Differentiable Halo Mass Prediction and the Cosmology-Dependence of Halo Mass Functions

[2507.03074] Differentiable Halo Mass Prediction and the Cosmology-Dependence of Halo Mass Functions Skip to main content Search Submit Donate Log in Astrophysics > Cosmology and Nongalactic Astrophysics arXiv:2507.03074 (astro-ph) [Submitted on 3 Jul 2025 ( v1 ), last revised 23 Aug 2026 (this version, v2)] Title: Differentiable Halo Mass Prediction and the Cosmology-Dependence of Halo Mass Functions Authors: Jim Buisman , Florian List , Oliver Hahn View PDF HTML (experimental) Abstract: Modern cosmological inference increasingly relies on differentiable models to enable efficient, gradient-based parameter estimation and uncertainty quantification. Here, we present a novel approach for predicting the abundance of dark matter haloes and their cosmology dependence using a differentiable, field-level neural network (NN) model, and study how well the cosmology dependence is captured by common parametrisations of the halo mass function (HMF), and by our NN-based approach. By training a 3D U-Net on initial density fields from fast N-body simulations with varying cosmological parameters, we enable direct, differentiable mapping from the linear density field to protohalo patches and their mass bins. Our method achieves competitive accuracy in identifying protohalo regions and in capturing the dependence of the HMF on cosmological parameters. Our NN derivatives agree well with finite differences of both analytical and emulated HMFs, at the level of the disagreement among the different models. We further demonstrate how the NN model can additionally be used to investigate the response of the HMF to changes in the initial Gaussian random field. Finally, we also demonstrate that a differentiable model can be used to extrapolate existing models at very high precision. Comments: 14 + 5 pages, 11 + 5 figures, Published in the Open Journal of Astrophysics, comments welcome Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO) ; Astrophysics of Galaxies (astro-ph.GA) Cite as: arXiv:2507.03074 [astro-ph.CO] (or arXiv:2507.03074v2 [astro-ph.CO] for this version) https://doi.org/10.48550/arXiv.2507.03074 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Open Journal of Astrophysics, Vol. 9, 2026 Related DOI : https://doi.org/10.33232/001c.168410 Focus to learn more DOI(s) linking to related resources Submission history From: Jim Buisman [ view email ] [v1] Thu, 3 Jul 2025 18:00:02 UTC (3,198 KB) [v2] Sun, 23 Aug 2026 17:05:49 UTC (3,827 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: astro-ph.CO < prev | next > new | recent | 2025-07 Change to browse by: astro-ph astro-ph.GA References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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