{"id":15463,"date":"2024-12-17T11:30:51","date_gmt":"2024-12-17T02:30:51","guid":{"rendered":"https:\/\/www.ecomottblog.com\/?p=15463"},"modified":"2025-03-14T17:10:48","modified_gmt":"2025-03-14T08:10:48","slug":"deeponet%ef%bc%9a%e3%83%87%e3%83%bc%e3%82%bf%e9%a7%86%e5%8b%95%e5%9e%8b%ef%bc%88data-driven%ef%bc%89%e3%81%ae%e6%a9%9f%e6%a2%b0%e5%ad%a6%e7%bf%92%e3%81%ab%e3%82%88%e3%82%8b%e9%ab%98%e9%80%9f%e3%82%b7","status":"publish","type":"post","link":"https:\/\/www.ecomottblog.com\/?p=15463","title":{"rendered":"DeepONet\uff1a\u30c7\u30fc\u30bf\u99c6\u52d5\u578b\uff08data-driven\uff09\u306e\u6a5f\u68b0\u5b66\u7fd2\u306b\u3088\u308b\u9ad8\u901f\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-15483 alignright\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2024-12-16-103631.png\" alt=\"\" width=\"280\" height=\"281\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2024-12-16-103631.png 555w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2024-12-16-103631-300x300.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2024-12-16-103631-150x150.png 150w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2024-12-16-103631-213x214.png 213w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/\u30b9\u30af\u30ea\u30fc\u30f3\u30b7\u30e7\u30c3\u30c8-2024-12-16-103631-259x260.png 259w\" sizes=\"(max-width: 280px) 100vw, 280px\" \/><br \/>\n\u3053\u3093\u306b\u3061\u306f\u3001\u30c7\u30fc\u30bf\u30a2\u30ca\u30ea\u30c6\u30a3\u30af\u30b9\u90e8\u9580\u306e\u30ed\u30d9\u30eb\u30c8\u30fb\u30d5\u30d0\u30c1\u3067\u3059\u3002<\/p>\n<p>\u79c1\u305f\u3061\u306f\u4eca\u3001\u307e\u3055\u306b\u300c\u30d3\u30c3\u30b0\u30c7\u30fc\u30bf\u6642\u4ee3\u300d\u306b\u751f\u304d\u3066\u3044\u307e\u3059\u3002\u65e5\u3005\u3001\u4eba\u3005\u306b\u3088\u3063\u3066\u81a8\u5927\u306a\u30c7\u30fc\u30bf\u304c\u751f\u6210\u30fb\u53ce\u96c6\u3055\u308c\u3066\u304a\u308a\u3001\u3053\u308c\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u3067\u8cb4\u91cd\u306a\u6d1e\u5bdf\u304c\u5f97\u3089\u308c\u308b\u4e00\u65b9\u3001\u5927\u304d\u306a\u8ab2\u984c\u3082\u751f\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u3046\u3057\u305f\u8ab2\u984c\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u3001\u65b0\u3057\u3044\u30c4\u30fc\u30eb\u3084\u6280\u8853\u304c\u6b21\u3005\u3068\u767b\u5834\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30c7\u30fc\u30bf\u3092\u52b9\u7387\u7684\u306b\u51e6\u7406\u3057\u3001\u4fa1\u5024\u3042\u308b\u60c5\u5831\u3092\u62bd\u51fa\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u30c4\u30fc\u30eb\u306e\u4e00\u4f8b\u304c\u3001\u4eca\u56de\u306e\u30d6\u30ed\u30b0\u3067\u7d39\u4ecb\u3059\u308b<strong>DeepONet\uff08Deep Operator Network\uff09<\/strong>\u3067\u3059\u3002<\/p>\n<p>DeepONet\u306f\u3001\u3042\u308b\u95a2\u6570\u3092\u5225\u306e\u95a2\u6570\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u7fd2\u3059\u308b\u305f\u3081\u306b\u8a2d\u8a08\u3055\u308c\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u3067\u3059\u3002\u5f93\u6765\u3001\u3053\u306e\u3088\u3046\u306a\u5909\u63db\u3092\u884c\u3046\u306b\u306f\u30012\u3064\u306e\u95a2\u6570\u306e\u95a2\u4fc2\u3092\u5b9a\u7fa9\u3059\u308b\u660e\u78ba\u306a\u898f\u5247\u304c\u5fc5\u8981\u3067\u3057\u305f\u3002\u3057\u304b\u3057\u3001DeepONet\u306f\u4e0e\u3048\u3089\u308c\u305f\u4f8b\u304b\u3089\u76f4\u63a5\u898f\u5247\u3092\u5b66\u7fd2\u3059\u308b\u305f\u3081\u3001\u5f93\u6765\u306e\u3088\u3046\u306a\u660e\u793a\u7684\u306a\u898f\u5247\u306f\u4e0d\u8981\u3067\u3059\u3002<\/p>\n<p>DeepONet\u306e\u6d3b\u7528\u4f8b\u3068\u3057\u3066\u3001\u4e0e\u3048\u3089\u308c\u305f\u95a2\u6570\u306e\u5b9a\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u30bf\u30b9\u30af\uff08\u8a73\u7d30\u306f\u4ee5\u4e0b\u53c2\u7167\uff09\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u6bd4\u8f03\u7684\u5358\u7d14\u306a\u30bf\u30b9\u30af\u3067\u3059\u304c\u3001DeepONet\u306f\u3055\u3089\u306b\u8907\u96d1\u306a\u30bf\u30b9\u30af\u306b\u3082\u5bfe\u5fdc\u53ef\u80fd\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u3055\u307e\u3056\u307e\u306a\u30d7\u30ed\u30bb\u30b9\u3084\u81ea\u7136\u73fe\u8c61\u306e\u30e2\u30c7\u30ea\u30f3\u30b0\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30bf\u30b9\u30af\u306f\u3001\u3057\u3070\u3057\u3070\u975e\u5e38\u306b\u8907\u96d1\u306a\u65b9\u7a0b\u5f0f\u3084\u898f\u5247\u304c\u95a2\u308f\u308b\u305f\u3081\u3001\u7406\u89e3\u306b\u306f\u5c02\u9580\u7684\u306a\u77e5\u8b58\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>DeepONet\u306e\u5229\u70b9\u306f\u3001\u8907\u96d1\u306a\u898f\u5247\u3092\u30c7\u30fc\u30bf\u304b\u3089\u76f4\u63a5\u5b66\u7fd2\u3067\u304d\u308b\u70b9\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5c02\u9580\u5bb6\u3067\u306a\u304f\u3066\u3082\u30d7\u30ed\u30bb\u30b9\u306e\u30e2\u30c7\u30ea\u30f3\u30b0\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001DeepONet\u3092\u4e00\u5ea6\u8a13\u7df4\u3059\u308c\u3070\u3001\u672a\u77e5\u306e\u6761\u4ef6\u4e0b\u3067\u306e\u554f\u984c\u3092\u5f93\u6765\u306e\u65b9\u6cd5\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u901f\u304f\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002<br \/>\n<!--more--><\/p>\n<h2>DeepONet\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3<\/h2>\n<p><strong>DeepONet<\/strong>[1]\u306f\u3001<strong>2\u3064\u306e\u30b5\u30d6\u30cd\u30c3\u30c8\u30ef\u30fc\u30af<\/strong>\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u56f31\uff09\uff1a<\/p>\n<ol>\n<li><strong>Branch Net<\/strong>\uff1a<br \/>\n\u9078\u629e\u3055\u308c\u305f\u70b9\uff08\u30bb\u30f3\u30b5\u30fc\u3068\u547c\u3070\u308c\u308b\uff09\u306b\u304a\u3051\u308b\u5165\u529b\u95a2\u6570\ud835\udc62\u306e\u5024\u3092\u51e6\u7406\u3057\u307e\u3059\u3002<\/li>\n<li><strong>Trunk Net<\/strong>\uff1a<br \/>\n\u51fa\u529b\u95a2\u6570\u306e\u5024\u3092\u8a08\u7b97\u3059\u308b\u4f4d\u7f6e\u60c5\u5831\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3057\u307e\u3059\u3002<\/li>\n<\/ol>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-15469\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-4.png\" alt=\"\" width=\"1024\" height=\"473\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-4.png 1024w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-4-300x139.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-4-768x355.png 768w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-4-304x140.png 304w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-4-282x130.png 282w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>\u56f3\uff11\uff0eDeepONet\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u3002<\/p>\n<p>\u56f31\u306e\u8a18\u53f7\u306e\u610f\u5473\uff1a<br \/>\n\ud835\udc62: \u5165\u529b\u95a2\u6570\u3001<br \/>\n\ud835\udc65\ud835\udc56(\ud835\udc56=1,2,\u2026,\ud835\udc5a): \u30bb\u30f3\u30b5\u30fc\uff08\ud835\udc62\u306e\u5024\u304c\u8a08\u7b97\u3055\u308c\u308b\u70b9\uff09\u3001<br \/>\n\ud835\udc66: \u51fa\u529b\u95a2\u6570\u306e\u5024\u304c\u8a08\u7b97\u3055\u308c\u308b\u4f4d\u7f6e\u3001<br \/>\nt1, t2, . . . , tp: Trunk Net\u306e\u51fa\u529b,<br \/>\nb1, b2, . . . , bp: Brunch Net\u306e\u51fa\u529b,<br \/>\n\ud835\udc3a: \u95a2\u6570\ud835\udc62\u306b\u4f5c\u7528\u3059\u308b\u6f14\u7b97\u5b50\u3001<br \/>\n\ud835\udc3a(\ud835\udc62)(\ud835\udc66): \u4f4d\u7f6e\ud835\udc66\u3067\u8a08\u7b97\u3055\u308c\u305f\u51fa\u529b\u95a2\u6570\u306e\u5024 (Trunk Net\u3068Brunch Net\u306e\u51fa\u529b\u306e\u5185\u7a4d)\u3002<\/p>\n<p>DeepONet\u306e\u8a13\u7df4\u4e2d\u3001\u4f4d\u7f6e\ud835\udc66\u306f\u30bb\u30f3\u30b5\u30fc\u306e\u70b9\u306b\u3088\u3063\u3066\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002\u8a13\u7df4\u306f\u3001\u4e88\u6e2c\u5024\u3068\u51fa\u529b\u95a2\u6570\u306e\u771f\u5024\uff08<strong>ground truth<\/strong>\uff09\u3068\u306e\u5dee\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u3067\u884c\u308f\u308c\u307e\u3059\u3002\u8a13\u7df4\u304c\u5b8c\u4e86\u3059\u308b\u3068\u3001DeepONet\u306f\u30e9\u30f3\u30c0\u30e0\u306a\u4f4d\u7f6e\uff08\u3064\u307e\u308a\u3001\u30e9\u30f3\u30c0\u30e0\u306a\ud835\udc66\u306e\u5024\uff09\u3067\u3082\u51fa\u529b\u95a2\u6570\u306e\u5024\u3092\u4e88\u6e2c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3089\u306e\u30b5\u30d6\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u306b\u306f\u53b3\u683c\u306a\u8981\u4ef6\u306f\u306a\u304f\u3001\u5358\u7d14\u306a\u5168\u7d50\u5408\u578b\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3067\u69cb\u6210\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u7573\u307f\u8fbc\u307f\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3084\u518d\u5e30\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306a\u3069\u3001\u3088\u308a\u8907\u96d1\u306a\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u306e\u7cbe\u5ea6\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002<\/p>\n<p>DeepONet\u306e\u52d5\u4f5c\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306b\u30012\u3064\u306e\u4f8b\u3092\u4f7f\u7528\u3059\u308b\u3002<\/p>\n<h2>\u4f8b1: \u4e0d\u5b9a\u7a4d\u5206\u6f14\u7b97\u5b50 (antiderivative operator)<\/h2>\n<p>\u3053\u306e\u6f14\u7b97\u5b50\u306e\u53b3\u5bc6\u306a\u6570\u5b66\u7684\u5b9a\u7fa9\u306b\u306f\u6df1\u5165\u308a\u3057\u307e\u305b\u3093\u304c\u3001\u5358\u7d14\u306b\u8a00\u3048\u3070\u300c\u95a2\u6570\u306e\u5fae\u5206\u306e\u9006\u64cd\u4f5c\u300d\u3092\u884c\u3046\u3082\u306e\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001DeepONet\u306e\u6587\u8108\u3067\u306f\u3001\u3053\u306e\u6f14\u7b97\u5b50\u306e\u30bf\u30b9\u30af\u306f\u3001\u95a2\u6570\ud835\udc62(\ud835\udc65)\u30920\u304b\u3089\ud835\udc65\ud835\udc56\u307e\u3067\u5b9a\u7a4d\u5206\u3059\u308b\u3053\u3068\u3068\u89e3\u91c8\u3067\u304d\u307e\u3059\uff08[1,2]\u53c2\u7167\uff09\u3002<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-15471\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-1.png\" alt=\"\" width=\"272\" height=\"63\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-1.png 315w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-1-300x70.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-1-304x70.png 304w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-1-282x65.png 282w\" sizes=\"(max-width: 272px) 100vw, 272px\" \/><\/p>\n<p>\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306f\u3001<strong>\u533a\u9593[0,1]\u304b\u3089\u9078\u3070\u308c\u305f\ud835\udc5a\u500b\u306e\u70b9\ud835\udc65\ud835\udc56<\/strong>\u3068\u3001<strong>\u591a\u69d8\u306a\u30bf\u30a4\u30d7\u3084\u7279\u6027\u3092\u6301\u3064\ud835\udc5b\u7a2e\u985e\u306e\u7570\u306a\u308b\u6570\u5b66\u95a2\u6570\ud835\udc62<\/strong>\u3067\u69cb\u6210\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u5404\u70b9\ud835\udc65\ud835\udc56\u306b\u304a\u3051\u308b\u5404\u95a2\u6570\u306e<strong>\u5b9a\u7a4d\u5206\u306e\u771f\u5024\uff08ground truth value\uff09<\/strong>\u3092\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<h3>\u30e2\u30c7\u30eb\u306e\u5165\u529b\u30c7\u30fc\u30bf<\/h3>\n<ol>\n<li><strong>\u70b9\ud835\udc65\ud835\udc56\u3092\u542b\u3080\u914d\u5217<\/strong>\uff08Trunk Net\u3078\u306e\u5165\u529b\uff09<\/li>\n<li><strong>\u5404\u70b9\ud835\udc65\ud835\udc56\u306b\u5bfe\u3059\u308b\u5404\u95a2\u6570\ud835\udc62\u306e\u5024\u3092\u542b\u3080\u884c\u5217<\/strong>\uff08Branch Net\u3078\u306e\u5165\u529b\uff09<\/li>\n<\/ol>\n<h3>\u30e2\u30c7\u30eb\u306e\u51fa\u529b<\/h3>\n<ul>\n<li>\u95a2\u6570\ud835\udc62\u306e\u5b9a\u7a4d\u5206\u306e\u4e88\u6e2c\u5024\u3092\u683c\u7d0d\u3057\u305f\u884c\u5217<\/li>\n<\/ul>\n<p>\u30c8\u30ec\u30fc\u30cb\u30f3\u30b0\u4e2d\u3001\u640d\u5931\u95a2\u6570\u306f\u30e2\u30c7\u30eb\u304c\u4e88\u6e2c\u3057\u305f\u7a4d\u5206\u5024\u3068\u3001\u4e8b\u524d\u306b\u8a08\u7b97\u3055\u308c\u305f\u771f\u306e\u7a4d\u5206\u5024\uff08ground truth\uff09\u3068\u306e\u5dee\u306b\u57fa\u3065\u3044\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/p>\n<h1>\u4f8b2: \u6d41\u4f53\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/h1>\n<p>\u6d41\u4f53\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3059\u308b\u306b\u306f\u3001\u901a\u5e38\u3001\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u30bb\u30c3\u30c8\u3092\u89e3\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001DeepONet\u306e\u30c7\u30fc\u30bf\u99c6\u52d5\u578b\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u7528\u3044\u308c\u3070\u3001\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3084\u5b9f\u9a13\u30c7\u30fc\u30bf\u304c\u5229\u7528\u53ef\u80fd\u306a\u5834\u5408\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/p>\n<p>\u3053\u306e\u624b\u6cd5\u306e\u9069\u7528\u4f8b\u3068\u3057\u3066\u3001\u8a18\u4e8b[3]\u3067\u7d39\u4ecb\u3055\u308c\u3066\u3044\u308b<strong>\u30d1\u30a4\u30d7\u5185\u306e\u6d41\u308c\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3<\/strong>\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u6bd4\u8f03\u7684\u7406\u89e3\u3057\u3084\u3059\u3044\u4f8b\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u3092\u9078\u3073\u307e\u3057\u305f\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-15498\" src=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-1024x420.png\" alt=\"\" width=\"1024\" height=\"420\" srcset=\"https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-1024x420.png 1024w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-300x123.png 300w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-768x315.png 768w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-1536x630.png 1536w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-304x125.png 304w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1-282x116.png 282w, https:\/\/www.ecomottblog.com\/wp-content\/uploads\/2024\/12\/image-6-1.png 1628w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><br \/>\n\u56f3\uff12.\u3000\u30d1\u30a4\u30d7\u5185\u306e\u6d41\u4f53\u306e\u6d41\u308c\u306e\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u7528DeepONet\u306e\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3<\/p>\n<p>\u56f32\u306e\u8a18\u53f7\u306e\u610f\u5473\uff1a<br \/>\n\u03a9: \u52d5\u4f5c\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u5f62\u72b6\u3002\u52d5\u4f5c\u30d1\u30e9\u30e1\u30fc\u30bf\u306f\u6d41\u4f53\u306e\u5165\u53e3\u901f\u5ea6\u3068\u305d\u306e\u7269\u7406\u7684\u7279\u6027\uff08\u5bc6\u5ea6\u3068\u7c98\u5ea6\uff09\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u3001\u5f62\u72b6\u306f\u30d1\u30a4\u30d7\u306e\u9577\u3055<em>(l<\/em>)\u3068\u76f4\u5f84 (<em>d<\/em>)\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002<br \/>\n\ud835\udc65,\ud835\udc66,\ud835\udc61: \u6642\u7a7a\u9593\u5ea7\u6a19\u30d9\u30af\u30c8\u30eb\u3002\ud835\udc65\u3068\ud835\udc66\u306f\u7a7a\u9593\u5185\u306e\u4f4d\u7f6e\uff08\u30d1\u30a4\u30d7\u306e\u5185\u90e8\uff09\u3092\u793a\u3057\u3001\ud835\udc61\u306f\u6642\u9593\u3092\u8868\u3059\u3002<br \/>\n\ud835\udc62(\ud835\udc65,\ud835\udc66,\ud835\udc61): \u7279\u5b9a\u306e\u4f4d\u7f6e(\ud835\udc65,\ud835\udc66)\u3068\u6642\u9593\ud835\udc61\u306b\u304a\u3051\u308b\u6d41\u4f53\u306e\u901f\u5ea6\u3092\u793a\u3059\u95a2\u6570\u3002<\/p>\n<p>\u3053\u306e\u554f\u984c\u3067DeepONet\u3092\u8a13\u7df4\u3059\u308b\u306b\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u03a9\u30bb\u30c3\u30c8\u306b\u5bfe\u3059\u308b\u95a2\u6570\ud835\udc62(\ud835\udc65,\ud835\udc66,\ud835\udc61)\u306e\u60c5\u5831\u304c\u5fc5\u8981\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u4e00\u5ea6\u8a13\u7df4\u304c\u5b8c\u4e86\u3059\u308c\u3070\u3001\u65b0\u3057\u3044\u672a\u77e5\u306e\u03a9\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u3001\u5f93\u6765\u306e\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u65b9\u6cd5\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u77ed\u3044\u6642\u9593\u3067\ud835\udc62(\ud835\udc65,\ud835\udc66,\ud835\udc61)\u3092\u4e88\u6e2c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2>\u6587\u732e\uff1a<\/h2>\n<p>[1] L. Lu, P. Jin and G. E. Karniadakis.:DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators, <a href=\"https:\/\/arxiv.org\/pdf\/1910.03193\"> arXiv:1910.03193<\/a><br \/>\n[2] H. Kumar: DeepONet <a href=\"https:\/\/www.kaggle.com\/code\/hari31416\/deeponet\/notebook\"> kaggle notebook<\/a><br \/>\n[3] Y. Luo, Y. Chen, Z. Zhang:CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics,<a href=\"https:\/\/arxiv.org\/pdf\/2310.05963\">arXiv: 2310.05963<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3093\u306b\u3061\u306f\u3001\u30c7\u30fc\u30bf\u30a2\u30ca\u30ea\u30c6\u30a3\u30af\u30b9\u90e8\u9580\u306e\u30ed\u30d9\u30eb\u30c8\u30fb\u30d5\u30d0\u30c1\u3067\u3059\u3002 \u79c1\u305f\u3061\u306f\u4eca\u3001\u307e\u3055\u306b\u300c\u30d3\u30c3\u30b0\u30c7\u30fc\u30bf\u6642\u4ee3\u300d\u306b\u751f\u304d\u3066\u3044\u307e\u3059\u3002\u65e5\u3005\u3001\u4eba\u3005\u306b\u3088\u3063\u3066\u81a8\u5927\u306a\u30c7\u30fc\u30bf\u304c\u751f\u6210\u30fb\u53ce\u96c6\u3055\u308c\u3066\u304a\u308a\u3001\u3053\u308c\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u3067\u8cb4\u91cd\u306a\u6d1e\u5bdf\u304c\u5f97\u3089\u308c\u308b\u4e00\u65b9\u3001\u5927\u304d [&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":[125,207,210,250,213,52],"_links":{"self":[{"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts\/15463"}],"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=15463"}],"version-history":[{"count":32,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts\/15463\/revisions"}],"predecessor-version":[{"id":16662,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=\/wp\/v2\/posts\/15463\/revisions\/16662"}],"wp:attachment":[{"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=15463"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=15463"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ecomottblog.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=15463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}