{"id":1992,"date":"2025-03-30T14:30:44","date_gmt":"2025-03-30T06:30:44","guid":{"rendered":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/?p=1992"},"modified":"2025-03-30T14:31:30","modified_gmt":"2025-03-30T06:31:30","slug":"solving-inversewave-problems-using-spacetime-radial-basis-functions-in-neural-networks","status":"publish","type":"post","link":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/?p=1992","title":{"rendered":"Solving InverseWave Problems Using Spacetime Radial Basis Functions in Neural Networks"},"content":{"rendered":"\n<p>Abstract: Conventional methods for solving inverse wave problems struggle with illposedness,<br>significant computational demands, and discretization errors. In this study,<br>we propose an innovative framework for solving inverse problems in wave equations by<br>using deep learning techniques with spacetime radial basis functions (RBFs). The proposed<br>method capitalizes on the pattern recognition strength of deep neural networks (DNNs) and<br>the precision of spacetime RBFs in capturing spatiotemporal dynamics. By utilizing initial<br>conditions, boundary data, and radial distances to construct spacetime RBFs, this approach<br>circumvents the need for wave equation discretization. Notably, the model maintains<br>accuracy even with incomplete or noisy boundary data, illustrating its robustness and<br>offering significant advancements over traditional techniques in solving wave equations.<br>Keywords: inverse problems; wave equations; deep learning; physics-informed neural<br>networks; radial basis functions<br>MSC: 35D35; 65M3<\/p>\n\n\n\n<p>Chih-Yu Liu, <strong>Cheng-Yu Ku<\/strong>*, Wei-Da Chen, Ying-Fan Lin and Jun-Hong Lin (2025), &#8220;Solving Inverse Wave Problems Using Spacetime Radial Basis Functions in Neural Networks,&#8221; Mathe<em>matics<\/em>\u00a02025,\u00a0<em>13(5)<\/em>, 725, pp. 1-21. (SCIE, IF 2.3, <strong>Q1, 21\/489 (4.3% JIF)<\/strong> in MATHEMATICS, JCR, 2023) <\/p>\n\n\n\n<p>Full paper download can be accessed by the following link.<\/p>\n\n\n\n<p>https:\/\/doi.org\/10.3390\/math13050725<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Abstract: Conventional methods for solving inverse wave [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":1993,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"class_list":["post-1992","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-clips"],"_links":{"self":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1992","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1992"}],"version-history":[{"count":1,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1992\/revisions"}],"predecessor-version":[{"id":1994,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/1992\/revisions\/1994"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=\/wp\/v2\/media\/1993"}],"wp:attachment":[{"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1992"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1992"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gsclab.ntou.edu.tw\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}