Skip to main content
SpringerLink
Log in

Deep learning waveform anomaly detector for numerical relativity catalogs

  • Research
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Numerical Relativity has been of fundamental importance for studying compact binary coalescence dynamics, waveform modelling, and eventually for gravitational waves observations. As the sensitivity of the detector network improves, more precise template modelling will be necessary to guarantee a more accurate estimation of astrophysical parameters. To help improve the accuracy of numerical relativity catalogs, we developed a deep learning model capable of detecting anomalous waveforms. We analyzed 1341 binary black hole simulations from the SXS catalog with various mass-ratios and spins, considering waveform dominant and higher modes. In the set of waveform analyzed, we found and categorised seven types of anomalies appearing in the coalescence phases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Notes

  1. In general the predicted waveform precision requirement for real events depends on the loudness of the signal, scaling as the inverse square of its signal-to-noise ratio. For current second generation detector [16] with signal-to-noise ratio \(\sim \textrm{few}\times 10\) a noise weighed “mismatch” of \(10^{-3}\) is usually required.

  2. We restricted our analysis to the 1341 simulations with mass ratio \(q\le 4\) because beyond this value simulations become sparser, and this can jeopardize the learning process of the neural network model training.

  3. To make it explict, we use the \((2,2),\,(2,1),\,(3,3),\,(3,2),\,(4,4),\,(4,3)\), i.e. 6 modes for each simulation in the catalog.

  4. For all numerical waveforms we used the best resolution available in the repository.

References

  1. Aasi, J.: Advanced LIGO. Class. Quantum Gravity 32, 074001 (2015). https://doi.org/10.1088/0264-9381/32/7/074001. arXiv:1411.4547 [gr-qc]

    Article  ADS  CAS  Google Scholar 

  2. Acernese, F.: Advanced Virgo: a second-generation interferometric gravitational wave detector. Class. Quantum Gravity 32(2), 024001 (2015). https://doi.org/10.1088/0264-9381/32/2/024001. arXiv:1408.3978 [gr-qc]

    Article  ADS  Google Scholar 

  3. Abbott, R., et al.: GWTC-3: compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run (2021). arXiv:2111.03606 [gr-qc]

  4. Wainstein, L.A., Zubakov, V.D.: Extraction of Signals from Noise. Dover Books on Physics and Mathematical Physics. Prentice-Hall, Englewood Cliffs (1962)

    Google Scholar 

  5. Abbott, B.P.: A guide to LIGO–Virgo detector noise and extraction of transient gravitational-wave signals. Class. Quantum Gravity 37(5), 055002 (2020). https://doi.org/10.1088/1361-6382/ab685e. arXiv:1908.11170 [gr-qc]

    Article  ADS  CAS  Google Scholar 

  6. Pratten, G.: Computationally efficient models for the dominant and subdominant harmonic modes of precessing binary black holes. Phys. Rev. D 103(10), 104056 (2021). https://doi.org/10.1103/PhysRevD.103.104056. arXiv:2004.06503 [gr-qc]

    Article  ADS  MathSciNet  CAS  Google Scholar 

  7. Pratten, G., Husa, S., Garcia-Quiros, C., Colleoni, M., Ramos-Buades, A., Estelles, H., Jaume, R.: Setting the cornerstone for a family of models for gravitational waves from compact binaries: the dominant harmonic for nonprecessing quasicircular black holes. Phys. Rev. D 102(6), 064001 (2020). https://doi.org/10.1103/PhysRevD.102.064001. arXiv:2001.11412 [gr-qc]

    Article  ADS  MathSciNet  CAS  Google Scholar 

  8. García-Quirós, C., Husa, S., Mateu-Lucena, M., Borchers, A.: Accelerating the evaluation of inspiral–merger–ringdown waveforms with adapted grids. Class. Quantum Gravity 38(1), 015006 (2021). https://doi.org/10.1088/1361-6382/abc36e. arXiv:2001.10897 [gr-qc]

    Article  ADS  MathSciNet  CAS  Google Scholar 

  9. García-Quirós, C., Colleoni, M., Husa, S., Estellés, H., Pratten, G., Ramos-Buades, A., Mateu-Lucena, M., Jaume, R.: Multimode frequency-domain model for the gravitational wave signal from nonprecessing black-hole binaries. Phys. Rev. D 102(6), 064002 (2020). https://doi.org/10.1103/PhysRevD.102.064002. arXiv:2001.10914 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  10. Ossokine, S.: Multipolar effective-one-body waveforms for precessing binary black holes: construction and validation. Phys. Rev. D 102(4), 044055 (2020). https://doi.org/10.1103/PhysRevD.102.044055. arXiv:2004.09442 [gr-qc]

    Article  ADS  MathSciNet  CAS  Google Scholar 

  11. Babak, S., Taracchini, A., Buonanno, A.: Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity. Phys. Rev. D 95(2), 024010 (2017). https://doi.org/10.1103/PhysRevD.95.024010. arXiv:1607.05661 [gr-qc]

    Article  ADS  Google Scholar 

  12. Pan, Y., Buonanno, A., Taracchini, A., Kidder, L.E., Mroué, A.H., Pfeiffer, H.P., Scheel, M.A., Szilágyi, B.: Inspiral–merger–ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism. Phys. Rev. D 89(8), 084006 (2014). https://doi.org/10.1103/PhysRevD.89.084006. arXiv:1307.6232 [gr-qc]

    Article  ADS  CAS  Google Scholar 

  13. Abbott, R.: GW190412: observation of a binary-black-hole coalescence with asymmetric masses. Phys. Rev. D 102(4), 043015 (2020). https://doi.org/10.1103/PhysRevD.102.043015. arXiv:2004.08342 [astro-ph.HE]

    Article  ADS  CAS  Google Scholar 

  14. Abbott, R.: GW190814: gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object. Astrophys. J. Lett. 896(2), 44 (2020). https://doi.org/10.3847/2041-8213/ab960f. arXiv:2006.12611 [astro-ph.HE]

    Article  ADS  CAS  Google Scholar 

  15. Abe, H.: The current status and future prospects of KAGRA, the large-scale cryogenic gravitational wave telescope built in the Kamioka Underground. Galaxies 10(3), 63 (2022). https://doi.org/10.3390/galaxies10030063

    Article  ADS  Google Scholar 

  16. Pürrer, M., Haster, C.-J.: Gravitational waveform accuracy requirements for future ground-based detectors. Phys. Rev. Res. 2(2), 023151 (2020). https://doi.org/10.1103/PhysRevResearch.2.023151. arXiv:1912.10055 [gr-qc]

    Article  Google Scholar 

  17. Scheel, M.A., Boyle, M., Chu, T., Kidder, L.E., Matthews, K.D., Pfeiffer, H.P.: High-accuracy waveforms for binary black hole inspiral, merger, and ringdown. Phys. Rev. D 79, 024003 (2009). https://doi.org/10.1103/PhysRevD.79.024003

    Article  ADS  CAS  Google Scholar 

  18. Boyle, M.: The SXS collaboration catalog of binary black hole simulations. Class. Quantum Gravity 36(19), 195006 (2019). https://doi.org/10.1088/1361-6382/ab34e2. arXiv:1904.04831 [gr-qc]

    Article  ADS  Google Scholar 

  19. Boyle, M., Lindblom, L., Pfeiffer, H., Scheel, M., Kidder, L.E.: Testing the accuracy and stability of spectral methods in numerical relativity. Phys. Rev. D 75, 024006 (2007). https://doi.org/10.1103/PhysRevD.75.024006. arXiv:gr-qc/0609047

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Rinne, O., Lindblom, L., Scheel, M.A.: Testing outer boundary treatments for the Einstein equations. Class. Quantum Gravity 24, 4053–4078 (2007). https://doi.org/10.1088/0264-9381/24/16/006. arXiv:0704.0782 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  21. Szilágyi, B.: Key elements of robustness in binary black hole evolutions using spectral methods. Int. J. Mod. Phys. D 23(07), 1430014 (2014). https://doi.org/10.1142/s0218271814300146

    Article  ADS  MathSciNet  Google Scholar 

  22. Pereira, T.: Waveform AnomaLy DetectOr (WALDO). Zenodo (2022). https://doi.org/10.5281/ZENODO.7127963

    Article  Google Scholar 

  23. Waveform AnomaLy DetectOr. https://github.com/tiberioap/grav_waldo. Accessed on 2023 12

  24. Waveform AnomaLy DetectOr. https://ascl.net/2301.021. Accessed on 2023 12

  25. Varma, V., Field, S.E., Scheel, M.A., Blackman, J., Gerosa, D., Stein, L.C., Kidder, L.E., Pfeiffer, H.P.: Surrogate models for precessing binary black hole simulations with unequal masses. Phys. Rev. Res. 1, 033015 (2019). https://doi.org/10.1103/PhysRevResearch.1.033015. arXiv:1905.09300 [gr-qc]

    Article  CAS  Google Scholar 

  26. Easter, P.J., Lasky, P.D., Casey, A.R., Rezzolla, L., Takami, K.: Computing fast and reliable gravitational waveforms of binary neutron star merger remnants. Phys. Rev. D 100(4), 043005 (2019). https://doi.org/10.1103/PhysRevD.100.043005. arXiv:1811.11183 [gr-qc]

    Article  ADS  CAS  Google Scholar 

  27. Gabbard, H., Williams, M., Hayes, F., Messenger, C.: Matching matched filtering with deep networks for gravitational-wave astronomy. Phys. Rev. Lett. (2018). https://doi.org/10.1103/physrevlett.120.141103

    Article  PubMed  Google Scholar 

  28. Varma, V., Gerosa, D., Stein, L.C., Hebert, F., Zhang, H.: High-accuracy mass, spin, and recoil predictions of generic black-hole merger remnants. Phys. Rev. Lett. 122(1), 011101 (2019). https://doi.org/10.1103/PhysRevLett.122.011101. arXiv:1809.09125 [gr-qc]

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  29. Shen, H., George, D., Huerta, E.A., Zhao, Z.: Denoising gravitational waves with enhanced deep recurrent denoising auto-encoders. In: ICASSP 2019—2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE (2019). https://doi.org/10.1109/icassp.2019.8683061

  30. Rebei, A., Huerta, A., Wang, S., Habib, S., Haas, R., Johnson, D., George, D.: Fusing numerical relativity and deep learning to detect higher-order multipole waveforms from eccentric binary black hole mergers. Phys. Rev. D (2019). https://doi.org/10.1103/physrevd.100.044025

    Article  MathSciNet  Google Scholar 

  31. Setyawati, Y., Pürrer, M., Ohme, F.: Regression methods in waveform modeling: a comparative study. Class. Quantum Gravity 37(7), 075012 (2020). https://doi.org/10.1088/1361-6382/ab693b. arXiv:1909.10986 [astro-ph.IM]

    Article  ADS  MathSciNet  Google Scholar 

  32. Haegel, L., Husa, S.: Predicting the properties of black-hole merger remnants with deep neural networks. Class. Quantum Gravity 37(13), 135005 (2020). https://doi.org/10.1088/1361-6382/ab905c. arXiv:1911.01496 [gr-qc]

    Article  ADS  MathSciNet  Google Scholar 

  33. Cuoco, E.: Enhancing gravitational-wave science with machine learning. Mach. Learn. Sci. Tech. 2(1), 011002 (2021). https://doi.org/10.1088/2632-2153/abb93a. arXiv:2005.03745 [astro-ph.HE]

    Article  MathSciNet  Google Scholar 

  34. Green, S.R., Simpson, C., Gair, J.: Gravitational-wave parameter estimation with autoregressive neural network flows. Phys. Rev. D (2020). https://doi.org/10.1103/physrevd.102.104057

    Article  MathSciNet  Google Scholar 

  35. Ormiston, R., Nguyen, T., Coughlin, M., Adhikari, R.X., Katsavounidis, E.: Noise reduction in gravitational-wave data via deep learning. Phys. Rev. Res. (2020). https://doi.org/10.1103/physrevresearch.2.033066

    Article  Google Scholar 

  36. Yu, H., Adhikari, R.X.: Nonlinear noise regression in gravitational-wave detectors with convolutional neural networks. arXiv (2021). https://doi.org/10.48550/ARXIV.2111.03295

  37. Schmidt, S., Breschi, M., Gamba, R., Pagano, G., Rettegno, P., Riemenschneider, G., Bernuzzi, S., Nagar, A., Pozzo, W.D.: Machine learning gravitational waves from binary black hole mergers. Phys. Rev. D (2021). https://doi.org/10.1103/physrevd.103.043020

    Article  MathSciNet  Google Scholar 

  38. Gabbard, H., Messenger, C., Heng, I.S., Tonolini, F., Murray-Smith, R.: Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy. Nat. Phys. 18(1), 112–117 (2021). https://doi.org/10.1038/s41567-021-01425-7

    Article  CAS  Google Scholar 

  39. Fragkouli, S.-C., Nousi, P., Passalis, N., Iosif, P., Stergioulas, N., Tefas, A.: Deep residual error and bag-of-tricks learning for gravitational wave surrogate modeling. arXiv (2022). https://doi.org/10.48550/ARXIV.2203.08434

  40. Yan, J., Avagyan, M., Colgan, R.E., Veske, D., Bartos, I., Wright, J., Márka, Z., Márka, S.: Generalized approach to matched filtering using neural networks. Phys. Rev. D (2022). https://doi.org/10.1103/physrevd.105.043006

    Article  MathSciNet  Google Scholar 

  41. Mroue, A.H., et al.: Catalog of 174 binary black hole simulations for gravitational wave astronomy. Phys. Rev. Lett. (2013). https://doi.org/10.1103/physrevlett.111.241104

    Article  PubMed  Google Scholar 

  42. Ajith, P.: Inspiral–merger–ringdown waveforms for black-hole binaries with non-precessing spins. Phys. Rev. Lett. 106, 241101 (2011). https://doi.org/10.1103/PhysRevLett.106.241101. arXiv:0909.2867 [gr-qc]

    Article  ADS  CAS  PubMed  Google Scholar 

  43. Schmidt, P., Ohme, F., Hannam, M.: Towards models of gravitational waveforms from generic binaries II: modelling precession effects with a single effective precession parameter. Phys. Rev. D 91(2), 024043 (2015). https://doi.org/10.1103/PhysRevD.91.024043. arXiv:1408.1810 [gr-qc]

    Article  ADS  CAS  Google Scholar 

  44. Schmidt, S., Breschi, M., Gamba, R., Pagano, G., Rettegno, P., Riemenschneider, G., Bernuzzi, S., Nagar, A., Del Pozzo, W.: Machine learning gravitational waves from binary black hole mergers. Phys. Rev. D 103(4), 043020 (2021). https://doi.org/10.1103/PhysRevD.103.043020. arXiv:2011.01958 [gr-qc]

    Article  ADS  MathSciNet  CAS  Google Scholar 

  45. Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. arXiv (2015). https://doi.org/10.48550/ARXIV.1505.04597

  46. Duchi, J.C., Hazan, E., Singer, Y.: Adaptive subgradient methods for online learning and stochastic optimization. J. Mach. Learn. Res. 12, 2121–2159 (2011)

    MathSciNet  Google Scholar 

  47. SXS Gravitational Waveform Database: Important Information. https://data.black-holes.org/waveforms/index.html. Accessed on 2023 08

  48. Reisswig, C., Pollney, D.: Notes on the integration of numerical relativity waveforms. Class. Quantum Gravity 28(19), 195015 (2011). https://doi.org/10.1088/0264-9381/28/19/195015

    Article  ADS  MathSciNet  Google Scholar 

  49. Ruiz, M., Alcubierre, M., Núñez, D., Takahashi, R.: Multiple expansions for energy and momenta carried by gravitational waves. Gen. Relativ. Gravit. 40(8), 1705–1729 (2007). https://doi.org/10.1007/s10714-007-0570-8

    Article  ADS  MathSciNet  Google Scholar 

  50. Nagar, A., Rezzolla, L.: Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes. Class. Quantum Gravity 23(12), 4297 (2006). https://doi.org/10.1088/0264-9381/23/12/c01

    Article  ADS  Google Scholar 

  51. Khan, S., Chatziioannou, K., Hannam, M., Ohme, F.: Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects. Phys. Rev. D (2019). https://doi.org/10.1103/physrevd.100.024059

    Article  Google Scholar 

  52. Taracchini, A., Buonanno, A., Pan, Y., Hinderer, T., Boyle, M., Hemberger, D.A., Kidder, L.E., Lovelace, G., Mroué, A.H., Pfeiffer, H.P., Scheel, M.A., Szilágyi, B., Taylor, N.W., Zenginoglu, A.: Effective-one-body model for black-hole binaries with generic mass ratios and spins. Phys. Rev. D (2014). https://doi.org/10.1103/physrevd.89.061502

    Article  Google Scholar 

  53. Blackman, J., Field, S.E., Galley, C.R., Szilágyi, B., Scheel, M.A., Tiglio, M., Hemberger, D.A.: Fast and accurate prediction of numerical relativity waveforms from binary black hole coalescences using surrogate models. Phys. Rev. Lett. (2015). https://doi.org/10.1103/physrevlett.115.121102

    Article  PubMed  Google Scholar 

  54. Blackman, J., Field, S.E., Scheel, M.A., Galley, C.R., Hemberger, D.A., Schmidt, P., Smith, R.: A surrogate model of gravitational waveforms from numerical relativity simulations of precessing binary black hole mergers. Phys. Rev. D (2017). https://doi.org/10.1103/physrevd.95.104023

    Article  MathSciNet  Google Scholar 

  55. Leaver, E.W.: An analytic representation for the quasi-normal modes of Kerr black holes. Proc. R. Soc. A Math. Phys. Eng. Sci. 402(1823), 285–298 (1985). https://doi.org/10.1098/rspa.1985.0119

    Article  ADS  MathSciNet  Google Scholar 

  56. Maggiore, M.: Physical interpretation of the spectrum of black hole quasinormal modes. Phys. Rev. Lett. (2008). https://doi.org/10.1103/physrevlett.100.141301

    Article  MathSciNet  PubMed  Google Scholar 

  57. Yang, H., Nichols, D.A., Zhang, F., Zimmerman, A., Zhang, Z., Chen, Y.: Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation. Phys. Rev. D (2012). https://doi.org/10.1103/physrevd.86.104006

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the International Institute of Physics for hospitality and support during most of this work. We thank Michael Boyle, from the SXS team, for the valuable discussions. TP is supported by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)—Graduate Research Fellowship. The work of RS is partly supported by CNPq under Grant 310165/2021-0 and RS would like to thank ICTP-SAIFR FAPESP Grant No. 2016/01343-7. The authors thank the High Performance Computing Center (NPAD) at UFRN for providing the computational resources necessary for this work.

Author information

Author notes

  1. Tibério Pereira and Riccardo Sturani have contributed equally to this work.

Authors and Affiliations

  1. Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-970, Brazil

    Tibério Pereira

  2. Instituto de Física Teórica, UNESP-Universidade Estadual Paulista and ICTP South American Institute for Fundamental Research, São Paulo, SP, 01140-070, Brazil

    Riccardo Sturani

Authors
  1. Tibério Pereira
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Riccardo Sturani
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Methodology: TP, RS; Software: TP; Data analyses: TP, RS; Writing original draft and preparation: TP, RS; Reviewing and editing: TP, RS.

Corresponding author

Correspondence to Tibério Pereira.

Ethics declarations

Conflict of interest

Riccardo Sturani reports financial support was provided by National Council for Scientific and Technological Development under Grant 310165/2021-0. Riccardo Sturani reports financial support was provided by ICTP South American Institute for Fundamental Research under Grant 2016/01343-7.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pereira, T., Sturani, R. Deep learning waveform anomaly detector for numerical relativity catalogs. Gen Relativ Gravit 56, 24 (2024). https://doi.org/10.1007/s10714-024-03216-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-024-03216-w

Keywords

Search

Navigation