{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T07:04:52Z","timestamp":1784012692127,"version":"3.55.0"},"publisher-location":"Singapore","reference-count":31,"publisher":"Springer Nature Singapore","isbn-type":[{"value":"9789819234431","type":"print"},{"value":"9789819234448","type":"electronic"}],"license":[{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T00:00:00Z","timestamp":1784073600000},"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":[[2027]]},"DOI":"10.1007\/978-981-92-3444-8_41","type":"book-chapter","created":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T06:18:33Z","timestamp":1784009913000},"page":"495-505","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["PINNs Integrating the Lattice Boltzmann Method: A Neural-Kinetic Operator Review"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-7150-1318","authenticated-orcid":false,"given":"Mengyu","family":"Feng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-2966-880X","authenticated-orcid":false,"given":"Ziyi","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1242-0005","authenticated-orcid":false,"given":"Minglei","family":"Shan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,15]]},"reference":[{"issue":"1","key":"41_CR1","doi-asserted-by":"publisher","first-page":"25","DOI":"10.2514\/1.J058291","volume":"58","author":"N Thuerey","year":"2020","unstructured":"Thuerey, N., Wei\u00dfenow, K., Prantl, L., Hu, X.: Deep learning methods for Reynolds-averaged Navier\u2013Stokes simulations of airfoil flows. AIAA J. 58(1), 25\u201336 (2020)","journal-title":"AIAA J."},{"key":"41_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.paerosci.2022.100849","volume":"134","author":"J Li","year":"2022","unstructured":"Li, J., Du, X., Martins, J.R.R.A.: Machine learning in aerodynamic shape optimization. Prog. Aerosp. Sci. 134, 100849 (2022)","journal-title":"Prog. Aerosp. Sci."},{"key":"41_CR3","volume-title":"International Conference on Learning Representations","author":"T Pfaff","year":"2020","unstructured":"Pfaff, T., Fortunato, M., Sanchez-Gonzalez, A., Battaglia, P.: Learning mesh-based simulation with graph networks. In: International Conference on Learning Representations (2020)"},{"issue":"8","key":"41_CR4","doi-asserted-by":"publisher","first-page":"2820","DOI":"10.2514\/1.J060131","volume":"59","author":"SL Brunton","year":"2021","unstructured":"Brunton, S.L., et al.: Data-driven aerospace engineering: reframing the industry with machine learning. AIAA J. 59(8), 2820\u20132847 (2021)","journal-title":"AIAA J."},{"key":"41_CR5","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":"5","key":"41_CR6","doi-asserted-by":"publisher","first-page":"A3055","DOI":"10.1137\/20M1318043","volume":"43","author":"S Wang","year":"2021","unstructured":"Wang, S., Teng, Y., Perdikaris, P.: Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM J. Sci. Comput. 43(5), A3055\u2013A3081 (2021)","journal-title":"SIAM J. Sci. Comput."},{"key":"41_CR7","doi-asserted-by":"crossref","unstructured":"Jagtap, A.D., Karniadakis, G.E.: Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential \u1e63equations. Commun. Comput. Phys. 28(5) (2020)","DOI":"10.4208\/cicp.OA-2020-0164"},{"key":"41_CR8","unstructured":"Chuang, P.-Y., Barba, L.A.: Predictive limitations of physics-informed neural networks in vortex shedding. arXiv preprint arXiv:2306.00230. (2023)"},{"issue":"22","key":"41_CR9","doi-asserted-by":"publisher","first-page":"3712","DOI":"10.3390\/math13223712","volume":"13","author":"M Feng","year":"2025","unstructured":"Feng, M., et al.: Hybrid physics-informed neural networks integrating multi-relaxation-time lattice Boltzmann method for forward and inverse flow problems. Mathematics. 13(22), 3712 (2025)","journal-title":"Mathematics"},{"issue":"11","key":"41_CR10","doi-asserted-by":"publisher","first-page":"2419","DOI":"10.1039\/D3SM01648J","volume":"20","author":"DPF Silva","year":"2024","unstructured":"Silva, D.P.F., Coelho, R.C.V., Pagonabarraga, I., Succi, S., da Gama, M.M.T., Ara\u00fajo, N.A.M.: Lattice Boltzmann simulation of deformable fluid-filled bodies: progress and perspectives. Soft Matter. 20(11), 2419\u20132441 (2024)","journal-title":"Soft Matter"},{"key":"41_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.commatsci.2022.111288","volume":"206","author":"R Samanta","year":"2022","unstructured":"Samanta, R., Chattopadhyay, H., Guha, C.: A review on the application of lattice Boltzmann method for melting and solidification problems. Comput. Mater. Sci. 206, 111288 (2022)","journal-title":"Comput. Mater. Sci."},{"key":"41_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultsonch.2019.104873","volume":"62","author":"Y Yang","year":"2020","unstructured":"Yang, Y., Shan, M., Kan, X., Shangguan, Y., Han, Q.: Thermodynamic of collapsing cavitation bubble investigated by pseudopotential and thermal MRT-LBM. Ultrason. Sonochem. 62, 104873 (2020)","journal-title":"Ultrason. Sonochem."},{"issue":"6","key":"41_CR13","doi-asserted-by":"publisher","first-page":"2077","DOI":"10.1016\/j.jrmge.2024.03.010","volume":"16","author":"Q Wang","year":"2024","unstructured":"Wang, Q., Kumar, K.: An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method. J. Rock Mech. Geotech. Eng. 16(6), 2077\u20132090 (2024)","journal-title":"J. Rock Mech. Geotech. Eng."},{"issue":"9","key":"41_CR14","doi-asserted-by":"publisher","first-page":"588","DOI":"10.3390\/axioms13090588","volume":"13","author":"Z Liu","year":"2024","unstructured":"Liu, Z., Zhang, C., Zhu, W., Huang, D.: A physics-informed neural network based on the Boltzmann equation with multiple-relaxation-time collision operators. Axioms. 13(9), 588 (2024)","journal-title":"Axioms"},{"issue":"11","key":"41_CR15","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/adfc43","volume":"34","author":"C Yang","year":"2025","unstructured":"Yang, C., et al.: Improved physics-informed neural networks incorporating lattice Boltzmann method optimized by tanh robust weight initialization. Chin. Phys. B. 34(11), 110701 (2025)","journal-title":"Chin. Phys. B"},{"key":"41_CR16","first-page":"1","volume-title":"2025 IEEE 7th Colombian Conference on Automatic Control (CCAC)","author":"CEP Velandia","year":"2025","unstructured":"Velandia, C.E.P., Mojica-Nava, E.: Solving fluid and diffusion dynamics problems using physics-informed neural networks and the lattice Boltzmann method. In: 2025 IEEE 7th Colombian Conference on Automatic Control (CCAC), pp. 1\u20136. IEEE (2025)"},{"key":"41_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110676","volume":"447","author":"Q Lou","year":"2021","unstructured":"Lou, Q., Meng, X., Karniadakis, G.E.: Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation. J. Comput. Phys. 447, 110676 (2021)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"41_CR18","doi-asserted-by":"publisher","first-page":"C451","DOI":"10.1137\/24M1668809","volume":"47","author":"J Oh","year":"2025","unstructured":"Oh, J., Cho, S.Y., Yun, S.-B., Park, E., Hong, Y.: Separable physics-informed neural networks for solving the BGK model of the Boltzmann equation. SIAM J. Sci. Comput. 47(2), C451\u2013C474 (2025)","journal-title":"SIAM J. Sci. Comput."},{"key":"41_CR19","doi-asserted-by":"publisher","first-page":"23761","DOI":"10.52202\/075280-1032","volume":"36","author":"J Cho","year":"2023","unstructured":"Cho, J., Nam, S., Yang, H., Yun, S.-B., Hong, Y., Park, E.: Separable physics-informed neural networks. Adv. Neural Inf. Proces. Syst. 36, 23761\u201323788 (2023)","journal-title":"Adv. Neural Inf. Proces. Syst."},{"key":"41_CR20","doi-asserted-by":"crossref","unstructured":"Li, Y., Liu, S., Xu, Z.: Spectral decomposition PINN-LBM for high Reynolds number turbulence simulation. Authorea Preprints. (2025)","DOI":"10.22541\/au.176046355.55971478\/v1"},{"issue":"3","key":"41_CR21","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1140\/epje\/s10189-023-00267-w","volume":"46","author":"A Corbetta","year":"2023","unstructured":"Corbetta, A., Gabbana, A., Gyrya, V., Livescu, D., Prins, J., Toschi, F.: Toward learning lattice Boltzmann collision operators. Eur. Phys. J. E. 46(3), 10 (2023)","journal-title":"Eur. Phys. J. E"},{"key":"41_CR22","doi-asserted-by":"crossref","unstructured":"Zhang, L., Ma, W., Lou, Q., Zhang, J.: Simulation of rarefied gas flows using physics-informed neural network combined with discrete velocity method. Phys. Fluids. 35(7) (2023)","DOI":"10.1063\/5.0156404"},{"key":"41_CR23","doi-asserted-by":"crossref","unstructured":"Aygun, A., Karakus, A.: Physics-informed neural networks for weakly compressible flows using Galerkin\u2013Boltzmann formulation. Phys. Fluids. 36(11) (2024)","DOI":"10.1063\/5.0235756"},{"issue":"19","key":"41_CR24","doi-asserted-by":"publisher","first-page":"4147","DOI":"10.3390\/math11194147","volume":"11","author":"Z Liu","year":"2023","unstructured":"Liu, Z., Chen, Y., Song, G., Song, W., Xu, J.: Combination of physics-informed neural networks and single-relaxation-time lattice Boltzmann method for solving inverse problems in fluid mechanics. Mathematics. 11(19), 4147 (2023)","journal-title":"Mathematics"},{"key":"41_CR25","doi-asserted-by":"crossref","unstructured":"Li, Y., Zhang, L.: Physics-informed neural networks for enhanced interface preservation in lattice Boltzmann multiphase simulations. arXiv preprint arXiv:2504.10539. (2025)","DOI":"10.1109\/ACDSA65407.2025.11166586"},{"key":"41_CR26","unstructured":"Fischer, P., Kaltenbach, S., Litvinov, S., Succi, S., Koumoutsakos, P.: Optimal lattice Boltzmann closures through multi-agent reinforcement learning. arXiv preprint arXiv:2504.14422. (2025)"},{"issue":"1","key":"41_CR27","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1038\/s42005-024-01832-1","volume":"7","author":"X Xue","year":"2024","unstructured":"Xue, X., Wang, S., Yao, H.D., Davidson, L., Coveney, P.V.: Physics informed data-driven near-wall modelling for lattice Boltzmann simulation of high Reynolds number turbulent flows. Commun. Phys. 7(1), 338 (2024)","journal-title":"Commun. Phys."},{"key":"41_CR28","doi-asserted-by":"crossref","unstructured":"Bedrunka, M., Wilde, D., Kliemank, M., Reith, D., Foysi, H., Kr\u00e4mer, A.: Lettuce: pytorch-based lattice Boltzmann framework, 40\u201355","DOI":"10.1007\/978-3-030-90539-2_3"},{"key":"41_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2024.109187","volume":"300","author":"M Ataei","year":"2024","unstructured":"Ataei, M., Salehipour, H.: Xlb: a differentiable massively parallel lattice Boltzmann library in python. Comput. Phys. Commun. 300, 109187 (2024)","journal-title":"Comput. Phys. Commun."},{"issue":"8","key":"41_CR30","doi-asserted-by":"publisher","first-page":"270","DOI":"10.3390\/fluids7080270","volume":"7","author":"J Yang","year":"2022","unstructured":"Yang, J., Xu, Y., Yang, L.: Taichi-lbm3d: a single-phase and multiphase lattice Boltzmann solver on cross-platform multicore cpu\/gpus. Fluids. 7(8), 270 (2022)","journal-title":"Fluids"},{"key":"41_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2020.101269","volume":"49","author":"M Bauer","year":"2021","unstructured":"Bauer, M., K\u00f6stler, H., R\u00fcde, U.: Lbm.Py: automatic code generation for efficient parallel lattice Boltzmann methods. J. Comput. Sci. 49, 101269 (2021)","journal-title":"J. Comput. Sci."}],"container-title":["Lecture Notes in Computer Science","Advanced Intelligent Computing Technology and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-981-92-3444-8_41","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T06:18:35Z","timestamp":1784009915000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-981-92-3444-8_41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,15]]},"ISBN":["9789819234431","9789819234448"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-981-92-3444-8_41","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,15]]},"assertion":[{"value":"15 July 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICIC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Intelligent Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Toronto","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2026","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 July 2026","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 July 2026","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icic2026a","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.ic-icc.cn\/2026\/index.htm","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}