[1] Liu Y P, Gao Y T, Wei G M 2012 Phys. A Stat. Mech. Appl. 391 535 doi: 10.1016/j.physa.2011.08.058
[2] Uthayakumar A, Han Y G, Lee S B 2006 Chaos Solitons Fractals 29 916 doi: 10.1016/j.chaos.2005.08.055
[3] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243 doi: 10.1103/PhysRevLett.80.5243
[4] El-Ganainy R, Makris K G, Christodoulides D N, Musslimani Z H 2007 Opt. Lett. 32 2632 doi: 10.1364/OL.32.002632
[5] Bender C M 2007 Rep. Prog. Phys. 70 947 doi: 10.1088/0034-4885/70/6/R03
[6] Baudouin L, Puel J P 2002 Inverse Probl. 18 1537 doi: 10.1088/0266-5611/18/6/307
[7] Avdonin S A, Mikhaylov A S, Mikhaylov V S, Park J C 2021 Inverse Problems 37 035002 doi: 10.1088/1361-6420/abd7cb
[8] Raissi M, Perdikaris P, Karniadakis G E 2019 J. Comput. Phys. 378 686 doi: 10.1016/j.jcp.2018.10.045
[9] Zhou Z, Yan Z 2021 Phys. Lett. A 387 127010 doi: 10.1016/j.physleta.2020.127010
[10] Li J, Li B 2021 Commun. Theor. Phys. 73 125001 doi: 10.1088/1572-9494/ac2055
[11] 张坤 2024 理论数学 14 117 doi: 10.12677/pm.2024.143091 Zhang K 2024 Pure Math. 14 117 doi: 10.12677/pm.2024.143091
[12] Qiu W X, Geng K L, Zhu B W, Liu W, Li J T, Dai C Q 2024 Nonlinear Dyn. 112 10215 doi: 10.1007/s11071-024-09605-9
[13] Song J, Yan Z 2023 Physica D 448 133729 doi: 10.1016/j.physd.2023.133729
[14] Wang S, Wang H, Perdikaris P 2021 Comput. Methods Appl. Mech. Eng. 384 113938 doi: 10.1016/j.cma.2021.113938
[15] Liu Y, Wu R, Jiang Y 2024 J. Comput. Phys. 518 113341 doi: 10.1016/j.jcp.2024.113341
[16] Karniadakis G E, Kevrekidis I G, Lu L, Perdikaris P, Wang S, Yang L 2021 Nat. Rev. Phys. 3 422 doi: 10.1038/s42254-021-00314-5
[17] Lu L, Meng X, Mao Z, Karniadakis G E 2021 SIAM Rev. 63 208 doi: 10.1137/19M1274067
[18] 孙志忠 2022 偏微分方程数值解法 (第三版) (北京: 科学出版社) 第 320—349页 Sun Z Z 2022 Numerical Solution of Partial Differential Equations. (3rd Ed.) (Beijing: Science Press) pp320–349
[19] Dembo R S, Eisenstat S C, Steihaug T 1982 SIAM J. Numer. Anal. 19 400 doi: 10.1137/0719025
[20] Göksel İ, Antar N, Bakırtaş İ 2015 Opt. Commun. 354 277 doi: 10.1016/j.optcom.2015.05.051