{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T06:41:40Z","timestamp":1778222500593,"version":"3.51.4"},"publisher-location":"Cham","reference-count":22,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783031301049","type":"print"},{"value":"9783031301056","type":"electronic"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-30105-6_1","type":"book-chapter","created":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T20:31:55Z","timestamp":1681331515000},"page":"3-14","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solving Partial Differential Equations Using Point-Based Neural Networks"],"prefix":"10.1007","author":[{"given":"Ning","family":"Hua","sequence":"first","affiliation":[]},{"given":"Wenlian","family":"Lu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,13]]},"reference":[{"issue":"5","key":"1_CR1","doi-asserted-by":"publisher","first-page":"987","DOI":"10.1109\/72.712178","volume":"9","author":"IE Lagaris","year":"1998","unstructured":"Lagaris, I.E., Likas, A., Fotiadis, D.I.: Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Networks 9(5), 987\u20131000 (1998)","journal-title":"IEEE Trans. Neural Networks"},{"issue":"7","key":"1_CR2","doi-asserted-by":"publisher","first-page":"1331","DOI":"10.1007\/s11425-019-9547-2","volume":"62","author":"J He","year":"2019","unstructured":"He, J., Xu, J.: Mgnet: a unified framework of multigrid and convolutional neural network. Sci. China Math. 62(7), 1331\u20131354 (2019)","journal-title":"Sci. China Math."},{"issue":"21","key":"1_CR3","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2101784118","volume":"118","author":"D Kochkov","year":"2021","unstructured":"Kochkov, D., Smith, J.A., Alieva, A., Wang, Q., Brenner, M.P., Hoyer, S.: Machine learning-accelerated computational fluid dynamics. Proc. Natl. Acad. Sci. 118(21), e2101784118 (2021)","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"6","key":"1_CR4","doi-asserted-by":"publisher","first-page":"1381","DOI":"10.1109\/TNN.2005.857945","volume":"16","author":"P Ramuhalli","year":"2005","unstructured":"Ramuhalli, P., Udpa, L., Udpa, S.S.: Finite-element neural networks for solving differential equations. IEEE Trans. Neural Networks 16(6), 1381\u20131392 (2005)","journal-title":"IEEE Trans. Neural Networks"},{"key":"1_CR5","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1017\/jfm.2016.615","volume":"807","author":"J Ling","year":"2016","unstructured":"Ling, J., Kurzawski, A., Templeton, J.: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155\u2013166 (2016)","journal-title":"J. Fluid Mech."},{"key":"1_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.108910","volume":"398","author":"A Beck","year":"2019","unstructured":"Beck, A., Flad, D., Munz, C.D.: Deep neural networks for data-driven les closure models. J. Comput. Phys. 398, 108910 (2019)","journal-title":"J. Comput. Phys."},{"key":"1_CR7","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","volume":"378","author":"M Raissi","year":"2019","unstructured":"Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686\u2013707 (2019)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"1_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s40304-018-0127-z","volume":"6","author":"E Weinan","year":"2018","unstructured":"Weinan, E., Yu, B.: The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems. Commun. Math. Stat. 6(1), 1\u201312 (2018)","journal-title":"Commun. Math. Stat."},{"key":"1_CR9","unstructured":"Anandkumar, A., et al.: Neural operator: graph kernel network for partial differential equations. In: ICLR 2020 Workshop on Integration of Deep Neural Models and Differential Equations (2020)"},{"key":"1_CR10","unstructured":"Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Stuart, A., Bhattacharya, K., Anandkumar, A.: Multipole graph neural operator for parametric partial differential equations. In: Advances in Neural Information Processing Systems, vol. 33 (2020)"},{"key":"1_CR11","unstructured":"Li, Z., et al.: Fourier neural operator for parametric partial differential equations. In: International Conference on Learning Representations (2020)"},{"key":"1_CR12","doi-asserted-by":"publisher","first-page":"121","DOI":"10.5802\/smai-jcm.74","volume":"7","author":"K Bhattacharya","year":"2021","unstructured":"Bhattacharya, K., Hosseini, B., Kovachki, N.B., Stuart, A.M.: Model reduction and neural networks for parametric PDEs. The SMAI J. Comput. Math. 7, 121\u2013157 (2021)","journal-title":"The SMAI J. Comput. Math."},{"key":"1_CR13","unstructured":"Qi, C.R., Su, H., Mo, K., Guibas, L.J.: Pointnet: Deep learning on point sets for 3d classification and segmentation. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 652\u2013660 (2017)"},{"key":"1_CR14","unstructured":"Qi, C.R., Yi, L., Su, H., Guibas, L.J.: Pointnet++: deep hierarchical feature learning on point sets in a metric space. In: Advances in Neural Information Processing Systems, vol. 30 (2017)"},{"key":"1_CR15","doi-asserted-by":"crossref","unstructured":"Thomas, H., Qi, C.R., Deschaud, J.E., Marcotegui, B., Goulette, F., Guibas, L.J.: Kpconv: flexible and deformable convolution for point clouds. In: Proceedings of the IEEE\/CVF International Conference on Computer Vision, pp. 6411\u20136420 (2019)","DOI":"10.1109\/ICCV.2019.00651"},{"key":"1_CR16","doi-asserted-by":"crossref","unstructured":"Wu, W., Qi, Z., Fuxin, L.: Pointconv: deep convolutional networks on 3D point clouds. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp. 9621\u20139630 (2019)","DOI":"10.1109\/CVPR.2019.00985"},{"issue":"5","key":"1_CR17","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","volume":"2","author":"K Hornik","year":"1989","unstructured":"Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Netw. 2(5), 359\u2013366 (1989)","journal-title":"Neural Netw."},{"issue":"6","key":"1_CR18","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","volume":"6","author":"M Leshno","year":"1993","unstructured":"Leshno, M., Lin, V.Y., Pinkus, A., Schocken, S.: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw. 6(6), 861\u2013867 (1993)","journal-title":"Neural Netw."},{"issue":"4","key":"1_CR19","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1109\/72.392253","volume":"6","author":"T Chen","year":"1995","unstructured":"Chen, T., Chen, H.: Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans. Neural Networks 6(4), 911\u2013917 (1995)","journal-title":"IEEE Trans. Neural Networks"},{"issue":"3","key":"1_CR20","doi-asserted-by":"publisher","first-page":"353","DOI":"10.2140\/pjm.1951.1.353","volume":"1","author":"J Dugundji","year":"1951","unstructured":"Dugundji, J.: An extension of Tietze\u2019s theorem. Pac. J. Math. 1(3), 353\u2013367 (1951)","journal-title":"Pac. J. Math."},{"key":"1_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1007\/978-3-319-24574-4_28","volume-title":"Medical Image Computing and Computer-Assisted Intervention \u2013 MICCAI 2015","author":"O Ronneberger","year":"2015","unstructured":"Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234\u2013241. Springer, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-24574-4_28"},{"key":"1_CR22","unstructured":"Hendrycks, D., Gimpel, K.: Gaussian error linear units (gelus). arXiv preprint arXiv:1606.08415 (2016)"}],"container-title":["Lecture Notes in Computer Science","Neural Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-30105-6_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,12]],"date-time":"2023-04-12T20:32:04Z","timestamp":1681331524000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-30105-6_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031301049","9783031301056"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-30105-6_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"13 April 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICONIP","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Neural Information Processing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"New Delhi","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"India","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 November 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 November 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"iconip2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/iconip2022.apnns.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easy Chair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"810","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"359","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"44% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"2.65","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"ICONIP 2022 consists of a two-volume set, LNCS & CCIS, which includes 146 and 213 papers","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}