{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T01:07:36Z","timestamp":1780448856179,"version":"3.54.1"},"reference-count":40,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.jcp.2026.115017","type":"journal-article","created":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T12:30:32Z","timestamp":1778243432000},"page":"115017","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Data-driven regularization for coefficient inverse problems in wave equations using partial observations"],"prefix":"10.1016","volume":"562","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4199-0998","authenticated-orcid":false,"given":"Qihang","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lianggen","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5961-7211","authenticated-orcid":false,"given":"Zhiyuan","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"5","key":"10.1016\/j.jcp.2026.115017_bib0001","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1088\/0266-5611\/10\/5\/003","article-title":"Inverse problems in ocean acoustics","volume":"10","author":"Collins","year":"1994","journal-title":"Inverse Probl."},{"key":"10.1016\/j.jcp.2026.115017_bib0002","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10915-013-9760-6","article-title":"Source estimation by full wave form inversion","volume":"59","author":"Sj\u00f6green","year":"2014","journal-title":"J. Sci. Comput."},{"issue":"4","key":"10.1016\/j.jcp.2026.115017_bib0003","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1137\/090748494","article-title":"Mathematical modeling in photoacoustic imaging of small absorbers","volume":"52","author":"Ammari","year":"2010","journal-title":"SIAM Rev."},{"issue":"12","key":"10.1016\/j.jcp.2026.115017_bib0004","doi-asserted-by":"crossref","DOI":"10.1088\/0266-5611\/31\/12\/125012","article-title":"Inverse transport problems in quantitative PAT for molecular imaging","volume":"31","author":"Ren","year":"2015","journal-title":"Inverse Probl."},{"issue":"1","key":"10.1016\/j.jcp.2026.115017_bib0005","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/aa9ade","article-title":"Reconstruction formulas for photoacoustic imaging in attenuating media","volume":"34","author":"Scherzer","year":"2017","journal-title":"Inverse Probl."},{"key":"10.1016\/j.jcp.2026.115017_bib0006","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.matpur.2019.06.006","article-title":"Stability for the inverse source problems in elastic and electromagnetic waves","volume":"134","author":"Bao","year":"2020","journal-title":"J. Math\u00e9matiques Pures Appliqu\u00e9es"},{"issue":"3","key":"10.1016\/j.jcp.2026.115017_bib0007","doi-asserted-by":"crossref","first-page":"1608","DOI":"10.1137\/140993648","article-title":"A recursive algorithm for multifrequency acoustic inverse source problems","volume":"53","author":"Bao","year":"2015","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2026.115017_bib0008","doi-asserted-by":"crossref","first-page":"4283","DOI":"10.1007\/s00208-025-03205-7","article-title":"Stable inversion of potential in nonlinear wave equations with cubic nonlinearity","volume":"392","author":"Chen","year":"2025","journal-title":"Math. Ann."},{"issue":"2","key":"10.1016\/j.jcp.2026.115017_bib0009","doi-asserted-by":"crossref","first-page":"1959","DOI":"10.1137\/22M1538399","article-title":"Inverse scattering for the biharmonic wave equation with a random potential","volume":"56","author":"Li","year":"2024","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"10.1016\/j.jcp.2026.115017_bib0010","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/S0021-7824(99)80010-5","article-title":"Uniqueness and stability in multidimensional hyperbolic inverse problems","volume":"78","author":"Yamamoto","year":"1999","journal-title":"J. Math\u00e9matiques Pures Appliqu\u00e9es"},{"issue":"4","key":"10.1016\/j.jcp.2026.115017_bib0011","doi-asserted-by":"crossref","first-page":"1097","DOI":"10.1137\/100786174","article-title":"Transient wave imaging with limited-view data","volume":"4","author":"Ammari","year":"2011","journal-title":"SIAM J. Img. Sci."},{"key":"10.1016\/j.jcp.2026.115017_bib0012","unstructured":"L. Baudouin, Lipschitz stability in an inverse problem for the wave equation, 2011. Available at https:\/\/hal.archives-ouvertes.fr\/hal-00598876\/fr\/."},{"issue":"12","key":"10.1016\/j.jcp.2026.115017_bib0013","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/aba892","article-title":"Stability for inverse source problems by Carleman estimates","volume":"36","author":"Huang","year":"2020","journal-title":"Inverse Probl."},{"issue":"05","key":"10.1016\/j.jcp.2026.115017_bib0014","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1142\/S0219530523500100","article-title":"Determination of source or initial values for acoustic equations with a time-fractional attenuation","volume":"21","author":"Huang","year":"2023","journal-title":"Anal. Appl."},{"key":"10.1016\/j.jcp.2026.115017_bib0015","unstructured":"S. Si, Inverse source problem for a hyperbolic equation by Carleman estimates, 2025. Available at https:\/\/api.semanticscholar.org\/CorpusID:279402864."},{"key":"10.1016\/j.jcp.2026.115017_bib0016","first-page":"1","article-title":"Determination of space-dependent sourse function in the one-dimensional wave equation","volume":"12","author":"Hussein","year":"2014","journal-title":"Electron. J. Bound. Elem."},{"key":"10.1016\/j.jcp.2026.115017_bib0017","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/s10665-015-9785-y","article-title":"Determination of forcing functions in the wave equation. Part I: the space-dependent case","volume":"96","author":"Hussein","year":"2016","journal-title":"J. Engrg. Math."},{"issue":"6","key":"10.1016\/j.jcp.2026.115017_bib0018","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1137\/20M1334267","article-title":"Stability for the acoustic inverse source problem in inhomogeneous media","volume":"80","author":"Li","year":"2020","journal-title":"SIAM J. Appl. Math."},{"issue":"4","key":"10.1016\/j.jcp.2026.115017_bib0019","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1137\/16M1088776","article-title":"Convergent algorithm based on carleman estimates for the recovery of a potential in the wave equation","volume":"55","author":"Baudouin","year":"2017","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2026.115017_bib0020","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.camwa.2022.10.021","article-title":"The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations","volume":"128","author":"Nguyen","year":"2022","journal-title":"Comput. Math. Appl."},{"issue":"6","key":"10.1016\/j.jcp.2026.115017_bib0021","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/ac637a","article-title":"Increasing stability in the linearized inverse Schr\u00f6dinger potential problem with power type nonlinearities*","volume":"38","author":"Lu","year":"2022","journal-title":"Inverse Probl."},{"key":"10.1016\/j.jcp.2026.115017_bib0022","doi-asserted-by":"crossref","unstructured":"X. Wu, J. Yang, Z. Zhou, Numerical reconstruction and analysis of backward semilinear subdiffusion problems, 2025. Available at https:\/\/api.semanticscholar.org\/CorpusID:278339110.","DOI":"10.1090\/mcom\/4116"},{"issue":"1","key":"10.1016\/j.jcp.2026.115017_bib0023","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/aca70e","article-title":"Convergence rate analysis of Galerkin approximation of inverse potential problem","volume":"39","author":"Jin","year":"2022","journal-title":"Inverse Probl."},{"key":"10.1016\/j.jcp.2026.115017_bib0024","unstructured":"B. Jin, q. Quan, w. Zhang, Stochastic convergence analysis of inverse potential problem, 2024. Available at https:\/\/doi.org\/10.48550\/arXiv.2410.14106."},{"key":"10.1016\/j.jcp.2026.115017_bib0025","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115017_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109409","article-title":"Weak adversarial networks for high-dimensional partial differential equations","volume":"411","author":"Zang","year":"2020","journal-title":"J. Comput. Phys."},{"issue":"5","key":"10.1016\/j.jcp.2026.115017_bib0027","doi-asserted-by":"crossref","first-page":"2002","DOI":"10.4208\/cicp.OA-2020-0164","article-title":"Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations","volume":"28","author":"Jagtap","year":"2020","journal-title":"Commun. Comput. Phys."},{"issue":"5","key":"10.1016\/j.jcp.2026.115017_bib0028","doi-asserted-by":"crossref","DOI":"10.1029\/2021JB023120","article-title":"Physics-informed neural networks (PINNs) for wave propagation and full waveform inversions","volume":"127","author":"Rasht-Behesht","year":"2022","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"10.1016\/j.jcp.2026.115017_bib0029","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2022.111769","article-title":"On stability and regularization for data-driven solution of parabolic inverse source problems","volume":"474","author":"Zhang","year":"2023","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115017_bib0030","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2025.117077","article-title":"Convergence analysis of a PINNs-based approach to the inverse source problem of the heat equation with local measurements","volume":"476","author":"Zhang","year":"2026","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.jcp.2026.115017_bib0031","doi-asserted-by":"crossref","first-page":"852","DOI":"10.4208\/csiam-am.SO-2023-0035","article-title":"Solving the inverse potential problem in the parabolic equation by the deep neural networks method","volume":"5","author":"Zhang","year":"2024","journal-title":"CSIAM Trans. Appl. Math."},{"issue":"5","key":"10.1016\/j.jcp.2026.115017_bib0032","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/add0d8","article-title":"Potential coefficient identification problem in parabolic equation with deep neural networks","volume":"41","author":"Cao","year":"2025","journal-title":"Inverse Probl."},{"key":"10.1016\/j.jcp.2026.115017_bib0033","first-page":"244","article-title":"Global uniqueness of a class of multidimensional inverse problems","volume":"24","author":"Bukhgeim","year":"1981","journal-title":"Sov. Math. Dokl."},{"key":"10.1016\/j.jcp.2026.115017_bib0034","series-title":"Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems","author":"Bellassoued","year":"2017"},{"issue":"2","key":"10.1016\/j.jcp.2026.115017_bib0035","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1093\/imanum\/drab032","article-title":"Estimates on the generalization error of physics-informed neural network for approximating a class of the inverse problems for PDEs","volume":"42","author":"Mishra","year":"2022","journal-title":"IMA J. Numer. Anal."},{"key":"10.1016\/j.jcp.2026.115017_bib0036","series-title":"Partial Diffrential Equation","author":"EVANs","year":"2012"},{"issue":"4","key":"10.1016\/j.jcp.2026.115017_bib0037","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1017\/S0956792513000107","article-title":"Time-reversal algorithms in viscoelastic media","volume":"24","author":"Ammari","year":"2013","journal-title":"Eur. J. Appl. Math."},{"key":"10.1016\/j.jcp.2026.115017_bib0038","series-title":"Photoacoustic Imaging for Attenuating Acoustic Media","first-page":"57","author":"Ammari","year":"2012"},{"issue":"6","key":"10.1016\/j.jcp.2026.115017_bib0039","doi-asserted-by":"crossref","first-page":"1435","DOI":"10.1016\/j.camwa.2017.06.030","article-title":"Reconstruction of space-dependent potential and\/or damping coefficients in the wave equation","volume":"74","author":"Hussein","year":"2017","journal-title":"Comput. Math. Appl."},{"key":"10.1016\/j.jcp.2026.115017_bib0040","doi-asserted-by":"crossref","DOI":"10.1088\/1361-6420\/acf408","article-title":"Recover all coefficients in second-order hyperbolic equations from finite sets of boundary measurements","volume":"39","author":"Liu","year":"2023","journal-title":"Inverse Probl."}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126003700?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126003700?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:41:26Z","timestamp":1780447286000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999126003700"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":40,"alternative-id":["S0021999126003700"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115017","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Data-driven regularization for coefficient inverse problems in wave equations using partial observations","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115017","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115017"}}