{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T16:38:33Z","timestamp":1770223113783,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T00:00:00Z","timestamp":1769990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["42476018"],"award-info":[{"award-number":["42476018"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Natural Science Foundation of Shandong Province, China","award":["ZR2024QF112"],"award-info":[{"award-number":["ZR2024QF112"]}]},{"name":"Key Laboratory of Ocean Observation and Information of Hainan Province","award":["HKLOOI-OF-2024-01"],"award-info":[{"award-number":["HKLOOI-OF-2024-01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Physics\u2013Informed Neural Networks (PINNs) have demonstrated efficacy in solving both forward and inverse problems for nonlinear partial differential equations (PDEs). However, they frequently struggle to accurately capture multiscale physical features, particularly in regions exhibiting sharp local variations such as shock waves and discontinuities, and often suffer from optimization difficulties in complex loss landscapes. To address these issues, we propose LocRes\u2013PINN, a physics\u2013informed neural network framework that integrates local awareness mechanisms with residual learning. This framework integrates a radial basis function (RBF) encoder to enhance the perception of local variations and embeds it within a residual backbone to facilitate stable gradient propagation. Furthermore, we incorporate a residual\u2013based adaptive refinement strategy and an adaptive weighted loss scheme to dynamically focus training on high\u2013error regions and balance multi\u2013objective constraints. Numerical experiments on the Extended Korteweg\u2013de Vries, Navier\u2013Stokes, and Burgers equations demonstrate that LocRes\u2013PINN reduces relative prediction errors by approximately 12% to 67% compared to standard benchmarks. The results also verify the model\u2019s robustness in parameter identification and noise resilience.<\/jats:p>","DOI":"10.3390\/computation14020037","type":"journal-article","created":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T12:49:44Z","timestamp":1770036584000},"page":"37","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["LocRes\u2013PINN: A Physics\u2013Informed Neural Network with Local Awareness and Residual Learning"],"prefix":"10.3390","volume":"14","author":[{"given":"Tangying","family":"Lv","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China"},{"name":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China"},{"name":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenming","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China"},{"name":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China"},{"name":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"},{"name":"Key Laboratory of Ocean Observation and Information of Hainan Province, Sanya Oceanographic Institution, Ocean University of China, Sanya 572025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6277-0775","authenticated-orcid":false,"given":"Hengkai","family":"Yao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China"},{"name":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China"},{"name":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingliang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China"},{"name":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China"},{"name":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yitong","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China"},{"name":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China"},{"name":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kuan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Ocean Observation and Information of Hainan Province, Sanya Oceanographic Institution, Ocean University of China, Sanya 572025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6194-3614","authenticated-orcid":false,"given":"Shanliang","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China"},{"name":"Qingdao Innovation Center of Artificial Intelligence Ocean Technology, Qingdao 266061, China"},{"name":"Shandong Engineering Research Center for Marine Scenarized Application of Artificial Intelligence Technology, Qingdao 266061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1007\/s10462-024-10874-4","article-title":"AI meets physics: A comprehensive survey","volume":"57","author":"Jiao","year":"2024","journal-title":"Artif. 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