{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T16:44:18Z","timestamp":1772556258465,"version":"3.50.1"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","funder":[{"name":"U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research","award":["DE-SC0024162"],"award-info":[{"award-number":["DE-SC0024162"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["World Sci. Ann. Rev. Artif. Intell."],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework\u2019s performance in modeling complex physical systems.<\/jats:p>","DOI":"10.1142\/s2811032325400016","type":"journal-article","created":{"date-parts":[[2025,3,1]],"date-time":"2025-03-01T00:49:33Z","timestamp":1740790173000},"source":"Crossref","is-referenced-by-count":3,"title":["Efficient Training of Deep Neural Operator Networks via Randomized Sampling"],"prefix":"10.1142","volume":"03","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6559-4404","authenticated-orcid":false,"given":"Sharmila","family":"Karumuri","sequence":"first","affiliation":[{"name":"Department of Civil & Systems Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5040-4909","authenticated-orcid":false,"given":"Lori","family":"Graham-Brady","sequence":"additional","affiliation":[{"name":"Department of Civil & Systems Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8255-9080","authenticated-orcid":false,"given":"Somdatta","family":"Goswami","sequence":"additional","affiliation":[{"name":"Department of Civil & Systems Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA"}]}],"member":"219","published-online":{"date-parts":[[2025,4,28]]},"reference":[{"key":"S2811032325400016BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.10.045"},{"key":"S2811032325400016BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109120"},{"key":"S2811032325400016BIB003","doi-asserted-by":"publisher","DOI":"10.1038\/s42256-021-00302-5"},{"key":"S2811032325400016BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/72.392253"},{"key":"S2811032325400016BIB005","unstructured":"Y. LeCun,  L. Bottou,  G. B. Orr and  K.R. M\u00fcller,  Neural Networks: Tricks of the Trade,  Lecture Notes in Computer Science,  Springer, 2002, vol.  7700,  pp. 9\u201348."},{"key":"S2811032325400016BIB006","unstructured":"N. S. Keskar, D. Mudigere, J. Nocedal, M. Smelyanskiy and P. T. P. Tang,\n                      On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima\n                      , arXiv preprint, arXiv:1609.04836 [cs.LG], 2016, https:\/\/arxiv.org\/abs\/1609.04836."},{"key":"S2811032325400016BIB007","unstructured":"P. Goyal, P. Dolla\u0155, R. Girshick, P. Noordhuis, L. Wesolowski, A. Kyrola, A. Tulloch, Y. Jia and K. He,\n                      Accurate\n                      ,\n                      Large Minibatch SGD: Training ImageNet in 1 Hour\n                      , arXiv preprint, arXiv:1706.02677 [cs.CV], 2017, https:\/\/arxiv.org\/abs\/1706.02677."},{"key":"S2811032325400016BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111793"},{"key":"S2811032325400016BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2023.102120"},{"key":"S2811032325400016BIB010","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2312159120"},{"key":"S2811032325400016BIB011","unstructured":"B. Bahmani, S. Goswami, I. G. Kevrekidis and M. D. Shields,\n                      A Resolution Independent Neural Operator\n                      , arXiv preprint, arXiv:2407.13010 [cs.LG], 2024, https:\/\/arxiv.org\/ abs\/2407.13010."},{"key":"S2811032325400016BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2023.107228"},{"key":"S2811032325400016BIB013","doi-asserted-by":"crossref","unstructured":"V. Kumar, S. Goswami, K. Kontolati, M. D. Shields and G. E. Karniadakis,\n                      Synergistic Learning with Multi-Task DeepONet for Efficient PDE Problem Solving\n                      , arXiv preprint, arXiv:2408.02198 [cs.LG], 2024, https:\/\/arxiv.org\/abs\/2408.02198.","DOI":"10.1016\/j.neunet.2024.107113"},{"key":"S2811032325400016BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2023.116277"},{"key":"S2811032325400016BIB015","doi-asserted-by":"publisher","DOI":"10.1137\/22M1477751"},{"key":"S2811032325400016BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2023.116681"},{"key":"S2811032325400016BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2023.130551"},{"key":"S2811032325400016BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2023.107258"},{"key":"S2811032325400016BIB019","doi-asserted-by":"crossref","unstructured":"L. Mandl, S. Goswami, L. Lambers and T. Ricken,\n                      Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning\n                      , arXiv preprint, arXiv:2407.15887 [cs.LG], 2024, https:\/\/arxiv.org\/abs\/2407.15887.","DOI":"10.1016\/j.cma.2024.117586"},{"key":"S2811032325400016BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-36644-4_6"},{"key":"S2811032325400016BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114587"},{"key":"S2811032325400016BIB022","doi-asserted-by":"publisher","DOI":"10.1126\/sciadv.abi8605"},{"key":"S2811032325400016BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112008"},{"key":"S2811032325400016BIB024","doi-asserted-by":"publisher","DOI":"10.1137\/23M1598751"},{"key":"S2811032325400016BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114778"}],"container-title":["World Scientific Annual Review of Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S2811032325400016","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T03:31:00Z","timestamp":1769743860000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S2811032325400016"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":25,"alternative-id":["10.1142\/S2811032325400016"],"URL":"https:\/\/doi.org\/10.1142\/s2811032325400016","relation":{},"ISSN":["2811-0323","2811-0331"],"issn-type":[{"value":"2811-0323","type":"print"},{"value":"2811-0331","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"article-number":"2540001"}}