime , journal =. Capse.jl: efficient and auto-differentiable. doi:10.21105/astro.2307.14339 , year =
-
[43]
Bonici, Marco and D'Amico, Guido and Bel, Julien and Carbone, Carmelita. Effort.jl: a fast and differentiable emulator for the Effective Field Theory of the Large Scale Structure of the Universe. Journal of Cosmology and Astroparticle Physics. 2025. doi:10.1088/1475-7516/2025/09/044. arXiv:2501.04639
-
[44]
The Astrophysical Journal Supplement Series , keywords =
Core Cosmology Library: Precision Cosmological Predictions for LSST. The Astrophysical Journal Supplement Series , keywords =. doi:10.3847/1538-4365/ab1658 , archivePrefix =. 1812.05995 , primaryClass =
-
[45]
CosmoSIS: modular cosmological parameter estimation
Zuntz, Joe and Paterno, Marc and Jennings, Elise and Rudd, Douglas and Manzotti, Alessandro and Dodelson, Scott and Bridle, Sarah and Sehrish, Saba and Kowalkowski, James. CosmoSIS: modular cosmological parameter estimation. Astronomy and Computing. 2015. doi:10.1016/j.ascom.2015.05.005. arXiv:1409.3409
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.ascom.2015.05.005 2015
-
[46]
Cobaya: Code for Bayesian Analysis of hierarchical physical models
Cobaya: code for Bayesian analysis of hierarchical physical models. Journal of Cosmology and Astroparticle Physics , keywords =. doi:10.1088/1475-7516/2021/05/057 , archivePrefix =. 2005.05290 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2021/05/057 2021
-
[47]
Cosmology Likelihood for Observables in Euclid (CLOE)
Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 6: Impact of systematic uncertainties on the cosmological analysis. A&A, accepted , keywords =. doi:10.48550/arXiv.2510.10021 , archivePrefix =. 2510.10021 , primaryClass =
-
[48]
Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 5. Extensions beyond the standard modelling of theoretical probes and systematic effects. A&A, accepted , keywords =. doi:10.48550/arXiv.2510.09147 , archivePrefix =. 2510.09147 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2510.09147
-
[49]
Cosmology Likelihood for Observables in Euclid (CLOE)
Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 4: Validation and Performance. A&A, accepted , keywords =. doi:10.48550/arXiv.2510.09141 , archivePrefix =. 2510.09141 , primaryClass =
-
[50]
Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 3. Inference and Forecasts. A&A, accepted , keywords =. doi:10.48550/arXiv.2510.09153 , archivePrefix =. 2510.09153 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2510.09153
-
[51]
Cosmology Likelihood for Observables in Euclid (CLOE)
Euclid preparation. Cosmology Likelihood for Observables in Euclid (CLOE). 2. Code implementation. A&A, accepted , keywords =
-
[52]
Cosmology Likelihood for Observables in (CLOE). 1. Theoretical recipe. A&A, accepted , keywords =. doi:10.48550/arXiv.2510.09118 , archivePrefix =. 2510.09118 , primaryClass =
-
[53]
Monthly Notices of the Royal Astronomical Society , volume =
Krause, Elisabeth and Eifler, Tim , title =. Monthly Notices of the Royal Astronomical Society , volume =. 2017 , month =. doi:10.1093/mnras/stx1261 , url =
-
[54]
The Open Journal of Astrophysics , keywords =
CosmoPower-JAX: high-dimensional Bayesian inference with differentiable cosmological emulators. The Open Journal of Astrophysics , keywords =. doi:10.21105/astro.2305.06347 , archivePrefix =. 2305.06347 , primaryClass =
-
[55]
Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument
Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument. aj , keywords =. doi:10.3847/1538-3881/ac882b , archivePrefix =. 2205.10939 , primaryClass =
work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-3881/ac882b
-
[56]
Journal of Cosmology and Astroparticle Physics , year =
Tsedrik, Maria and Bose, Benjamin and Carrilho, Pedro and Pourtsidou, Alkistis and Pamuk, Sefa and Casas, Santiago and Lesgourgues, Julien , title =. Journal of Cosmology and Astroparticle Physics , year =. doi:10.1088/1475-7516/2024/10/099 , eprint =
-
[57]
LSST: From Science Drivers to Reference Design and Anticipated Data Products , journal =
Ivezi. LSST: From Science Drivers to Reference Design and Anticipated Data Products , journal =. 2019 , month =. doi:10.3847/1538-4357/ab042c , url =
-
[58]
Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory. arXiv e-prints , keywords =. doi:10.48550/arXiv.2104.14568 , archivePrefix =. 2104.14568 , primaryClass =
-
[59]
Monthly Notices of the Royal Astronomical Society , keywords =
The BACCO simulation project: exploiting the full power of large-scale structure for cosmology. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/stab2018 , archivePrefix =. 2004.06245 , primaryClass =
-
[60]
Monthly Notices of the Royal Astronomical Society , keywords =
The BACCO simulation project: a baryonification emulator with neural networks. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/stab1911 , archivePrefix =. 2011.15018 , primaryClass =
-
[61]
Euclid: An emulator for baryonic effects on the matter bispectrum. , keywords =. doi:10.1051/0004-6361/202556061 , archivePrefix =. 2506.18974 , primaryClass =
-
[62]
Monthly Notices of the Royal Astronomical Society , keywords =
The BACCO simulation project: biased tracers in real space. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/stad2008 , archivePrefix =. 2101.12187 , primaryClass =
-
[63]
Monthly Notices of the Royal Astronomical Society , keywords =
On the road to per cent accuracy IV: ReACT - computing the non-linear power spectrum beyond CDM. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/staa2696 , archivePrefix =. 2005.12184 , primaryClass =
-
[64]
The Open Journal of Astrophysics , keywords =
mochi\_class: Modelling Optimisation to Compute Horndeski In class. The Open Journal of Astrophysics , keywords =. doi:10.33232/001c.123470 , archivePrefix =. 2407.11968 , primaryClass =
-
[65]
Journal of Cosmology and Astroparticle Physics , abstract =
Bellini, Emilio and Sawicki, Ignacy and Zumalacárregui, Miguel , title =. Journal of Cosmology and Astroparticle Physics , abstract =. 2020 , month =. doi:10.1088/1475-7516/2020/02/008 , url =
-
[66]
Euclid preparation: IX. EuclidEmulator2 - power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations. Monthly Notices of the Royal Astronomical Society , keywords =. doi:10.1093/mnras/stab1366 , archivePrefix =. 2010.11288 , primaryClass =
-
[67]
Sakr, Z. and Martinelli, M. , title =. Journal of Cosmology and Astroparticle Physics , abstract =. 2022 , month =. doi:10.1088/1475-7516/2022/05/030 , url =
-
[68]
The FLAMINGO project: baryon effects on the matter power spectrum. , keywords =. doi:10.1093/mnras/staf569 , archivePrefix =. 2410.17109 , primaryClass =
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.