A gradient based method for modeling baryons and matter in halos of fast simulations
Open accessAbstract
Fast N-body PM simulations with a small number of time steps such as FastPM or COLA have been remarkably successful in modeling the galaxy statistics, but their lack of small scale force resolution and long time steps cannot give accurate halo matter profiles or matter power spectrum. High resolution N-body simulations can improve on this, but lack baryonic effects, which can only be properly included in hydro simulations. Here we present a scheme to calibrate the fast simulations to mimic the precision of the hydrodynamic simulations or high resolution N-body simulations. The scheme is based on a gradient descent of either effective gravitational potential, which mimics the short range force, or of effective enthalpy, which mimics gas hydrodynamics and feedback. The scheme is fast and differentiable, and can be incorporated as a post-processing step into any simulation. It gives very good results for the matter power spectrum for several of the baryonic feedback and dark matter simulations, and also gives improved dark matter halo profiles. The scheme is even able to find the large subhalos, and increase the correlation coefficient between the fast simulations and the high resolution N-body or hydro simulations. It can also be used to add baryonic effects to the high resolution N-body simulations. While the method has free parameters that can be calibrated on various simulations, they can also be viewed as astrophysical nuisance parameters describing baryonic effects that can be marginalized over during the data analysis. In this view these parameters can be viewed as an efficient parametrization of baryonic effects.
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Dai et al. (2018) can emulate to within 5% accuracy the Illustris-3 simulation from only a 10 step FastPM simulation.
“With this simple, yet powerful, scheme the authors can emulate to within 5% accuracy the Illustris-3 simulation from only a 10 step FastPM simulation.”
From The Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys (2023) · cites this paper as Dai et al. (2018)
Cites
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“Comparing to dark-matter-only simulation, AGN feedback in hydrodynamical simulation moves a large amount of gas from the center of halos to large radii [8, 10].”
BackgroundFastPM: a new scheme for fast simulations of dark matter and haloes
Feng, Y., Chu, M., Seljak, U., & McDonald, P. (2016) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw2123 · Cited by 177 · cited 5× · see citing works
“Although the halo catalog from the quasi N-body simulations are well correlated to a true N-body simulation of the same initial condition [1], the dark matter density distribution is less accurate, since it requires not just the center of mass of a dark matter halo but also its density profile.”
BackgroundMethodResultInfluentialSelf-citationThe impact of galaxy formation on the total mass, mass profile and abundance of haloes
Velliscig, M., van Daalen, M. P., Schaye, J., McCarthy, I. G., Cacciato, M., Brun, A. M. C. L., & Vecchia, C. D. (2014) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stu1044 · Cited by 176 · see citing works
A new method to quantify the effects of baryons on the matter power spectrum
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Towards optimal extraction of cosmological information from nonlinear data
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Kitaura, F.-S., & Heß, S. (2013) · Monthly Notices of the Royal Astronomical Society Letters · doi:10.1093/mnrasl/slt101 · Cited by 106 · cited 2× · see citing works
“However, ALPT assumed the analytical spherical collapse model and determined the small scale displacement with local density, while our method is based on a PM solver and solves a modified potential.”
ResultLarge-scale mass distribution in the Illustris simulation
Haider, M., Steinhauser, D., Vogelsberger, M., Genel, S., Springel, V., Torrey, P., & Hernquist, L. (2016) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw077 · Cited by 86 · see citing works
Dark matter statistics for large galaxy catalogues: power spectra and covariance matrices
Klypin, A. A., & Prada, F. (2018) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/sty1340 · Cited by 78 · cited 1× · see citing works
“Methods in this family includes FastPM [1], COLA [2], subcycle TreePM [3], and PPM-GLAM [4].”
MethodICE-COLA: towards fast and accurate synthetic galaxy catalogues optimizing a quasi-N-body method
Izard, A., Crocce, M., & Fosalba, P. (2015) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw797 · Cited by 71 · cited 1× · see citing works
“[5] proposed ICE-COLA, in which the code parameters are optimized to achieve a matter power spectrum within 1 percent for k .”
MethodRECONSTRUCTING THE INITIAL DENSITY FIELD OF THE LOCAL UNIVERSE: METHODS AND TESTS WITH MOCK CATALOGS
Wang, H.-Y., Mo, H.-J., Yang, X.-H., & van den Bosch, F. C. (2013) · The Astrophysical Journal · doi:10.1088/0004-637x/772/1/63 · Cited by 64 · see citing works
The contributions of matter inside and outside of haloes to the matter power spectrum
van Daalen, M. P., & Schaye, J. (2015) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stv1456 · Cited by 56 · see citing works
Exploring ντ−νsmixing with cascade events in DeepCore
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Leclercq, F., Jasche, J., Gil-Marín, H., & Wandelt, B. D. (2013) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2013/11/048 · Cited by 33 · see citing works
Truthing the stretch: non-perturbative cosmological realizations with multiscale spherical collapse
Neyrinck, M. C. (2015) · Monthly Notices of the Royal Astronomical Society Letters · doi:10.1093/mnrasl/slv141 · Cited by 26 · cited 1× · see citing works
“Other similar methods include one point remapping [16] and MUSCLE [17].”
MethodEfficient construction of mock catalogs for baryon acoustic oscillation surveys
Sunayama, T., Padmanabhan, N., Heitmann, K., Habib, S., & Rangel, E. (2016) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2016/05/051 · Cited by 15 · see citing works
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Quantifying baryon effects on the matter power spectrum and the weak lensing shear correlation
Schneider, A., Teyssier, R., Stadel, J., Chisari, N., Brun, A. L., Amara, A., & Réfrégier, A. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/03/020 · Cited by 142 · see citing works
Large-scale dark matter simulations
Angulo, R., & Hahn, O. (2021) · Living Reviews in Computational Astrophysics · doi:10.1007/s41115-021-00013-z · Cited by 119 · see citing works
The Websky extragalactic CMB simulations
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“Rather, small scale observations and hydrodynamic simulations can be used to calibrate efficient large-scale models by a halo model [58] or the dark matter-only distribution [59].”
Modelling baryonic physics in future weak lensing surveys
Huang, H.-J., Eifler, T. F., Mandelbaum, R., & Dodelson, S. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz1714 · Cited by 114 · see citing works
“Finally, a gradient-based method is proposed recently by Dai et al. (2018).”
MethodThe Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys
Huertas-Company, M., & Lanusse, F. (2023) · Publications of the Astronomical Society of Australia · doi:10.1017/pasa.2022.55 · Cited by 102 · see citing works
“The method proposed in Dai et al. (2018) is to learn an additional displacement of the particles, moving them deeper into their local gravitational potential, which has the effect of sharpening the halo profiles.”
MethodInfluentialAI-assisted superresolution cosmological simulations
Li, Y., Ni, Y., Croft, R. A. C., Matteo, T. D., Bird, S., & Yu, F. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2022038118 · Cited by 99 · see citing works
“In other work, (17, 18) sharpened the particle distribution using a potential gradient descent (PGD) method starting from low-resolution simulations.”
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A hydrodynamical halo model for weak-lensing cross correlations
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“A variant of this method is investigated by Dai et al. (2018) who use the actual equations of motion governing gas physics to perform the halo deformation.”
MethodSingh, S., Mandelbaum, R., Seljak, U., Rodríguez-Torres, S. A., & Slosar, A. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz2922 · Cited by 64 · see citing works
“To estimate the impact of such changes, we compute the ratio of the projected matter distribution around haloes in dark matter only and Illustris simulations (Genel et al. 2014) using halo profiles provided by Dai et al. (2018), as shown in Fig.”
MethodSelf-citationTranslation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis
Dai, B., & Seljak, U. (2022) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stac2010 · Cited by 48 · see citing works
Self-citationDark energy survey year 1 results: Constraining baryonic physics in the Universe
Huang, H.-J., Eifler, T. F., Mandelbaum, R., Bernstein, G. M., Chen, A., Choi, A., García-Bellido, J., Dragan Huterer, A., Krause, E., Rozo, E., et al. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab357 · Cited by 47 · see citing works
Horowitz, B., Lee, K., White, M., Krolewski, A., & Ata, M. (2019) · Astrophysical Journal · doi:10.3847/1538-4357/ab4d4c · Cited by 36 · see citing works
Dai, B., & Seljak, U. (2020) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.2020324118 · Cited by 37 · see citing works
“…of such a process applied to time and spatial coarse graining is the dark matter evolution with a few time steps only, which combines ideas such as the approximate N-body solvers, with a force sharpening process called the Potential Gradient Descent (PGD) to capture the coarse graining [31, 32].”
BackgroundMethodSelf-citationBayer, A., Banerjee, A., & Feng, Y. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2021/01/016 · Cited by 39 · see citing works
“all scales, typically . 1Mpc=h, this has recently been addressed within FastPM by traversing the gravitational potential using gradient descent techniques to increase the small scale force resolution [73]. The purpose of this work is to add neutrino particles to FastPM by employing the methods of [67] to enable study…”
MethodSelf-citationκTNG: effect of baryonic processes on weak lensing with IllustrisTNG simulations
Osato, K., Liu, J., & Haiman, Z. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab395 · Cited by 23 · see citing works
Accurate predictions from small boxes: variance suppression via the Zel'dovich approximation
Kokron, N., Chen, S.-F., White, M. J., DeRose, J., & Maus, M. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/09/059 · Cited by 31 · see citing works
Effective cosmic density field reconstruction with convolutional neural network
Chen, X., Zhu, F., Gaines, S., & Padmanabhan, N. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad1868 · Cited by 24 · see citing works
“Moreover, CNN also helps generate cosmological simulations more rapidly, by learning 𝑁-body simulations, or 𝑁-body emulation with deep learning, etc. (e.g., Dai et al. 2018; Mustafa et al. 2019).”
BackgroundHorowitz, B., Zhang, B. J., Lee, K., & Kooistra, R. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/abca35 · Cited by 14 · see citing works
Enabling matter power spectrum emulation in beyond-ΛCDM cosmologies with COLA
Brando, G., Fiorini, B., Koyama, K., & Winther, H. A. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/09/051 · Cited by 22 · see citing works
“There are several methods proposed to improve the accuracy of COLA and PM simulations [17, 26, 48].”
BackgroundMethodHigh mass and halo resolution from fast low resolution simulations
Dai, B., Feng, Y., Seljak, U., & Singh, S. (2020) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/04/002 · Cited by 22 · see citing works
“We show that the fully coupled PGD correction improves the matter power spectrum measured from static snapshot at all redshifts, just as the previously studied static PGD method [10].”
BackgroundMethodInfluentialSelf-citationEffects of baryonic feedback on the cosmic web
Sunseri, J., Li, Z., & Liu, J. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.023514 · Cited by 19 · see citing works
Fast and realistic large-scale structure from machine-learning-augmented random field simulations
Piras, D., Joachimi, B., & Villaescusa-Navarro, F. (2023) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stad052 · Cited by 19 · see citing works
MADLens, a python package for fast and differentiable non-Gaussian lensing simulations
Böhm, V., Feng, Y., Lee, M. E., & Dai, B. (2020) · Astronomy and Computing · doi:10.1016/j.ascom.2021.100490 · Cited by 16 · see citing works
“Another, more safeguard approach is to use machinelearning inspired techniques to boost the accuracy of low resolution N-body simulations (Dai et al., 2020; Dai and Seljak, 2020) and to construct lightcones from those.”
BackgroundSelf-citationA field-level emulator for modelling baryonic effects across hydrodynamic simulations
Anonymous, Dai, B., Villaescusa-Navarro, F., & Seljak, U. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf355 · Cited by 13 · see citing works
Self-citationXu, J., Eifler, T. F., Miranda, V., Fang, X., Saraivanov, E., Krause, E., Huang, H.-J., Benabed, K., & Zhong, K. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.063532 · Cited by 11 · see citing works
Horowitz, B., & Lukić, Z. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf1785 · Cited by 8 · see citing works
syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum
Kammerer, L., Bartlett, D. J., Kronberger, G., Desmond, H., & Ferreira, P. G. (2025) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202555887 · Cited by 5 · see citing works
The Cosmological analysis of X-ray cluster surveys
Cerardi, N., Pierre, M., Lanusse, F., & Corap, X. (2025) · Astronomy and Astrophysics · doi:10.1051/0004-6361/202453553 · Cited by 4 · see citing works
Doeser, L., Ata, M., & Jasche, J. (2025) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staf1289 · Cited by 4 · see citing works
Dynamic zoom simulations: A fast, adaptive algorithm for simulating light-cones
Garaldi, E., Nori, M., & Baldi, M. (2020) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/staa2064 · Cited by 4 · see citing works
“Additionally, this method does not allow the treatment of baryons (although it has been proposed to use a gradient-based method to mimic the output of hydrodynamical simulations, at the cost of introducing nuisance parameters, see e.g. Dai et al. 2018).”
MethodImproving the accuracy of halo mass based statistics for fast approximate N-body simulations
Wu, Y., Guo, H., & Springel, V. (2024) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stae1439 · Cited by 2 · see citing works
Modeling nonlinear scales with the comoving Lagrangian acceleration method: Preparing for LSST Y1
Gordon, J., de Aguiar, B. F., Rebouças, J., Brando, G., Falciano, F. T., Miranda, V., Koyama, K., & Winther, H. A. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.083529 · Cited by 2 · see citing works
Cosmological Analysis with Calibrated Neural Quantile Estimation and Approximate Simulators
He, J. (2026) · Physical Review Letters · doi:10.1103/d2dl-kznp · Cited by 1 · see citing works
“However, for practical applications involving halo models and/or redshift-space observables, Lagrangian-space emulators [26–28, 30 While this work focuses on inference performance under the assumption that the high-fidelity simulations perfectly represent real-world data, we do not address the…”
Anonymous, & Zhang, P. (2026) · Physical Review Letters · doi:10.1103/8kpm-r54z · Cited by 1 · see citing works
Suppressing the sample variance of DESI-like galaxy clustering with fast simulations
Ding, Z., Variu, A., Alam, S., Yu, Y., Chuang, C.-H., Paillas, E., García-Quintero, C., Chen, X., Mena-Fernández, J., Aguilar, J., et al. (2025) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2025/01/143
“In addition, several methods have been proposed to further improve the FastPM matter and halo clustering at small scales [62, 63].”
- Authors
- Dai, B., Feng, Y., & Seljak, U.
- Affiliations
- Peking University (CN)
- University of California, Berkeley (US)
- Lawrence Berkeley National Laboratory (US)
- Venue
- Journal of Cosmology and Astroparticle Physics
- Publisher
- IOP Publishing
- Published
- 2018-11-07
- Volume
- 2018
- Issue
- 11
- Pages
- 009-009
- ISSN
- 1475-7508 (ISSN-L)
- 1475-7516
- OpenAlex
- W2795959938
- Cited by
- 35
- References
- 34
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 3 · 2023: 4 · 2022: 4 · 2021: 7 · 2020: 5 · 2019: 4
- FWCI
- 2.15
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Journal of Cosmology and Astroparticle Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Aeronautics and Space Administration (NNX15AL17G)
- National Energy Research Scientific Computing Center
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Galaxies: Formation, Evolution, Phenomena
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Dark Matter and Cosmic Phenomena
- Keywords
- cola, effective gravitational potential, baryonic feedback, dark matter halo profiles, matter power spectrum, subhalos, hydrodynamic modeling
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