\begin{document}$ \Lambda $\end{document}CDM and a purely data-driven block, yields smooth and robust reconstructions and enables the derivation of D'(z). By combining these reconstructed quantities, we assess the curvature diagnostic function \begin{document}$ {\cal{O}}_k(z) $\end{document}. Analyses of the Pantheon+ sample support spatial flatness at the 1\begin{document}$ \sigma $\end{document} level over 0 < z < 2.5, with a mild tendency toward negative curvature at high redshift. Reconstructions based on Union3 and DESY5, however, show stronger departures toward negative curvature at intermediate and high redshifts. These results highlight the need for expanded and refined observational datasets to conclusively resolve these tensions and comprehensively investigate cosmic geometry."> Null test of cosmic curvature using deep learning method -
  • [1]

    N. Aghanimet al. (Planck Collaboration), Astron. Astrophys.641, A6 (2020) [Erratum: Astron. Astrophys. 652, C4 (2021)].

  • [2]

    T. M. C. Abbottet al. (DES Collaboration), Astrophys. J. Lett.973(1), L14 (2024)

  • [3]

    P. J. Wu and X. Zhang, Phys. Rev. D112(6), 063514 (2025)

  • [4]

    J.-Q. Jiang, D. Pedrotti, S. S. da Costaet al., Phys. Rev. D110(12), 123519 (2024)

  • [5]

    C. Gao, Y. Chen, and J. Zheng, Res. Astron. Astrophys.20(9), 151 (2020)

  • [6]

    A. G. Riess, S. Casertano, W. Yuanet al., Astrophys. J.855(2), 136 (2018)

  • [7]

    A. G. Riess, S. Casertano, W. Yuanet al., Astrophys. J.876(1), 85 (2019)

  • [8]

    A. G. Riess, W. Yuan, L. M. Macriet al., Astrophys. J. Lett.934(1), L7 (2022)

  • [9]

    G. Bernstein, Astrophys. J.637, 598 (2006)

  • [10]

    C. Clarkson, B. Bassett, and T. H. C. Lu, Phys. Rev. Lett.101, 011301 (2008)

  • [11]

    D. Sapone, E. Majerotto, and S. Nesseris, Phys. Rev. D90(2), 023012 (2014)

  • [12]

    S. Räsänen, K. Bolejko, and A. Finoguenov, Phys. Rev. Lett.115(10), 101301 (2015)

  • [13]

    R. G. Cai, Z. K. Guo, and T. Yang, Phys. Rev. D93(4), 043517 (2016)

  • [14]

    T. Collett, F. Montanari, and S. Rasanen, Phys. Rev. Lett.123(23), 231101 (2019)

  • [15]

    Y. J. Wang, J. Z. Qi, B. Wanget al., Mon. Not. Roy. Astron. Soc.516(4), 5187 (2022)

  • [16]

    S. S. Du, J. J. Wei, Z. Q. Youet al., Mon. Not. Roy. Astron. Soc.521(4), 4963 (2023)

  • [17]

    J. Q. Xia, H. Yu, G. J. Wanget al., Astrophys. J.834(1), 75 (2017)

  • [18]

    J. Z. Qi, S. Cao, S. Zhanget al., Mon. Not. Roy. Astron. Soc.483(1), 1104 (2019)

  • [19]

    T. Liu, S. Cao, J. Zhanget al., Mon. Not. Roy. Astron. Soc.496, 708 (2020)

  • [20]

    B. Wang, J. Z. Qi, J. F. Zhanget al., Astrophys. J.898(2), 100 (2020)

  • [21]

    L. Liu, L. J. Hu, L. Tanget al., Res. Astron. Astrophys.23(12), 125012 (2023)

  • [22]

    J. J. Wei and X. F. Wu, Astrophys. J.838(2), 160 (2017)

  • [23]

    G. J. Wang, J. J. Wei, Z. X. Liet al., Astrophys. J.847(1), 45 (2017)

  • [24]

    C. Z. Ruan, F. Melia, Y. Chenet al., Astrophys. J.881, 137 (2019)

  • [25]

    J. F. Jesus, R. Valentim, P. H. R. S. Moraeset al., Mon. Not. Roy. Astron. Soc.500(2), 2227 (2020)

  • [26]

    Y. Yang and Y. Gong, Mon. Not. Roy. Astron. Soc.504(2), 3092 (2021)

  • [27]

    J. Z. Qi, P. Meng, J. F. Zhanget al., Phys. Rev. D108(6), 063522 (2023)

  • [28]

    T. Liu, S. Wang, H. Wuet al., Astrophys. J. Lett.981(2), L24 (2025)

  • [29]

    P. J. Wu, J. Z. Qi, and X. Zhang, Chin. Phys. C47(5), 055106 (2023)

  • [30]

    C. Escamilla-Rivera, M. A. C. Quintero, and S. Capozziello, JCAP03, 008 (2020)

  • [31]

    G. J. Wang, X. J. Ma, S. Y. Liet al., Astrophys. J. Suppl.246(1), 13 (2020)

  • [32]

    L. Tang, X. Li, H. N. Linet al., Astrophys. J.907(2), 121 (2021)

  • [33]

    D. Scolnic, D. Brout, A. Carret al., Astrophys. J.938(2), 113 (2022)

  • [34]

    D. Rubin, B. Rose, R. Hounsellet al., arXiv: 2306.17222 [astro-ph.IM]

  • [35]

    C. Clarkson, M. Cortes, and B. A. Bassett, JCAP08, 011 (2007)

  • [36]

    D. Brout, D. Scolnic, B. Popovicet al., Astrophys. J.938(2), 110 (2022)

  • [37]

    Y. Chen, S. Kumar, B. Ratraet al., Astrophys. J. Lett.964(1), L4 (2024)

  • [38]

    D. Scolnic, A. Rest, A. Riesset al., Astrophys. J.795(1), 45 (2014)

  • [39]

    K. He, X. Zhang, S. Renet al., inProceedings of the IEEE Conference on Computer Vision and Pattern Recognition(CVPR), (2016), p. 770

  • [40]

    Y. Gal and Z. Ghahramani, arXiv: 1506.02142

  • [41]

    M. Zhang, B. Wang, P. J. Wuet al., Astrophys. J.918(2), 56 (2021)

  • [42]

    P. J. Wu and X. Zhang, JCAP01(01), 060 (2022)

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