{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T05:39:05Z","timestamp":1778391545884,"version":"3.51.4"},"reference-count":38,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100018537","name":"National Science and Technology Major Project","doi-asserted-by":"publisher","award":["2024ZD1001502"],"award-info":[{"award-number":["2024ZD1001502"]}],"id":[{"id":"10.13039\/501100018537","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015314","name":"China University of Geosciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100015314","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42522404"],"award-info":[{"award-number":["42522404"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42220104002"],"award-info":[{"award-number":["42220104002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers &amp; Geosciences"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.cageo.2026.106161","type":"journal-article","created":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T16:50:44Z","timestamp":1774630244000},"page":"106161","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Efficient multi-GPU distributed training strategies for neural operator networks: Application to magnetotelluric forward modeling"],"prefix":"10.1016","volume":"212","author":[{"given":"Juntong","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiyang","family":"Liao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2025-8960","authenticated-orcid":false,"given":"Ronghua","family":"Peng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongzhu","family":"Cai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangyun","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.cageo.2026.106161_b1","series-title":"TensorFlow: Large-scale machine learning on heterogeneous systems","author":"Abadi","year":"2015"},{"key":"10.1016\/j.cageo.2026.106161_b2","doi-asserted-by":"crossref","DOI":"10.1016\/j.jappgeo.2021.104290","article-title":"Machine learning based fast forward modelling of groundbased time-domain electromagnetic data","volume":"187","author":"Bording","year":"2021","journal-title":"J. Appl. Geophys."},{"key":"10.1016\/j.cageo.2026.106161_b3","doi-asserted-by":"crossref","DOI":"10.1016\/j.compchemeng.2022.107898","article-title":"Perspectives on the integration between first-principles and data-driven modeling","volume":"166","author":"Bradley","year":"2022","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.cageo.2026.106161_b4","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.cageo.2019.03.002","article-title":"Inverting magnetotelluric responses in a three-dimensional earth using fast forward approximations based on artificial neural networks","volume":"127","author":"Conway","year":"2019","journal-title":"Comput. Geosci."},{"key":"10.1016\/j.cageo.2026.106161_b5","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109550","article-title":"Data driven approximation of parametrized pdes by reduced basis and neural networks","volume":"416","author":"Dal Santo","year":"2020","journal-title":"J. Comput. Phys."},{"issue":"7","key":"10.1016\/j.cageo.2026.106161_b6","doi-asserted-by":"crossref","first-page":"4417","DOI":"10.1109\/TGRS.2019.2891206","article-title":"A machine learning-based fast-forward solver for ground penetrating radar with application to full-waveform inversion","volume":"57","author":"Giannakis","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"10.1016\/j.cageo.2026.106161_b7","series-title":"Pipedream: Fast and efficient pipeline parallel dnn training","author":"Harlap","year":"2018"},{"key":"10.1016\/j.cageo.2026.106161_b8","doi-asserted-by":"crossref","unstructured":"Heigold, G., McDermott, E., Vanhoucke, V., et al., 2014. Asynchronous stochastic optimization for sequence training of deep neural networks. In: 2014 IEEE International Conference on Acoustics, Speech and Signal Processing. ICASSP, pp. 5587\u20135591.","DOI":"10.1109\/ICASSP.2014.6854672"},{"key":"10.1016\/j.cageo.2026.106161_b9","article-title":"Gpipe: Efficient training of giant neural networks using pipeline parallelism","volume":"32","author":"Huang","year":"2019","journal-title":"Adv. Neural Inf. Process. Syst."},{"issue":"3","key":"10.1016\/j.cageo.2026.106161_b10","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1093\/gji\/ggac029","article-title":"Application of multiscale magnetotelluric data to mineral exploration: an example from the east tennant region, northern Australia","volume":"229","author":"Jiang","year":"2022","journal-title":"Geophys. J. Int."},{"key":"10.1016\/j.cageo.2026.106161_b11","series-title":"Deep Learning with Python: Learn Best Practices of Deep Learning Models with PyTorch","first-page":"27","article-title":"Introduction to pytorch","author":"Ketkar","year":"2021"},{"key":"10.1016\/j.cageo.2026.106161_b12","series-title":"One weird trick for parallelizing convolutional neural networks","author":"Krizhevsky","year":"2014"},{"issue":"388","key":"10.1016\/j.cageo.2026.106161_b13","first-page":"1","article-title":"Fourier neural operator with learned deformations for pdes on general geometries","volume":"24","author":"Li","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.cageo.2026.106161_b14","series-title":"Fourier neural operator for parametric partial differential equations","author":"Li","year":"2020"},{"key":"10.1016\/j.cageo.2026.106161_b15","series-title":"Physics-informed neural operator for learning partial differential equations","author":"Li","year":"2021"},{"key":"10.1016\/j.cageo.2026.106161_b16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TGRS.2022.3230932","article-title":"3-d joint inversion of MT and CSEM data for imaging a high-temperature geothermal system in Yanggao region, Shanxi province, China","volume":"60","author":"Liao","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"2","key":"10.1016\/j.cageo.2026.106161_b17","doi-asserted-by":"crossref","first-page":"F11","DOI":"10.1190\/geo2023-0613.1","article-title":"Fast forward modeling of magnetotelluric data in complex continuous media using an extended Fourier DeepONet architecture","volume":"90","author":"Liao","year":"2025","journal-title":"Geophysics"},{"key":"10.1016\/j.cageo.2026.106161_b18","first-page":"3208","article-title":"Pde-net: Learning pdes from data","author":"Long","year":"2018","journal-title":"Int. Conf. Mach. Learn."},{"key":"10.1016\/j.cageo.2026.106161_b19","series-title":"Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators","author":"Lu","year":"2019"},{"issue":"3","key":"10.1016\/j.cageo.2026.106161_b20","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1038\/s42256-021-00302-5","article-title":"Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators","volume":"3","author":"Lu","year":"2021","journal-title":"Nat. Mach. Intell."},{"key":"10.1016\/j.cageo.2026.106161_b21","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.epsl.2013.12.026","article-title":"Deep electrical resistivity structure of the northwestern US derived from 3-D inversion of USArray magnetotelluric data","volume":"402","author":"Meqbel","year":"2014","journal-title":"Earth Planet. Sci. Lett."},{"key":"10.1016\/j.cageo.2026.106161_b22","doi-asserted-by":"crossref","unstructured":"Narayanan, D., Harlap, A., Phanishayee, A., et al., 2019. PipeDream: Generalized pipeline parallelism for DNN training. In: Proceedings of the 27th ACM Symposium on Operating Systems Principles. pp. 1\u201315.","DOI":"10.1145\/3341301.3359646"},{"issue":"5","key":"10.1016\/j.cageo.2026.106161_b23","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s10712-017-9439-x","article-title":"Magnetotelluric studies for hydrocarbon and geothermal resources: Examples from the Asian region","volume":"38","author":"Patro","year":"2017","journal-title":"Surv. Geophys."},{"issue":"18","key":"10.1016\/j.cageo.2026.106161_b24","doi-asserted-by":"crossref","DOI":"10.1029\/2012GL053080","article-title":"Magnetotelluric monitoring of a fluid injection: Example from an enhanced geothermal system","volume":"39","author":"Peacock","year":"2012","journal-title":"Geophys. Res. Lett."},{"key":"10.1016\/j.cageo.2026.106161_b25","doi-asserted-by":"crossref","DOI":"10.1016\/j.cageo.2023.105360","article-title":"Rapid surrogate modeling of magnetotelluric in the frequency domain using physics-driven deep neural networks","volume":"176","author":"Peng","year":"2023","journal-title":"Comput. Geosci."},{"key":"10.1016\/j.cageo.2026.106161_b26","first-page":"1","article-title":"Rapid surrogate modeling of electromagnetic data in frequency domain using neural operator","volume":"60","author":"Peng","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"5","key":"10.1016\/j.cageo.2026.106161_b27","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"},{"issue":"5","key":"10.1016\/j.cageo.2026.106161_b28","doi-asserted-by":"crossref","first-page":"R659","DOI":"10.1190\/geo2020-0370.1","article-title":"Seismic data inversion with acquisition adaptive convolutional neural network for geologic forward prospecting in tunnels","volume":"86","author":"Ren","year":"2021","journal-title":"Geophysics"},{"key":"10.1016\/j.cageo.2026.106161_b29","series-title":"Horovod: fast and easy distributed deep learning in TensorFlow","author":"Sergeev","year":"2018"},{"key":"10.1016\/j.cageo.2026.106161_b30","first-page":"1","article-title":"Application of multitask learning for 2-d modeling of magnetotelluric surveys: Te case","volume":"60","author":"Shan","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"3","key":"10.1016\/j.cageo.2026.106161_b31","doi-asserted-by":"crossref","first-page":"1503","DOI":"10.1093\/gji\/ggac399","article-title":"Simulating seismic multifrequency wavefields with the fourier feature physics-informed neural network","volume":"232","author":"Song","year":"2023","journal-title":"Geophys. J. Int."},{"issue":"1","key":"10.1016\/j.cageo.2026.106161_b32","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1046\/j.1365-246x.2000.00065.x","article-title":"Artificial neural network inversion of magnetotelluric data in terms of three-dimensional earth macroparameters","volume":"142","author":"Spichak","year":"2000","journal-title":"Geophys. J. Int."},{"key":"10.1016\/j.cageo.2026.106161_b33","series-title":"Dokl. Akad. Nauk. SSSR","first-page":"295","article-title":"On determining electrical characteristics of the deep layers of the earth\u2019s crust","volume":"Vol. 73","author":"Tikhonov","year":"1950"},{"key":"10.1016\/j.cageo.2026.106161_b34","doi-asserted-by":"crossref","DOI":"10.1016\/j.advwatres.2022.104180","article-title":"U-FNO\u2014An enhanced Fourier neural operator-based deep-learning model for multiphase flow","volume":"163","author":"Wen","year":"2022","journal-title":"Adv. Water Resour."},{"key":"10.1016\/j.cageo.2026.106161_b35","unstructured":"Willard, J., Jia, X., Xu, S., et al., 2020. Integrating physics-based modeling with machine learning: A survey arXiv preprint arXiv:2003.04919 1 1\u201334."},{"key":"10.1016\/j.cageo.2026.106161_b36","series-title":"Dive into Deep Learning","author":"Zhang","year":"2023"},{"key":"10.1016\/j.cageo.2026.106161_b37","doi-asserted-by":"crossref","DOI":"10.1016\/j.geothermics.2022.102505","article-title":"Three-dimensional magnetotelluric inversion reveals the typical geothermal structure of yanggao geothermal field in datong basin, northern China","volume":"105","author":"Zhou","year":"2022","journal-title":"Geothermics"},{"key":"10.1016\/j.cageo.2026.106161_b38","article-title":"Parallelized stochastic gradient descent","volume":"23","author":"Zinkevich","year":"2010","journal-title":"Adv. Neural Inf. Process. Syst."}],"container-title":["Computers &amp; Geosciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0098300426000580?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0098300426000580?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T13:43:12Z","timestamp":1776346992000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0098300426000580"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":38,"alternative-id":["S0098300426000580"],"URL":"https:\/\/doi.org\/10.1016\/j.cageo.2026.106161","relation":{},"ISSN":["0098-3004"],"issn-type":[{"value":"0098-3004","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Efficient multi-GPU distributed training strategies for neural operator networks: Application to magnetotelluric forward modeling","name":"articletitle","label":"Article Title"},{"value":"Computers & Geosciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cageo.2026.106161","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"106161"}}