- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Flexible, GPU-accelerated approach for the joint characterization of LISA instrumental noise and stochastic gravitational wave backgrounds

Alessandro Santini1,*, Martina Muratore1, Jonathan Gair1, and Olaf Hartwig1,2,3

  • *Contact author: alessandro.santini@aei.mpg.de
PDF

Phys. Rev. D 112, 084050 – Published 17 October, 2025

DOI: https://doi.org/10.1103/csx9-9trp

Abstract

LISA data analysis represents one of the most challenging tasks ahead for gravitational wave (GW) astronomy. Characterizing the instrument’s noise properties while fitting for all the other detectable sources is a key requirement of any robust inference pipeline. Noise estimation will also play a crucial role in searches and parameter estimation of cosmological and astrophysical stochastic signals. Previous studies have tackled this topic by assuming perfect knowledge of the spectral shape of the instrumental noise and of different possible types of stochastic GW backgrounds (SGWBs), usually resorting to parametrized templates. Recently, various works that employ template-agnostic methods have been presented. In this work, we take an additional step further, introducing flexible spectral shapes in both the instrumental noise and the stochastic signals. We account for the lack of knowledge of the exact shape of the individual contributions to the overall power spectral density by using splines to represent arbitrary perturbations of the noise and signal spectral densities. We implement a data-driven reversible jump Markov chain Monte Carlo algorithm to fit different components simultaneously and to infer the level of flexibility required under different scenarios. We test this approach on simulated LISA data produced under different assumptions. We investigate the impact of this increased flexibility on the reconstruction of both the injected signal and the noise level, and we discuss the prospects for claiming a successful SGWB detection.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (119)

  1. M. Colpi et al., .
  2. B. P. Abbott et al., Phys. Rev. X 9, 031040 (2019).
  3. R. Abbott et al., Phys. Rev. X 11, 021053 (2021).
  4. R. Abbott et al., Phys. Rev. D 109, 022001 (2024).
  5. R. Abbott et al., Phys. Rev. X 13, 041039 (2023).
  6. J. Antoniadis et al. (EPTA Collaboration and InPTA Collaboration), Astron. Astrophys. 685, A94 (2024).
  7. A. Afzal et al. (NANOGrav Collaboration), Astrophys. J. Lett. 951, L11 (2023); 971, L27(E) (2024).
  8. D. J. Reardon et al., Astrophys. J. Lett. 951, L6 (2023).
  9. H. Xu et al., Res. Astron. Astrophys. 23, 075024 (2023).
  10. A. Klein et al., Phys. Rev. D 93, 024003 (2016).
  11. V. Korol et al., Astron. Astrophys. 638, A153 (2020).
  12. S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau, and A. Klein, Phys. Rev. D 95, 103012 (2017).
  13. D. Gerosa, S. Ma, K. W. K. Wong, E. Berti, R. O’Shaughnessy, Y. Chen, and K. Belczynski, Phys. Rev. D 99, 103004 (2019).
  14. R. Buscicchio, A. Klein, E. Roebber, C. J. Moore, D. Gerosa, E. Finch, and A. Vecchio, Phys. Rev. D 104, 044065 (2021).
  15. A. Toubiana, S. Babak, S. Marsat, and S. Ossokine, Phys. Rev. D 106, 104034 (2022).
  16. N. Karnesis, S. Babak, M. Pieroni, N. Cornish, and T. Littenberg, Phys. Rev. D 104, 043019 (2021).
  17. A. J. Farmer and E. S. Phinney, Mon. Not. R. Astron. Soc. 346, 1197 (2003).
  18. S. Babak, C. Caprini, D. G. Figueroa, N. Karnesis, P. Marcoccia, G. Nardini, M. Pieroni, A. Ricciardone, A. Sesana, and J. Torrado, J. Cosmol. Astropart. Phys. 08 (2023) 034.
  19. L. Barack and C. Cutler, Phys. Rev. D 70, 122002 (2004).
  20. M. Bonetti and A. Sesana, Phys. Rev. D 102, 103023 (2020).
  21. F. Pozzoli, S. Babak, A. Sesana, M. Bonetti, and N. Karnesis, Phys. Rev. D 108, 103039 (2023).
  22. L. S. S. Team, Report No. ESA-L3-EST-SCI-RS-001 5, 65 (2018).
  23. C. Caprini, J. Phys. Conf. Ser. 610, 012004 (2015).
  24. C. Caprini et al., J. Cosmol. Astropart. Phys. 03 (2020) 024.
  25. C. Caprini, D. G. Figueroa, R. Flauger, G. Nardini, M. Peloso, M. Pieroni, A. Ricciardone, and G. Tasinato, J. Cosmol. Astropart. Phys. 11 (2019) 017.
  26. C. Caprini et al., J. Cosmol. Astropart. Phys. 04 (2016) 001.
  27. P. Auclair, J. J. Blanco-Pillado, D. G. Figueroa, A. C. Jenkins, M. Lewicki, M. Sakellariadou, S. Sanidas, L. Sousa, D. A. Steer, J. M. Wachter, and S. Kuroyanagi (LISA Cosmology Working Group), J. Cosmol. Astropart. Phys. 04 (2020) 034.
  28. A. Ricciardone, J. Phys. Conf. Ser. 840, 012030 (2017).
  29. R.-g. Cai, S. Pi, and M. Sasaki, Phys. Rev. Lett. 122, 201101 (2019).
  30. N. Bartolo, V. De Luca, G. Franciolini, A. Lewis, M. Peloso, and A. Riotto, Phys. Rev. Lett. 122, 211301 (2019).
  31. P. Auclair et al. (LISA Cosmology Working Group), Living Rev. Relativity 26, 5 (2023).
  32. T. B. Littenberg and N. J. Cornish, Phys. Rev. D 107, 063004 (2023).
  33. M. L. Katz, N. Karnesis, N. Korsakova, J. R. Gair, and N. Stergioulas, Phys. Rev. D 111, 024060 (2025).
  34. S. Deng, S. Babak, M. Le Jeune, S. Marsat, E. Plagnol, and A. Sartirana, Phys. Rev. D 111, 103014 (2025).
  35. S. H. Strub, L. Ferraioli, C. Schmelzbach, S. C. Stähler, and D. Giardini, Phys. Rev. D 110, 024005 (2024).
  36. G. Boileau, N. Christensen, C. Gowling, M. Hindmarsh, and R. Meyer, J. Cosmol. Astropart. Phys. 02 (2023) 056.
  37. M. R. Adams and N. J. Cornish, Phys. Rev. D 89, 022001 (2014).
  38. O. Hartwig, M. Lilley, M. Muratore, and M. Pieroni, Phys. Rev. D 107, 123531 (2023).
  39. A. W. Criswell, S. Rieck, and V. Mandic, Phys. Rev. D 111, 023025 (2025).
  40. M. Armano et al., Phys. Rev. Lett. 116, 231101 (2016).
  41. M. Armano et al. (LISA Pathfinder Collaboration), Phys. Rev. D 110, 042004 (2024).
  42. M. Muratore, J. Gair, and L. Speri, Phys. Rev. D 109, 042001 (2024).
  43. C. Caprini, D. G. Figueroa, R. Flauger, G. Nardini, M. Peloso, M. Pieroni, A. Ricciardone, and G. Tasinato, J. Cosmol. Astropart. Phys. 11 (2019) 017.
  44. R. Flauger, N. Karnesis, G. Nardini, M. Pieroni, A. Ricciardone, and J. Torrado, J. Cosmol. Astropart. Phys. 01 (2021) 059.
  45. Q. Baghi, N. Karnesis, J.-B. Bayle, M. Besançon, and H. Inchauspé, J. Cosmol. Astropart. Phys. 04 (2023) 066.
  46. F. Pozzoli, R. Buscicchio, C. J. Moore, F. Haardt, and A. Sesana, Phys. Rev. D 109, 083029 (2024).
  47. C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (The MIT Press, Cambridge, MA, 2005).
  48. M. Tinto and S. V. Dhurandhar, Living Rev. Relativity 8, 4 (2005).
  49. C. Cutler and E. E. Flanagan, Phys. Rev. D 49, 2658 (1994).
  50. M. Vallisneri, Phys. Rev. D 77, 042001 (2008).
  51. P. Amaro-Seoane et al., arXiv:1702.00786.
  52. M. Tinto, G. Giampieri, R. W. Hellings, P. L. Bender, and J. E. Faller, in Proceedings of the 7th Marcel Grossmann Meeting on General Relativity (MG 7) (1994), pp. 1668–1670.
  53. J. W. Armstrong, F. B. Estabrook, and M. Tinto, Astrophys. J. 527, 814 (1999).
  54. D. A. Shaddock, B. Ware, R. E. Spero, and M. Vallisneri, Phys. Rev. D 70, 081101 (2004).
  55. D. A. Shaddock, M. Tinto, F. B. Estabrook, and J. W. Armstrong, Phys. Rev. D 68, 061303 (2003).
  56. M. Vallisneri, Phys. Rev. D 72, 042003 (2005); 76, 109903(E) (2007).
  57. S. Paczkowski, R. Giusteri, M. Hewitson, N. Karnesis, E. D. Fitzsimons, G. Wanner, and G. Heinzel, Phys. Rev. D 106, 042005 (2022).
  58. M.-S. Hartig and G. Wanner, Phys. Rev. D 108, 022008 (2023).
  59. G. Wanner, S. Shah, M. Staab, H. Wegener, and S. Paczkowski, Phys. Rev. D 110, 022003 (2024).
  60. M.-S. Hartig, S. Schuster, and G. Wanner, J. Opt. 24, 065601 (2022).
  61. M. Chwalla, K. Danzmann, M. D. Álvarez, J. E. Delgado, G. Fernández Barranco, E. Fitzsimons, O. Gerberding, G. Heinzel, C. Killow, M. Lieser, M. Perreur-Lloyd, D. Robertson, J. Rohr, S. Schuster, T. Schwarze, M. Tröbs, G. Wanner, and H. Ward, Phys. Rev. Appl. 14, 014030 (2020).
  62. O. Hartwig and J.-B. Bayle, Phys. Rev. D 103, 123027 (2021).
  63. O. Hartwig and M. Muratore, Phys. Rev. D 105, 062006 (2022).
  64. M. Muratore, Time delay interferometry for LISA science and instrument characterization, Ph.D. thesis, Trento University, 2021.
  65. O. Hartwig, Instrumental modelling and noise reduction algorithms for the Laser Interferometer Space Antenna, Ph.D. thesis, Leibniz University, Hannover, 2021.
  66. M. B. Staab, Time-delay interferometric ranging for LISA: Statistical analysis of bias-free ranging using laser noise minimization, Ph.D. thesis, Leibniz University, Hannover, 2023.
  67. J. N. Reinhardt, Intersatellite clock synchronization and absolute ranging for space-based gravitational-wave detectors, Ph.D. thesis, Leibniz University, Hannover, 2025.
  68. M. Muratore, O. Hartwig, D. Vetrugno, S. Vitale, and W. J. Weber, Phys. Rev. D 107, 082004 (2023).
  69. M. Muratore, D. Vetrugno, and S. Vitale, Classical Quantum Gravity 37, 185019 (2020).
  70. LISA Data Challenges Working Group, LISA Data Challenges (2022).
  71. LISA Data Challenges Working Group, Radler dataset description.
  72. LISA Data Challenges Working Group, Sangria dataset description.
  73. LISA Data Challenges Working Group, Spritz dataset description.
  74. T. A. Prince, M. Tinto, S. L. Larson, and J. W. Armstrong, Phys. Rev. D 66, 122002 (2002).
  75. S. Babak, M. Hewitson, and A. Petiteau, arXiv:2108.01167.
  76. C. Caprini and D. G. Figueroa, Classical Quantum Gravity 35, 163001 (2018).
  77. N. Aghanim et al., Astron. Astrophys. 641, A6 (2020).
  78. L. Lehoucq, I. Dvorkin, R. Srinivasan, C. Pellouin, and A. Lamberts, Mon. Not. R. Astron. Soc. 526, 4378 (2023).
  79. P. Binetruy, A. Bohe, C. Caprini, and J.-F. Dufaux, J. Cosmol. Astropart. Phys. 06 (2012) 027.
  80. https://github.com/martinaAEI/noise_knowledge_uncertainty.
  81. E. Thrane and J. D. Romano, Phys. Rev. D 88, 124032 (2013).
  82. G. Janssen, G. Hobbs, M. McLaughlin, C. Bassa, A. Deller, M. Kramer, K. Lee, C. Mingarelli, P. Rosado, S. Sanidas, A. Sesana, L. Shao, I. Stairs, B. Stappers, and J. P. W. Verbiest, Proc. Sci., AASKA14 (2015) 037 [arXiv:1501.00127].
  83. M. C. Edwards, P. Maturana-Russel, R. Meyer, J. Gair, N. Korsakova, and N. Christensen, Phys. Rev. D 102, 084062 (2020).
  84. D. Quang Nam, Y. Lemière, A. Petiteau, J.-B. Bayle, O. Hartwig, J. Martino, and M. Staab, Phys. Rev. D 108, 082004 (2023).
  85. D. Quang Nam, J. Martino, Y. Lemière, A. Petiteau, J.-B. Bayle, O. Hartwig, and M. Staab, Phys. Rev. D 108, 082004 (2023).
  86. O. Hartwig, M. Lilley, M. Muratore, and M. Pieroni, Phys. Rev. D 107, 123531 (2023).
  87. H. Akima, J. ACM 17, 589 (1970).
  88. Virtanen, Pauli, et al., Nat. Methods 17, 261 (2020).
  89. M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Phys. Rev. D 104, 064047 (2021).
  90. C. E. A. Chapman-Bird et al., arXiv:2506.09470.
  91. P. J. Green, Biometrika 82, 711 (1995).
  92. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, Publ. Astron. Soc. Pac. 125, 306 (2013).
  93. N. Karnesis, M. L. Katz, N. Korsakova, J. R. Gair, and N. Stergioulas, Mon. Not. R. Astron. Soc. 526, 4814 (2023).
  94. M. Katz, N. Karnesis, and N. Korsakova, mikekatz04/eryn: first full release (2023).
  95. M. Muratore, J. Gair, O. Hartwig, M. L. Katz, and A. Toubiana, Phys. Rev. D 112, 063041 (2025).
  96. A. Santini, asantini29/cudakima: First official release (2024), https://github.com/asantini29/CudAkima.
  97. R. Okuta, Y. Unno, D. Nishino, S. Hido, and C. Loomis, in Proceedings of Workshop on Machine Learning Systems (LearningSys) in The Thirty-first Annual Conference on Neural Information Processing Systems (NIPS) (2017).
  98. J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: composable transformations of Python+NumPy programs (2018).
  99. J. Goodman and J. Weare, Commun. Appl. Math. Comput. Sci. 5, 65 (2010).
  100. W. Xie, P. O. Lewis, Y. Fan, L. Kuo, and M.-H. Chen, Syst. Biol. 60, 150 (2010).
  101. W. Del Pozzo, J. Veitch, and A. Vecchio, Phys. Rev. D 83, 082002 (2011).
  102. A. Toubiana, K. W. K. Wong, S. Babak, E. Barausse, E. Berti, J. R. Gair, S. Marsat, and S. R. Taylor, Phys. Rev. D 104, 083027 (2021).
  103. A. Toubiana, L. Pompili, A. Buonanno, J. R. Gair, and M. L. Katz, Phys. Rev. D 109, 104019 (2024).
  104. P. Maturana-Russel, R. Meyer, J. Veitch, and N. Christensen, Phys. Rev. D 99, 084006 (2019).
  105. E. M. Zahraoui, P. Maturana-Russel, W. van Straten, R. Meyer, and S. Gulyaev, Mon. Not. R. Astron. Soc. 540, 3818 (2025).
  106. P. Whittle, J. R. Stat. Soc. Ser. B 15, 125 (1953).
  107. G. Franciolini, M. Pieroni, A. Ricciardone, and J. D. Romano, arXiv:2505.24695.
  108. M. Muratore, D. Vetrugno, S. Vitale, and O. Hartwig, Phys. Rev. D 105, 023009 (2022).
  109. R. E. Kass and A. E. Raftery, J. Am. Stat. Assoc. 90, 773 (1995).
  110. F. Pozzoli, J. Gair, R. Buscicchio, and L. Speri, Phys. Rev. D 112, 064035 (2025).
  111. D. J. Spiegelhalter, N. G. Best, B. P. Carlin, and A. Van Der Linde, J. R. Stat. Soc. Ser. B 64, 583 (2002).
  112. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, Texts in Statistical Science Series (Chapman & Hall/CRC, Boca Raton, FL, 2004), 2nd ed., pp. xxvi–668.
  113. D. J. C. MacKay, Information Theory, Inference & Learning Algorithms (Cambridge University Press, Cambridge, England, 2002).
  114. A. Santini, asantini29/lisa-ps: First release (2025), https://github.com/asantini29/lisa-ps.
  115. C. R. Harris et al., Nature (London) 585, 357 (2020).
  116. J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007).
  117. S. K. Lam, A. Pitrou, and S. Seibert, in Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC (2015), pp. 1–6.
  118. A. Santini, asantini29/pysco: First release (2024).
  119. The data used for this publication are available at: https://zenodo.org/records/17203220. The main code base used for the analysis is available at https://github.com/asantini29/lisa-ps.

Outline

Information

Phys. Rev. D 112, 084050– Published 17 October, 2025
  • Received 25 July 2025
  • Accepted 25 September 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation