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Title: Learning to predict the cosmological structure formation

Abstract

Matter evolved under the influence of gravity from minuscule density fluctuations. Nonperturbative structure formed hierarchically over all scales and developed non-Gaussian features in the Universe, known as the cosmic web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and use a large ensemble of computer simulations to compare with the observed data to extract the full information of our own Universe. However, to evolve billions of particles over billions of years, even with the simplest physics, is a daunting task. We build a deep neural network, the Deep Density Displacement Model ( D 3 M ), which learns from a set of prerun numerical simulations, to predict the nonlinear large-scale structure of the Universe with the Zel’dovich Approximation (ZA), an analytical approximation based on perturbation theory, as the input. Our extensive analysis demonstrates that D 3 M outperforms the second-order perturbation theory (2LPT), the commonly used fast-approximate simulation method, in predicting cosmic structure in the nonlinear regime. We also show that D 3 M is able to accurately extrapolate far beyond its training data and predict structure formation for significantly different cosmological parameters. Our study proves that deep learning is a practical and accurate alternative to approximate 3D simulations of the gravitational structure formation of the Universe.

Authors:
ORCiD logo [1];  [2];  [3];  [4];  [5];  [6];  [7]
  1. Carnegie Mellon Univ., Pittsburgh, PA (United States); Flatiron Inst. New York, NY (United States); Univ. of Tokyo (Japan)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Tokyo (Japan)
  3. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  4. Carnegie Mellon Univ., Pittsburgh, PA (United States); Flatiron Inst. New York, NY (United States); Univ. of Tokyo (Japan); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  5. Univ. of British Columbia, Vancouver, BC (Canada)
  6. Flatiron Inst. New York, NY (United States)
  7. Carnegie Mellon Univ., Pittsburgh, PA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); National Aeronautics and Space Administration (NASA); Simons Foundation
OSTI Identifier:
1561927
Grant/Contract Number:  
AC02-05CH11231; 15-WFIRST15-0008; 12-EUCLID12-0004
Resource Type:
Accepted Manuscript
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 116; Journal Issue: 28; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences, Washington, DC (United States)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; cosmology; deep learning; simulation

Citation Formats

He, Siyu, Li, Yin, Feng, Yu, Ho, Shirley, Ravanbakhsh, Siamak, Chen, Wei, and Póczos, Barnabás. Learning to predict the cosmological structure formation. United States: N. p., 2019. Web. doi:10.1073/pnas.1821458116.
He, Siyu, Li, Yin, Feng, Yu, Ho, Shirley, Ravanbakhsh, Siamak, Chen, Wei, & Póczos, Barnabás. Learning to predict the cosmological structure formation. United States. doi:10.1073/pnas.1821458116.
He, Siyu, Li, Yin, Feng, Yu, Ho, Shirley, Ravanbakhsh, Siamak, Chen, Wei, and Póczos, Barnabás. Mon . "Learning to predict the cosmological structure formation". United States. doi:10.1073/pnas.1821458116. https://www.osti.gov/servlets/purl/1561927.
@article{osti_1561927,
title = {Learning to predict the cosmological structure formation},
author = {He, Siyu and Li, Yin and Feng, Yu and Ho, Shirley and Ravanbakhsh, Siamak and Chen, Wei and Póczos, Barnabás},
abstractNote = {Matter evolved under the influence of gravity from minuscule density fluctuations. Nonperturbative structure formed hierarchically over all scales and developed non-Gaussian features in the Universe, known as the cosmic web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and use a large ensemble of computer simulations to compare with the observed data to extract the full information of our own Universe. However, to evolve billions of particles over billions of years, even with the simplest physics, is a daunting task. We build a deep neural network, the Deep Density Displacement Model (D3M), which learns from a set of prerun numerical simulations, to predict the nonlinear large-scale structure of the Universe with the Zel’dovich Approximation (ZA), an analytical approximation based on perturbation theory, as the input. Our extensive analysis demonstrates that D3M outperforms the second-order perturbation theory (2LPT), the commonly used fast-approximate simulation method, in predicting cosmic structure in the nonlinear regime. We also show that D3M is able to accurately extrapolate far beyond its training data and predict structure formation for significantly different cosmological parameters. Our study proves that deep learning is a practical and accurate alternative to approximate 3D simulations of the gravitational structure formation of the Universe.},
doi = {10.1073/pnas.1821458116},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 28,
volume = 116,
place = {United States},
year = {2019},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 13 works
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Figures / Tables:

Fig. 1 Fig. 1: The displacement vector field (Left) and the resulting density field (Right) produced by D3M. The vectors in Left are uniformly scaled down for better visualization.

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    Works referencing / citing this record:

    CosmoFlow: Using Deep Learning to Learn the Universe at Scale
    conference, November 2018

    • Mathuriya, Amrita; Bard, Deborah; Mendygral, Peter
    • SC18: International Conference for High Performance Computing, Networking, Storage and Analysis
    • DOI: 10.1109/sc.2018.00068

    Simulation as an engine of physical scene understanding
    journal, October 2013

    • Battaglia, P. W.; Hamrick, J. B.; Tenenbaum, J. B.
    • Proceedings of the National Academy of Sciences, Vol. 110, Issue 45
    • DOI: 10.1073/pnas.1306572110

    Bayesian physical reconstruction of initial conditions from large-scale structure surveys
    journal, April 2013

    • Jasche, Jens; Wandelt, Benjamin D.
    • Monthly Notices of the Royal Astronomical Society, Vol. 432, Issue 2
    • DOI: 10.1093/mnras/stt449

    Predicting the sequence specificities of DNA- and RNA-binding proteins by deep learning
    journal, July 2015

    • Alipanahi, Babak; Delong, Andrew; Weirauch, Matthew T.
    • Nature Biotechnology, Vol. 33, Issue 8
    • DOI: 10.1038/nbt.3300

    Fast automated analysis of strong gravitational lenses with convolutional neural networks
    journal, August 2017

    • Hezaveh, Yashar D.; Levasseur, Laurence Perreault; Marshall, Philip J.
    • Nature, Vol. 548, Issue 7669
    • DOI: 10.1038/nature23463

    The 6dF Galaxy Survey: final redshift release (DR3) and southern large-scale structures
    journal, October 2009


    Sdss-Iii: Massive Spectroscopic Surveys of the Distant Universe, the Milky way, and Extra-Solar Planetary Systems
    journal, August 2011

    • Eisenstein, Daniel J.; Weinberg, David H.; Agol, Eric
    • The Astronomical Journal, Vol. 142, Issue 3
    • DOI: 10.1088/0004-6256/142/3/72

    Newtonian Image Understanding: Unfolding the Dynamics of Objects in Static Images
    conference, June 2016

    • Mottaghi, Roozbeh; Bagherinezhad, Hessam; Rastegari, Mohammad
    • 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
    • DOI: 10.1109/cvpr.2016.383

    Cosmology and fundamental physics with the Euclid satellite
    journal, April 2018

    • Amendola, Luca; Appleby, Stephen; Avgoustidis, Anastasios
    • Living Reviews in Relativity, Vol. 21, Issue 1
    • DOI: 10.1007/s41114-017-0010-3

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    • Silver, David; Huang, Aja; Maddison, Chris J.
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    • DOI: 10.1038/nature16961

    Lagrangian theory of gravitational instability of Friedman-Lematre cosmologies - a generic third-order model for non-linear clustering
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    journal, March 2018

    • Segler, Marwin H. S.; Preuss, Mike; Waller, Mark P.
    • Nature, Vol. 555, Issue 7698
    • DOI: 10.1038/nature25978

    The Zel'dovich approximation
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    • White, Martin
    • Monthly Notices of the Royal Astronomical Society, Vol. 439, Issue 4
    • DOI: 10.1093/mnras/stu209

    DeepCMB: Lensing reconstruction of the cosmic microwave background with deep neural networks
    journal, July 2019


    Deep learning
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    • LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey
    • Nature, Vol. 521, Issue 7553
    • DOI: 10.1038/nature14539

    How filaments of galaxies are woven into the cosmic web
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    Long-term recurrent convolutional networks for visual recognition and description
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    • Feng, Yu; Seljak, Uroš; Zaldarriaga, Matias
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    Opportunities and obstacles for deep learning in biology and medicine
    journal, April 2018

    • Ching, Travers; Himmelstein, Daniel S.; Beaulieu-Jones, Brett K.
    • Journal of The Royal Society Interface, Vol. 15, Issue 141
    • DOI: 10.1098/rsif.2017.0387

    Star–galaxy classification using deep convolutional neural networks
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    • Kim, Edward J.; Brunner, Robert J.
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    Densely Connected Convolutional Networks
    conference, July 2017

    • Huang, Gao; Liu, Zhuang; Maaten, Laurens van der
    • 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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    TreePM: A code for cosmological N-body simulations
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    • Bagla, J. S.
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    The evolution of large-scale structure in a universe dominated by cold dark matter
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    • Davis, M.; Efstathiou, G.; Frenk, C. S.
    • The Astrophysical Journal, Vol. 292
    • DOI: 10.1086/163168

    A new parallel code for very large-scale cosmological simulations
    journal, December 1998


    The Sdss-Iv Extended Baryon Oscillation Spectroscopic Survey: Overview and Early data
    journal, February 2016

    • Dawson, Kyle S.; Kneib, Jean-Paul; Percival, Will J.
    • The Astronomical Journal, Vol. 151, Issue 2
    • DOI: 10.3847/0004-6256/151/2/44

    The Baryon Oscillation Spectroscopic Survey of Sdss-Iii
    journal, December 2012

    • Dawson, Kyle S.; Schlegel, David J.; Ahn, Christopher P.
    • The Astronomical Journal, Vol. 145, Issue 1
    • DOI: 10.1088/0004-6256/145/1/10

    Computing the three-point correlation function of galaxies in $\mathcal {O}(N^2)$ time
    journal, October 2015

    • Slepian, Zachary; Eisenstein, Daniel J.
    • Monthly Notices of the Royal Astronomical Society, Vol. 454, Issue 4
    • DOI: 10.1093/mnras/stv2119

    GADGET: a code for collisionless and gasdynamical cosmological simulations
    journal, April 2001


    Photometric Supernova Classification with Machine Learning
    journal, August 2016

    • Lochner, Michelle; McEwen, Jason D.; Peiris, Hiranya V.
    • The Astrophysical Journal Supplement Series, Vol. 225, Issue 2
    • DOI: 10.3847/0067-0049/225/2/31

    FastPM: a new scheme for fast simulations of dark matter and haloes
    journal, August 2016

    • Feng, Yu; Chu, Man-Yat; Seljak, Uroš
    • Monthly Notices of the Royal Astronomical Society, Vol. 463, Issue 3
    • DOI: 10.1093/mnras/stw2123

    Physics 101: Learning Physical Object Properties from Unlabeled Videos
    conference, January 2016

    • Wu, Jiajun; Lim, Joseph; Zhang, Hongyi
    • Procedings of the British Machine Vision Conference 2016
    • DOI: 10.5244/c.30.39

    The initial conditions of the Universe from constrained simulations
    journal, November 2012

    • Kitaura, Francisco-Shu
    • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 429, Issue 1
    • DOI: 10.1093/mnrasl/sls029

    A volumetric deep Convolutional Neural Network for simulation of mock dark matter halo catalogues
    journal, November 2018

    • Berger, Philippe; Stein, George
    • Monthly Notices of the Royal Astronomical Society, Vol. 482, Issue 3
    • DOI: 10.1093/mnras/sty2949

    DeepSphere: Efficient spherical convolutional neural network with HEALPix sampling for cosmological applications
    journal, April 2019


    Planck 2015 results : XIII. Cosmological parameters
    journal, September 2016


    Galaxy And Mass Assembly (GAMA): end of survey report and data release 2
    journal, July 2015

    • Liske, J.; Baldry, I. K.; Driver, S. P.
    • Monthly Notices of the Royal Astronomical Society, Vol. 452, Issue 2
    • DOI: 10.1093/mnras/stv1436

    nbodykit: An Open-source, Massively Parallel Toolkit for Large-scale Structure
    journal, September 2018


    Human-level control through deep reinforcement learning
    journal, February 2015

    • Mnih, Volodymyr; Kavukcuoglu, Koray; Silver, David
    • Nature, Vol. 518, Issue 7540
    • DOI: 10.1038/nature14236

    CMU DeepLens: deep learning for automatic image-based galaxy–galaxy strong lens finding
    journal, July 2017

    • Lanusse, François; Ma, Quanbin; Li, Nan
    • Monthly Notices of the Royal Astronomical Society, Vol. 473, Issue 3
    • DOI: 10.1093/mnras/stx1665

    V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation
    conference, October 2016

    • Milletari, Fausto; Navab, Nassir; Ahmadi, Seyed-Ahmad
    • 2016 Fourth International Conference on 3D Vision (3DV)
    • DOI: 10.1109/3dv.2016.79

    Toward Improved Predictions in Ungauged Basins: Exploiting the Power of Machine Learning
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      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.