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 nonGaussian 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 ( ${\mathrm{D}}^{3}\mathrm{M}$), which learns from a set of prerun numerical simulations, to predict the nonlinear largescale 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 ${\mathrm{D}}^{3}\mathrm{M}$ outperforms the secondorder perturbation theory (2LPT), the commonly used fastapproximate simulation method, in predicting cosmic structure in the nonlinear regime. We also show that ${\mathrm{D}}^{3}\mathrm{M}$ 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:

 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); Univ. of Tokyo (Japan)
 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 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)
 Univ. of British Columbia, Vancouver, BC (Canada)
 Flatiron Inst. New York, NY (United States)
 Carnegie Mellon Univ., Pittsburgh, PA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Laboratory (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:
 AC0205CH11231; 15WFIRST150008; 12EUCLID120004
 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 00278424
 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. https://doi.org/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. https://doi.org/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 nonGaussian 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 largescale 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 secondorder perturbation theory (2LPT), the commonly used fastapproximate 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}
}
Web of Science
Figures / Tables:
Works referenced in this record:
How filaments of galaxies are woven into the cosmic web
journal, April 1996
 Bond, J. Richard; Kofman, Lev; Pogosyan, Dmitry
 Nature, Vol. 380, Issue 6575
The Baryon Oscillation Spectroscopic Survey of SdssIii
journal, December 2012
 Dawson, Kyle S.; Schlegel, David J.; Ahn, Christopher P.
 The Astronomical Journal, Vol. 145, Issue 1
Computing the threepoint 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
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
A new parallel code for very largescale cosmological simulations
journal, December 1998
 MacFarland, Tom; Couchman, H. M. P.; Pearce, F. R.
 New Astronomy, Vol. 3, Issue 8
The SdssIv Extended Baryon Oscillation Spectroscopic Survey: Overview and Early data
journal, February 2016
 Dawson, Kyle S.; Kneib, JeanPaul; Percival, Will J.
 The Astronomical Journal, Vol. 151, Issue 2
Deep learning
journal, May 2015
 LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey
 Nature, Vol. 521, Issue 7553
Planck 2015 results : X. Diffuse component separation: Foreground maps
journal, September 2016
 Adam, R.; Ade, P. A. R.; Aghanim, N.
 Astronomy & Astrophysics, Vol. 594
Mastering the game of Go with deep neural networks and tree search
journal, January 2016
 Silver, David; Huang, Aja; Maddison, Chris J.
 Nature, Vol. 529, Issue 7587
The Zel'dovich approximation
journal, February 2014
 White, Martin
 Monthly Notices of the Royal Astronomical Society, Vol. 439, Issue 4
nbodykit: An Opensource, Massively Parallel Toolkit for Largescale Structure
journal, September 2018
 Hand, Nick; Feng, Yu; Beutler, Florian
 The Astronomical Journal, Vol. 156, Issue 4
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
DeepSphere: Efficient spherical convolutional neural network with HEALPix sampling for cosmological applications
journal, April 2019
 Perraudin, N.; Defferrard, M.; Kacprzak, T.
 Astronomy and Computing, Vol. 27
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)
Cosmology and Fundamental Physics with the Euclid Satellite
journal, September 2013
 Amendola, Luca; Appleby, Stephen; Bacon, David
 Living Reviews in Relativity, Vol. 16, Issue 1
VNet: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation
conference, October 2016
 Milletari, Fausto; Navab, Nassir; Ahmadi, SeyedAhmad
 2016 Fourth International Conference on 3D Vision (3DV)
FastPM: a new scheme for fast simulations of dark matter and haloes
journal, August 2016
 Feng, Yu; Chu, ManYat; Seljak, Uroš
 Monthly Notices of the Royal Astronomical Society, Vol. 463, Issue 3
CMU DeepLens: deep learning for automatic imagebased 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
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
Planck 2015 results : XXIII. The thermal SunyaevZeldovich effectcosmic infrared background correlation
journal, September 2016
 Ade, P. A. R.; Aghanim, N.; Arnaud, M.
 Astronomy & Astrophysics, Vol. 594
Predicting the sequence specificities of DNA and RNAbinding proteins by deep learning
journal, July 2015
 Alipanahi, Babak; Delong, Andrew; Weirauch, Matthew T.
 Nature Biotechnology, Vol. 33, Issue 8
Bayesian physical reconstruction of initial conditions from largescale structure surveys
journal, April 2013
 Jasche, Jens; Wandelt, Benjamin D.
 Monthly Notices of the Royal Astronomical Society, Vol. 432, Issue 2
Planck 2015 results : XIII. Cosmological parameters
journal, September 2016
 Ade, P. A. R.; Aghanim, N.; Arnaud, M.
 Astronomy & Astrophysics, Vol. 594
The 2dF Galaxy Redshift Survey: spectra and redshifts
journal, December 2001
 Colless, Matthew; Dalton, Gavin; Maddox, Steve
 Monthly Notices of the Royal Astronomical Society, Vol. 328, Issue 4
GADGET: a code for collisionless and gasdynamical cosmological simulations
journal, April 2001
 Springel, Volker; Yoshida, Naoki; White, Simon D. M.
 New Astronomy, Vol. 6, Issue 2
Lagrangian theory of gravitational instability of FriedmanLematre cosmologies  a generic thirdorder model for nonlinear clustering
journal, April 1994
 Buchert, T.
 Monthly Notices of the Royal Astronomical Society, Vol. 267, Issue 4
The initial conditions of the Universe from constrained simulations
journal, November 2012
 Kitaura, FranciscoShu
 Monthly Notices of the Royal Astronomical Society: Letters, Vol. 429, Issue 1
Planck 2015 results : XVI. Isotropy and statistics of the CMB
journal, September 2016
 Ade, P. A. R.; Aghanim, N.; Akrami, Y.
 Astronomy & Astrophysics, Vol. 594
Solving the quantum manybody problem with artificial neural networks
journal, February 2017
 Carleo, Giuseppe; Troyer, Matthias
 Science, Vol. 355, Issue 6325
Star–galaxy classification using deep convolutional neural networks
journal, October 2016
 Kim, Edward J.; Brunner, Robert J.
 Monthly Notices of the Royal Astronomical Society, Vol. 464, Issue 4
UNet: Convolutional Networks for Biomedical Image Segmentation
book, November 2015
 Ronneberger, Olaf; Fischer, Philipp; Brox, Thomas
 Medical Image Computing and ComputerAssisted Intervention – MICCAI 2015: 18th International Conference, Munich, Germany, October 59, 2015, Proceedings, Part III
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
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)
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
LongTerm Recurrent Convolutional Networks for Visual Recognition and Description
journal, April 2017
 Donahue, Jeff; Hendricks, Lisa Anne; Rohrbach, Marcus
 IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 39, Issue 4
Planck 2015 results : XXVI. The Second
journal, September 2016
 Ade, P. A. R.; Aghanim, N.; Argüeso, F.
 Astronomy & Astrophysics, Vol. 594
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
Exploring the posterior surface of the large scale structure reconstruction
journal, July 2018
 Feng, Yu; Seljak, Uroš; Zaldarriaga, Matias
 Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 07
SdssIii: Massive Spectroscopic Surveys of the Distant Universe, the Milky way, and ExtraSolar Planetary Systems
journal, August 2011
 Eisenstein, Daniel J.; Weinberg, David H.; Agol, Eric
 The Astronomical Journal, Vol. 142, Issue 3
Humanlevel control through deep reinforcement learning
journal, February 2015
 Mnih, Volodymyr; Kavukcuoglu, Koray; Silver, David
 Nature, Vol. 518, Issue 7540
Opportunities and obstacles for deep learning in biology and medicine
journal, April 2018
 Ching, Travers; Himmelstein, Daniel S.; BeaulieuJones, Brett K.
 Journal of The Royal Society Interface, Vol. 15, Issue 141
Cosmology and fundamental physics with the Euclid satellite
text, January 2018
 Amendola, Luca; Appleby, Stephen; Avgoustidis, Anastasios
 ETH Zurich
The 6dF Galaxy Survey: final redshift release (DR3) and southern largescale structures
journal, October 2009
 Jones, D. Heath; Read, Mike A.; Saunders, Will
 Monthly Notices of the Royal Astronomical Society, Vol. 399, Issue 2
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
Longterm recurrent convolutional networks for visual recognition and description
conference, June 2015
 Donahue, Jeff; Hendricks, Lisa Anne; Guadarrama, Sergio
 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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
Planning chemical syntheses with deep neural networks and symbolic AI
journal, March 2018
 Segler, Marwin H. S.; Preuss, Mike; Waller, Mark P.
 Nature, Vol. 555, Issue 7698
DeepCMB: Lensing reconstruction of the cosmic microwave background with deep neural networks
journal, July 2019
 Caldeira, J.; Wu, W. L. K.; Nord, B.
 Astronomy and Computing, Vol. 28
The evolution of largescale structure in a universe dominated by cold dark matter
journal, May 1985
 Davis, M.; Efstathiou, G.; Frenk, C. S.
 The Astrophysical Journal, Vol. 292
Helmholtz decomposition of the Lagrangian displacement
journal, April 2014
 Chan, Kwan Chuen
 Physical Review D, Vol. 89, Issue 8
Cosmology and fundamental physics with the Euclid satellite
text, January 2012
 Amendola, Luca; Appleby, Stephen; Bacon, David
 arXiv
The Baryon Oscillation Spectroscopic Survey of SDSSIII
text, January 2012
 Dawson, Kyle S.; Schlegel, David J.; Ahn, Christopher P.
 arXiv
Longterm Recurrent Convolutional Networks for Visual Recognition and Description
preprint, January 2014
 Donahue, Jeff; Hendricks, Lisa Anne; Rohrbach, Marcus
 arXiv
Planck 2015 results. XIII. Cosmological parameters
text, January 2015
 Collaboration, Planck; Ade, P. A. R.; Aghanim, N.
 arXiv
The SDSSIV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data
text, January 2015
 Dawson, Kyle S.; Kneib, JeanPaul; Percival, Will J.
 arXiv
Photometric Supernova Classification With Machine Learning
text, January 2016
 Lochner, Michelle; McEwen, Jason D.; Peiris, Hiranya V.
 arXiv
VNet: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation
preprint, January 2016
 Milletari, Fausto; Navab, Nassir; Ahmadi, SeyedAhmad
 arXiv
Densely Connected Convolutional Networks
preprint, January 2016
 Huang, Gao; Liu, Zhuang; van der Maaten, Laurens
 arXiv
Exploring the posterior surface of the large scale structure reconstruction
text, January 2018
 Feng, Yu; Seljak, Uros; Zaldarriaga, Matias
 arXiv
A volumetric deep Convolutional Neural Network for simulation of mock dark matter halo catalogues
text, January 2018
 Berger, Philippe; Stein, George
 arXiv
TreePM: A code for cosmological Nbody simulations
journal, December 2002
 Bagla, J. S.
 Journal of Astrophysics and Astronomy, Vol. 23, Issue 34
DeepSphere: Efficient spherical convolutional neural network with HEALPix sampling for cosmological applications
journal, April 2019
 Perraudin, N.; Defferrard, M.; Kacprzak, T.
 Astronomy and Computing, Vol. 27
Deep learning
journal, May 2015
 LeCun, Yann; Bengio, Yoshua; Hinton, Geoffrey
 Nature, Vol. 521, Issue 7553
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
Planning chemical syntheses with deep neural networks and symbolic AI
journal, March 2018
 Segler, Marwin H. S.; Preuss, Mike; Waller, Mark P.
 Nature, Vol. 555, Issue 7698
Predicting the sequence specificities of DNA and RNAbinding proteins by deep learning
journal, July 2015
 Alipanahi, Babak; Delong, Andrew; Weirauch, Matthew T.
 Nature Biotechnology, Vol. 33, Issue 8
Deep learning for regulatory genomics
journal, August 2015
 Park, Yongjin; Kellis, Manolis
 Nature Biotechnology, Vol. 33, Issue 8
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
Exploring the posterior surface of the large scale structure reconstruction
journal, July 2018
 Feng, Yu; Seljak, Uroš; Zaldarriaga, Matias
 Journal of Cosmology and Astroparticle Physics, Vol. 2018, Issue 07
Bayesian physical reconstruction of initial conditions from largescale structure surveys
journal, April 2013
 Jasche, Jens; Wandelt, Benjamin D.
 Monthly Notices of the Royal Astronomical Society, Vol. 432, Issue 2
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
Machine learning for quantum physics
journal, February 2017
 Hush, Michael R.
 Science, Vol. 355, Issue 6325
Ready or Not, Here We Go
journal, June 2016
 Dyster, Timothy; Sheth, Sameer A.; McKhann, Guy M.
 Neurosurgery, Vol. 78, Issue 6
Cosmology and Fundamental Physics with the Euclid Satellite
journal, September 2013
 Amendola, Luca; Appleby, Stephen; Bacon, David
 Living Reviews in Relativity, Vol. 16, Issue 1
Computing the ThreePoint Correlation Function of Galaxies in $\mathcal{O}(N^2)$ Time
text, January 2015
 Slepian, Zachary; Eisenstein, Daniel J.
 arXiv
Learning Visual Predictive Models of Physics for Playing Billiards
preprint, January 2015
 Fragkiadaki, Katerina; Agrawal, Pulkit; Levine, Sergey
 arXiv
Learning Physical Intuition of Block Towers by Example
preprint, January 2016
 Lerer, Adam; Gross, Sam; Fergus, Rob
 arXiv
Accelerating Eulerian Fluid Simulation With Convolutional Networks
preprint, January 2016
 Tompson, Jonathan; Schlachter, Kristofer; Sprechmann, Pablo
 arXiv
Lagrangian theory of gravitational instability of FriedmanLemaitre cosmologies  generic thirdorder model for nonlinear clustering
text, January 1993
 Buchert, Thomas
 arXiv
A New Parallel P3M Code for Very LargeScale Cosmological Simulations
text, January 1998
 MacFarland, Tom; Couchman, H. M. P.; Pearce, F. R.
 arXiv
Works referencing / citing this record:
Toward Improved Predictions in Ungauged Basins: Exploiting the Power of Machine Learning
journal, December 2019
 Kratzert, Frederik; Klotz, Daniel; Herrnegger, Mathew
 Water Resources Research, Vol. 55, Issue 12
A Hybrid Deep Learning Approach to Cosmological Constraints from Galaxy Redshift Surveys
journal, February 2020
 Ntampaka, Michelle; Eisenstein, Daniel J.; Yuan, Sihan
 The Astrophysical Journal, Vol. 889, Issue 2
Painting halos from cosmic density fields of dark matter with physically motivated neural networks
journal, August 2019
 Kodi Ramanah, Doogesh; Charnock, Tom; Lavaux, Guilhem
 Physical Review D, Vol. 100, Issue 4
Unveiling the predictive power of static structure in glassy systems
journal, April 2020
 Bapst, V.; Keck, T.; GrabskaBarwińska, A.
 Nature Physics, Vol. 16, Issue 4
Painting halos from cosmic density fields of dark matter with physically motivated neural networks
text, January 2019
 Ramanah, Doogesh Kodi; Charnock, Tom; Lavaux, Guilhem
 arXiv
A Hybrid Deep Learning Approach to Cosmological Constraints From Galaxy Redshift Surveys
text, January 2019
 Ntampaka, Michelle; Eisenstein, Daniel J.; Yuan, Sihan
 arXiv
Investigating cosmological GAN emulators using latent space interpolation
journal, July 2021
 Tamosiunas, Andrius; Winther, Hans A.; Koyama, Kazuya
 Monthly Notices of the Royal Astronomical Society, Vol. 506, Issue 2
Learning to Simulate Complex Physics with Graph Networks
preprint, January 2020
 SanchezGonzalez, Alvaro; Godwin, Jonathan; Pfaff, Tobias
 arXiv
Learning effective physical laws for generating cosmological hydrodynamics with Lagrangian Deep Learning
text, January 2020
 Dai, Biwei; Seljak, Uros
 arXiv
Fast and Accurate NonLinear Predictions of Universes with Deep Learning
preprint, January 2020
 de Oliveira, Renan Alves; Li, Yin; VillaescusaNavarro, Francisco
 arXiv
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