{"id":15362,"date":"2024-10-23T09:00:32","date_gmt":"2024-10-23T00:00:32","guid":{"rendered":"https:\/\/www.ecomottblog.com\/?p=15362"},"modified":"2025-03-14T17:13:14","modified_gmt":"2025-03-14T08:13:14","slug":"%e6%b8%ac%e5%ae%9a%e7%b5%90%e6%9e%9c%e3%82%84%e5%ae%9f%e9%a8%93%e7%b5%90%e6%9e%9c%e3%82%92%e5%87%a6%e7%90%86%e3%81%99%e3%82%8b%e3%81%9f%e3%82%81%e3%81%ae%e7%89%a9%e7%90%86%e6%83%85%e5%a0%b1%e3%83%8b","status":"publish","type":"post","link":"https:\/\/www.ecomottblog.com\/?p=15362","title":{"rendered":"\u6e2c\u5b9a\u7d50\u679c\u3084\u5b9f\u9a13\u7d50\u679c\u3092\u51e6\u7406\u3059\u308b\u305f\u3081\u306e\u7269\u7406\u60c5\u5831\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af(PINN)"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-15364 alignright\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_1.png\" alt=\"\" width=\"296\" height=\"297\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_1.png 674w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_1-300x300.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_1-150x150.png 150w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_1-213x214.png 213w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_1-259x260.png 259w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/>\u3053\u3093\u306b\u3061\u306f\u30c7\u30fc\u30bf\u30a2\u30ca\u30ea\u30c6\u30a3\u30af\u30b9\u90e8\u306e\u30ed\u30d9\u30eb\u30c8\u30fb\u30d5\u30d0\u30c1\u3067\u3059\u3002\u5c11\u3057\u524d\u306b\u3001<a 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\u304c\u4f7f\u308f\u308c\u307e\u3059\u3002\u3053\u308c\u306fPINN\u306e\u53ef\u80fd\u6027\u3092\u793a\u3059\u305f\u3081\u306b\u306f\u6709\u7528\u3067\u3059\u304c\u3001\u5b9f\u7528\u7684\u306a\u89b3\u70b9\u304b\u3089\u898b\u308b\u3068\u3001\u305d\u308c\u307b\u3069\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002\u65e2\u306b\u6570\u5024\u89e3\u304c\u5f97\u3089\u308c\u3066\u3044\u308b\u306e\u3067\u3001\u65b0\u3057\u3044\u8a08\u7b97\u3092\u884c\u3046\u5fc5\u8981\u304c\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u65b0\u3057\u3044\u6761\u4ef6\u4e0b\u3067\u306e\u4e88\u6e2c\u306b\u3082\u4f7f\u3048\u308b\u3088\u308a\u5b9f\u7528\u7684\u306a\u65b9\u6cd5\u3068\u3057\u3066\u3001\u5b9f\u9a13\u3084\u6e2c\u5b9a\u7d50\u679c\u3068\u7d44\u307f\u5408\u308f\u305b\u305fPINN\u304c\u63d0\u6848\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4eca\u56de\u306f\u3053\u306e\u6d3b\u7528\u4f8b\u30922\u3064\u7d39\u4ecb\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<br \/>\n<!--more--><\/p>\n<h1>\u533b\u7642\u753b\u50cf\u7528\u306ePINN<\/h1>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-15370\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2-1024x486.png\" alt=\"\" width=\"1024\" height=\"486\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2-1024x486.png 1024w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2-300x142.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2-768x365.png 768w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2-304x144.png 304w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2-282x134.png 282w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_2.png 1249w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>\u56f3\uff11\uff0e\u533b\u7642\u753b\u50cf\u89e3\u6790\u306b\u304a\u3051\u308bPINN\u306e\u5229\u7528\u4f8b\u3002\u56f3\u306f[1]\u304a\u3088\u3073[2]\u306b\u57fa\u3065\u3044\u3066\u4f5c\u6210\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n<p>\u8ad6\u6587[1]\u3068[2]\u3067\u306f\u3001MRI\u3084\u8d85\u97f3\u6ce2\u691c\u67fb\u3067\u5f97\u3089\u308c\u305f\u753b\u50cf\u3092\u7528\u3044\u3066\u3001\u4eba\u4f53\u306e\u81d3\u5668\u306e\u5909\u5f62\u3092\u89e3\u6790\u3059\u308b\u305f\u3081\u306ePINN\u306e\u8208\u5473\u6df1\u3044\u5fdc\u7528\u304c\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u56f31\u306b\u30e2\u30c7\u30eb\u304c\u793a\u3055\u308c\u3066\u3044\u307e\u3059\uff09\u3002\u3053\u306e\u7814\u7a76\u3067\u306f\u7279\u306b\u3001\u30d0\u30a4\u30aa\u30d7\u30b7\u30fc\u624b\u8853\u3084\u8d85\u97f3\u6ce2\u691c\u67fb\u4e2d\u306e\u5727\u529b\u306b\u3088\u3063\u3066\u5f15\u304d\u8d77\u3053\u3055\u308c\u308b\u524d\u7acb\u817a\u306e\u5909\u5f62\u306b\u6ce8\u76ee\u3057\u3066\u3044\u307e\u3059\u3002\u8d85\u97f3\u6ce2\u3084MRI\u3067\u5f97\u3089\u308c\u305f\u81d3\u5668\u306e\u753b\u50cf\u306f\u3001\u4e09\u6b21\u5143\u306e\u70b9\u7fa4\u30c7\u30fc\u30bf\u306b\u5909\u63db\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u30e2\u30c7\u30eb\u306b\u306f\u3001\u5909\u5f62\u524d\u306e\u81d3\u5668\u3092\u8868\u3059\u70b9\u7fa4\u3068\u5909\u5f62\u5f8c\u306e\u70b9\u7fa4\u306e2\u3064\u304c\u5165\u529b\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u70b9\u7fa4\u306e\u7279\u5fb4\u3092\u62bd\u51fa\u3059\u308b\u305f\u3081\u306b\u3001<a href=\"https:\/\/arxiv.org\/abs\/1612.00593\"> PointNet <\/a>\u3068\u3044\u3046\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<br \/>\n\u62bd\u51fa\u3055\u308c\u305f\u7279\u5fb4\u306f\u3001\u305d\u306e\u5f8c2\u3064\u306e\u5225\u3005\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u9001\u4fe1\u3055\u308c\u307e\u3059\u30021\u3064\u76ee\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u81d3\u5668\u306e\u5909\u5f62\u3092\u4e88\u6e2c\u3057\u3001Chamfer\u8ddd\u96e2\u304c\u640d\u5931\u95a2\u6570\u3068\u3057\u3066\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u8ddd\u96e2\u306f\u3001\u5b9f\u969b\u306e\u70b9\u7fa4\u3068\u30e2\u30c7\u30eb\u306b\u3088\u3063\u3066\u4e88\u6e2c\u3055\u308c\u305f\u70b9\u7fa4\u306e\u9055\u3044\u3092\u6e2c\u5b9a\u3057\u307e\u3059\u30022\u3064\u76ee\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u3001\u5f3e\u6027\u7406\u8ad6\u306b\u57fa\u3065\u304f\u7269\u7406\u65b9\u7a0b\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u5909\u5f62\u3092\u8aac\u660e\u3057\u307e\u3059\u3002\u640d\u5931\u95a2\u6570\uff08\u7269\u7406\u30d9\u30fc\u30b9\u306e\u640d\u5931\u95a2\u6570\uff09\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306e\u4e21\u5074\u3092\u4e00\u81f4\u3055\u305b\u308b\u3088\u3046\u306b\u6700\u9069\u5316\u3055\u308c\u3001\u7269\u7406\u7684\u306b\u6b63\u78ba\u306a\u7d50\u679c\u3092\u5f97\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059\u3002<br \/>\n\u3053\u306e\u30e2\u30c7\u30eb\u306f\u81d3\u5668\u306e\u5909\u5f62\u3092\u4e88\u6e2c\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u81d3\u5668\u306e\u7279\u6027\u3092\u8a3a\u65ad\u3059\u308b\u3053\u3068\u306b\u3082\u5229\u7528\u3067\u304d\u3001\u75c5\u6c17\u306e\u8a3a\u65ad\u306b\u5f79\u7acb\u3064\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h1>PIV\u88dc\u6b63\u306e\u305f\u3081\u306ePINN<\/h1>\n<p>\u8ad6\u6587[3]\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u308b\u30e2\u30c7\u30eb\u306f\u3001\u7523\u696d\u6a5f\u5668\u5185\u306e\u6db2\u4f53\u306e\u6d41\u308c\u306e\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u3092\u6e2c\u5b9a\u3059\u308b\u969b\u306e\u8aa4\u5dee\u88dc\u6b63\u3084\u30ce\u30a4\u30ba\u9664\u53bb\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002<br \/>\n\u3053\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u9060\u5fc3\u30d5\u30a1\u30f3\u304c\u5bfe\u8c61\u3067\u3059\u3002\u6e2c\u5b9a\u306f<a href=\"https:\/\/en.wikipedia.org\/wiki\/Particle_image_velocimetry\"> PIV<\/a> \u7c92\u5b50\u753b\u50cf\u6d41\u901f\u6e2c\u5b9a\u6cd5\uff09\u3092\u7528\u3044\u3066\u884c\u308f\u308c\u307e\u3057\u305f\u3002<br \/>\nPIV\u306f\u3001\u975e\u5e38\u306b\u5c0f\u3055\u3044\u7c92\u5b50\u3092\u6db2\u4f53\u306b\u52a0\u3048\u308b\u3053\u3068\u3067\u3001\u305d\u306e\u6d41\u308c\u3092\u8996\u899a\u5316\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002\u3053\u306e\u65b9\u6cd5\u3067\u306f\u3001\u5c02\u7528\u306e\u5149\u5b66\u30b7\u30b9\u30c6\u30e0\u3092\u4f7f\u7528\u3057\u3066\u3001\u88c5\u7f6e\u5185\u306e2\u6b21\u5143\u5e73\u9762\u5185\uff08\u56f32\uff09\u3067\u3053\u308c\u3089\u306e\u7c92\u5b50\u306e\u52d5\u304d\u3092\u8a18\u9332\u3057\u307e\u3059\u3002\u305d\u308c\u306b\u57fa\u3065\u3044\u3066\u3001\u89b3\u6e2c\u3055\u308c\u305f\u5e73\u9762\u5185\u306e\u6d41\u4f53\u306e\u6c34\u5e73\u304a\u3088\u3073\u5782\u76f4\u306e\u901f\u5ea6\u6210\u5206\u304c\u8a08\u7b97\u3055\u308c\u307e\u3057\u305f\u3002\u305f\u3060\u3057\u3001\u3053\u308c\u3089\u306e\u6e2c\u5b9a\u306b\u306f\u8aa4\u5dee\u304c\u3042\u308a\u3001\u6570\u5024\u8a08\u7b97\u7d50\u679c\u3068\u6bd4\u8f03\u3059\u308b\u3068\u30c7\u30fc\u30bf\u306b\u6b20\u640d\u304c\u751f\u3058\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u3089\u306e\u6e2c\u5b9a\u306b\u306f\u8aa4\u5dee\u88dc\u6b63\u304c\u5fc5\u8981\u3067\u3059\u3002<br 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loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-15397\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-1024x618.png\" alt=\"\" width=\"1024\" height=\"618\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-1024x618.png 1024w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-300x181.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-768x464.png 768w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-1536x927.png 1536w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-304x184.png 304w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1-282x170.png 282w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/10\/fig_6-1.png 1703w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><br 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data-teams=\"true\"><span class=\"ui-provider a b c d e f g h i j k l m n o p q r s t u v w x y z ab ac ae af ag ah ai aj ak\" dir=\"ltr\">\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u81ea\u52d5\u5fae\u5206\u3068\u306f\u5bfe\u7167\u7684\u306b\u3001\u7573\u307f\u8fbc\u307f\u30d5\u30a3\u30eb\u30bf\u30fc\u306f\u8a13\u7df4\u3092\u5fc5\u8981\u3068\u3057\u307e\u305b\u3093\u3002<\/span><\/span>\u305d\u306e\u7d50\u679c\u3001\u8a13\u7df4\u3055\u308c\u305f\u30e2\u30c7\u30eb\u306f\u3001\u6e2c\u5b9a\u6761\u4ef6\uff08\u3064\u307e\u308a\u30d7\u30ed\u30bb\u30b9\u306e\u9032\u884c\u72b6\u6cc1\uff09\u304c\u5909\u5316\u3057\u305f\u5834\u5408\u306b\u3082\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h1>\u6587\u732e\uff1a<\/h1>\n<p>[1] Z. Min, Z.M.C. Baum, S.U. Saeed, M. Emberton, D.C. Barratt, Z.A. Taylor, and Y. Hu (2024): Biomechanics-informed Non-rigid Medical Image Registration and its Inverse Material Property Estimation with Linear and Nonlinear Elasticit, <a href=\"https:\/\/arxiv.org\/abs\/2407.03292\"> arXiv:2407.03292v2<\/a><br \/>\n[2] Z. Min, Z.M.C. Baum, S.U. Saeed, M. Emberton, D.C. Barratt1, Z.A. Taylor, and Y. Hu (2023): Non-rigid Medical Image Registration using Physics-informed Neural Networks, <a href=\"https:\/\/arxiv.org\/abs\/2302.10343\"> arXiv:2302.10343v1 <\/a><br \/>\n[3] M. Soltani, G. Akbari, and N. Montazerin (2024): Trade-off between reconstruction accuracy and physical validity in modeling turbomachinery particle image velocimetry data by physics-informed convolutional neural networks, <a href=\"https:\/\/arxiv.org\/abs\/2403.00183\"> arXiv:2403.00183 <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3093\u306b\u3061\u306f\u30c7\u30fc\u30bf\u30a2\u30ca\u30ea\u30c6\u30a3\u30af\u30b9\u90e8\u306e\u30ed\u30d9\u30eb\u30c8\u30fb\u30d5\u30d0\u30c1\u3067\u3059\u3002\u5c11\u3057\u524d\u306b\u3001\u300c\u7269\u7406\u60c5\u5831\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08PINN\uff09\u300d\u7269\u7406\u60c5\u5831\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff09\u306b\u3064\u3044\u3066\u66f8\u304d\u307e\u3057\u305f\u3002\u3053\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u3001\u81ea\u7136\u754c\u3084\u5de5\u696d\u3067\u8d77\u304d\u308b\u73fe\u8c61\u3092\u8a18\u8ff0\u3059\u308b\u504f [&hellip;]<\/p>\n","protected":false},"author":104,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27],"tags":[249,125,248,247],"_links":{"self":[{"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts\/15362"}],"collection":[{"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/users\/104"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=15362"}],"version-history":[{"count":34,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts\/15362\/revisions"}],"predecessor-version":[{"id":16664,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts\/15362\/revisions\/16664"}],"wp:attachment":[{"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}