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Peer-reviewedCC BY 4.0The Astrophysical Journal

Introducing sapphire : Towards Hybrid Physics-informed, Data-driven Modeling of Galaxy Formation

  • Viraj Pandya1
  • Greg L. Bryan1,2
  • T. Lucas Makinen3,4
  • Austen Gabrielpillai1
  • Christopher Carr1,5
  • Drummond B. Fielding6
  • Lars Hernquist7
  • Matthew Ho1
  • Kartheik Iyer1,2
  • Christian Kragh Jespersen5
  • Sophie Koudmani8,3
  • Marta Laska9
9 more authors
  • Pablo Lemos10,11,12
  • Christopher C. Lovell3,13
  • Lucia A. Perez2,5
  • William F. Robinson1
  • Rachel S. Somerville2
  • Tjitske K. Starkenburg14,15
  • Richard Stiskalek16
  • Bryan Terrazas17
  • G. Mark Voit18
18 affiliations
  1. 1Columbia University
  2. 2Flatiron Institute
  3. 3University of Cambridge
  4. 4Imperial Centre for Inference and Cosmology (ICIC) & Astrophysics Group
  5. 5Princeton University
  6. 6New York University
  7. 7Center for Astrophysics—Harvard & Smithsonian
  8. 8University of Hertfordshire
  9. 9The Pennsylvania State University
  10. 10Université de Montréal
  11. 11Mila - Quebec AI Institute
  12. 12Ciela
  13. 13Institute of Astronomy
  14. 14Northwestern University
  15. 15NSF-Simons AI Institute for the Sky (SkAI)
  16. 16University of Oxford
  17. 17Oberlin College
  18. 18Michigan State University
Open at sourcePDFDOICite

Abstract

Semianalytic models (SAMs) have been treating galaxy populations as dynamical systems for ≳50 yr, but their evolution equations remain poorly constrained. We introduce sapphire , a modular, automatically differentiable, GPU-accelerated SAM written in JAX . For the first time, we compute exact Jacobian and Hessian matrices of a galaxy formation SAM, using the V. Pandya et al. (2023) nonlinear differential equation system as an example. These allow efficient, interpretable local and global sensitivity analyses, which reveal that supernova energy loading is the key astrophysical parameter. We use gradient descent and Hamiltonian Monte Carlo (HMC) to perform comprehensive mock parameter recovery tests. These indicate that the z = 0 stellar-to-halo-mass relation alone does not contain enough information to infer many astrophysical parameters. Using observations of star-forming galaxies from the MaNGA survey and the P. Behroozi et al. (2019) empirical model as one baseline, we derive multiple posteriors assuming different combinations of data, including z = 0 interstellar medium gas fractions and metallicities. The inferred physical parameters suggest that galaxies self-regulate their star formation primarily through preventative rather than ejective feedback, though this remains uncertain due to the lack of satellite galaxies, black holes, and multiphase galactic atmosphere physics. Both Fisher and HMC forecasts demonstrate the potential of sapphire to enable precision inference for galaxy formation and cosmology in a hybrid physics-informed, data-driven way, but more work is needed to expand its library of models and methods. We make sapphire publicly available at https://github.com/virajpandya/sapphire .

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Cite

BibTeXRIS
BibTeX
@article{pandya2026introducing,
  title = {{Introducing sapphire : Towards Hybrid Physics-informed, Data-driven Modeling of Galaxy Formation}},
  author = {Viraj Pandya and Greg L. Bryan and T. Lucas Makinen and Austen Gabrielpillai and Christopher Carr and Drummond B. Fielding and Lars Hernquist and Matthew Ho and Kartheik Iyer and Christian Kragh Jespersen and Sophie Koudmani and Marta Laska and Pablo Lemos and Christopher C. Lovell and Lucia A. Perez and William F. Robinson and Rachel S. Somerville and Tjitske K. Starkenburg and Richard Stiskalek and Bryan Terrazas and G. Mark Voit},
  journal = {The Astrophysical Journal},
  year = {2026},
  month = oct,
  doi = {10.3847/1538-4357/aea55e},
  url = {https://iopscience.iop.org/article/10.3847/1538-4357/aea55e},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Introducing sapphire : Towards Hybrid Physics-informed, Data-driven Modeling of Galaxy Formation
AU  - Viraj Pandya
AU  - Greg L. Bryan
AU  - T. Lucas Makinen
AU  - Austen Gabrielpillai
AU  - Christopher Carr
AU  - Drummond B. Fielding
AU  - Lars Hernquist
AU  - Matthew Ho
AU  - Kartheik Iyer
AU  - Christian Kragh Jespersen
AU  - Sophie Koudmani
AU  - Marta Laska
AU  - Pablo Lemos
AU  - Christopher C. Lovell
AU  - Lucia A. Perez
AU  - William F. Robinson
AU  - Rachel S. Somerville
AU  - Tjitske K. Starkenburg
AU  - Richard Stiskalek
AU  - Bryan Terrazas
AU  - G. Mark Voit
PY  - 2026
DA  - 2026/10/26
JO  - The Astrophysical Journal
DO  - 10.3847/1538-4357/aea55e
UR  - https://iopscience.iop.org/article/10.3847/1538-4357/aea55e
AB  - Semianalytic models (SAMs) have been treating galaxy populations as dynamical systems for ≳50 yr, but their evolution equations remain poorly constrained. We introduce sapphire , a modular, automatically differentiable, GPU-accelerated SAM written in JAX . For the first time, we compute exact Jacobian and Hessian matrices of a galaxy formation SAM, using the V. Pandya et al. (2023) nonlinear differential equation system as an example. These allow efficient, interpretable local and global sensitivity analyses, which reveal that supernova energy loading is the key astrophysical parameter. We use gradient descent and Hamiltonian Monte Carlo (HMC) to perform comprehensive mock parameter recovery tests. These indicate that the z = 0 stellar-to-halo-mass relation alone does not contain enough information to infer many astrophysical parameters. Using observations of star-forming galaxies from the MaNGA survey and the P. Behroozi et al. (2019) empirical model as one baseline, we derive multiple posteriors assuming different combinations of data, including z = 0 interstellar medium gas fractions and metallicities. The inferred physical parameters suggest that galaxies self-regulate their star formation primarily through preventative rather than ejective feedback, though this remains uncertain due to the lack of satellite galaxies, black holes, and multiphase galactic atmosphere physics. Both Fisher and HMC forecasts demonstrate the potential of sapphire to enable precision inference for galaxy formation and cosmology in a hybrid physics-informed, data-driven way, but more work is needed to expand its library of models and methods. We make sapphire publicly available at https://github.com/virajpandya/sapphire .
SN  - 0004-637X
SN  - 1538-4357
ER  -