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Cited by 48Cosmology and Gravitation TheoriesGalaxies: Formation, Evolution, PhenomenaModel Reduction and Neural Networks

Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis

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Dai, Biwei, Seljak, Uroš·2022·Monthly Notices of the Royal Astronomical Society
DOI 10.1093/mnras/stac2010
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Abstract

Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On non-linear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

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Crossref · 10.1093/mnras/stac2010

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  • The TRENF model accurately captures the high-dimensional likelihood of dark matter density fields and can be used for generating these fields and inferring cosmological parameters.

    “The authors demonstrate that this approach accurately captures the high-dimensional likelihood of dark matter density fields and that it can be used not only for generating these fields, but also for inferring cosmological parameters.”

    From The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys (2023) · cites this paper as Dai & Seljak (2022)

  • Dai & Seljak (2022) introduce a Translation and Rotation Equivariant Normalising Flow (TRENF) model.

    “In this paper, the authors introduce a Translation and Rotation Equivariant Normalising Flow (TRENF) model.”

    From The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys (2023) · cites this paper as Dai & Seljak (2022)

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Authors
Dai, B., & Seljak, U.
Affiliations
  • University of California, Berkeley (US)
  • Lawrence Berkeley National Laboratory (US)
Corresponding author
Dai, Biwei
ORCID
Venue
Monthly Notices of the Royal Astronomical Society
Publisher
Oxford University Press (OUP)
Published
2022-07-23
Volume
516
Issue
2
Pages
2363-2373
ISSN
  • 0035-8711 (ISSN-L)
  • 1365-2966
DOI
10.1093/mnras/stac2010
OpenAlex
W4226352008
Cited by
48
References
35
Citations by year
2026: 8 · 2025: 16 · 2024: 11 · 2023: 10 · 2022: 3
FWCI
4.00
Type
journal article
Language
en
Open access
Licence
academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor, 1 d)
Locations
  • Monthly Notices of the Royal Astronomical Society (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • eScholarship (California Digital Library) (submittedVersion, cc-by-nc)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1814370)
  • NASA (80NSSC18K1274)
  • U.S. Department of Energy (DE-AC02-05CH11231)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
Keywords
normalizing flows, translation equivariance, rotation equivariance, cosmological parameter estimation, likelihood-based inference, Gaussian random fields, Fisher information, N-body simulations, generative models, periodic boundary conditions, summary statistics

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