{"id":13403,"date":"2024-06-05T09:00:13","date_gmt":"2024-06-05T00:00:13","guid":{"rendered":"https:\/\/www.ecomottblog.com\/?p=13403"},"modified":"2024-06-05T13:13:54","modified_gmt":"2024-06-05T04:13:54","slug":"%e5%81%8f%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e4%bf%9d%e6%8c%81%e3%81%97%e3%81%9f%e3%83%8b%e3%83%a5%e3%83%bc%e3%83%a9%e3%83%ab%e3%83%8d%e3%83%83%e3%83%88%e3%83%af%e3%83%bc%e3%82%af","status":"publish","type":"post","link":"https:\/\/www.ecomottblog.com\/?p=13403","title":{"rendered":"\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u4fdd\u6301\u3057\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af"},"content":{"rendered":"

\"\"
\n\u3053\u3093\u306b\u3061\u306f\u30c7\u30fc\u30bf\u30a2\u30ca\u30ea\u30c6\u30a3\u30af\u30b9\u90e8\u306e\u30d5\u30d0\u30c1(Robert Hubacz)\u3067\u3059\u3002\u4ee5\u524d\u3001\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\uff08PDE\uff09\u3092\u89e3\u304f\u305f\u3081\u306e\u7279\u5225\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308b\u300c\u7269\u7406\u60c5\u5831\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08PINN\uff09\u300d<\/a>\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002PDE\u306f\u81ea\u7136\u73fe\u8c61\u3084\u79d1\u5b66\u7684\u30a4\u30d9\u30f3\u30c8\u3092\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002PINN\u306f\u5c11\u91cf\u306e\u30c7\u30fc\u30bf\u3084\u30c7\u30fc\u30bf\u304c\u306a\u304f\u3066\u3082\u6a5f\u80fd\u3059\u308b\u305f\u3081\u3001\u591a\u304f\u306e\u7814\u7a76\u8005\u304c\u95a2\u5fc3\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001PINN\u306f\u4e00\u5ea6\u8a13\u7df4\u3055\u308c\u308b\u3068\u3001\u72b6\u6cc1\u304c\u5909\u308f\u3063\u305f\u5834\u5408\u306b\u306f\u518d\u8a13\u7df4\u304c\u5fc5\u8981\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u30d1\u30a4\u30d7\u5185\u306e\u6c34\u306e\u6d41\u308c\u304c\u5c11\u3057\u5909\u308f\u308b\u3060\u3051\u3067\u3082\u3001PINN\u3092\u518d\u8a13\u7df4\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u4e00\u65b9\u3001\u672a\u77e5\u306e\u72b6\u6cc1\u3092\u4e88\u6e2c\u3059\u308b\u3053\u3068\u306f\u3001\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304c\u4f5c\u3089\u308c\u305f\u4e3b\u306a\u7406\u7531\u306e\u4e00\u3064\u3067\u3059\u3002<\/p>\n

\u305d\u3053\u3067\u3001\u3053\u306e\u30d6\u30ed\u30b0\u3067\u306fPDE\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u8a2d\u8a08\u3055\u308c\u305f\u5225\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u3001\u89e3\u6c7a\u3092\u76ee\u6307\u3059PDE\u306e\u69cb\u9020\u3092\u53cd\u6620\u3059\u308b\u3088\u3046\u306b\u8a2d\u8a08\u3055\u308c\u3066\u3044\u307e\u3059\uff08Sharma et al., 2023\uff09\u3002\u5177\u4f53\u4f8b\u3068\u3057\u3066\u3001PDE\u3092\u4fdd\u6301\u3057\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08PPNN\uff09\u3068\u3044\u3046\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3067\u3059\uff08Liu et al., 2024\uff09\u3002
\n<\/p>\n

\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f<\/h2>\n

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\n\u53cd\u5fdc\u62e1\u6563\u65b9\u7a0b\u5f0f\uff1a\u5316\u5b66\u53cd\u5fdc\u304c\u767a\u751f\u3059\u308b\u7a7a\u9593\u306b\u304a\u3051\u308b\u7279\u5b9a\u306e\u7269\u8cea\u306e\u6fc3\u5ea6\u306e\u5909\u5316\u3092\u8868\u3057\u307e\u3059\u3002
\n\u6ce2\u52d5\u65b9\u7a0b\u5f0f\uff1a\u97f3\u6ce2\u306a\u3069\u306e\u632f\u52d5\u3084\u6ce2\u306e\u52d5\u304d\u3092\u8aac\u660e\u3057\u307e\u3059\u3002
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\n\u30e9\u30d7\u30e9\u30b9\u65b9\u7a0b\u5f0f\uff1a\u771f\u7a7a\u4e2d\u3067\u306e\u96fb\u4f4d\u306e\u5909\u5316\u306a\u3069\u3001\u7279\u5b9a\u306e\u96fb\u6c17\u7684\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306b\u95a2\u9023\u3057\u307e\u3059\u3002
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\n\u3053\u308c\u3089\u306ePDE\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u79d1\u5b66\u7684\u304a\u3088\u3073\u5de5\u5b66\u7684\u554f\u984c\u306e\u7406\u89e3\u3068\u89e3\u6c7a\u306b\u4e0d\u53ef\u6b20\u3067\u3059\u3002<\/p>\n

\"\"<\/p>\n

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 <\/div>\n

\"\"<\/p>\n

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\"\"<\/p>\n

\u56f3\uff13\uff0eCNN\u3092\u4f7f\u7528\u3057\u3066\u30e9\u30d7\u30e9\u30b7\u30a2\u30f3\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/h4>\n

PDE\u3092\u4fdd\u6301\u3057\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af<\/h2>\n

\u6700\u8fd1\u306e\u7814\u7a76\u3067\u3001\u30b0\u30ea\u30c3\u30c9\u30dd\u30a4\u30f3\u30c8\u3067\u8868\u3055\u308c\u308b\u7a7a\u9593\u306f\u30d4\u30af\u30bb\u30eb\u3067\u69cb\u6210\u3055\u308c\u305f\u753b\u50cf\u306e\u3088\u3046\u306b\u8003\u3048\u3089\u308c\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u985e\u4f3c\u6027\u304b\u3089\u3001\u5c02\u9580\u5bb6\u305f\u3061\u306f\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u3088\u308a\u52b9\u7387\u7684\u306b\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u7573\u307f\u8fbc\u307f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08CNN\uff09\u3068\u547c\u3070\u308c\u308b\u4eba\u5de5\u77e5\u80fd\u306e\u4e00\u7a2e\u3092\u4f7f\u7528\u3057\u59cb\u3081\u307e\u3057\u305f\u3002\u3053\u306e\u3088\u3046\u306a\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u3001PDE\u304c\u3069\u306e\u3088\u3046\u306b\u96e2\u6563\u5316\u3055\u308c\u308b\u304b\u306b\u57fa\u3065\u3044\u3066\u8a2d\u8a08\u3055\u308c\u3001PDE\u3092\u4fdd\u6301\u3057\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08PPNN\uff09\u3068\u547c\u3070\u308c\u307e\u3059\uff08 Liu et al., 2024\uff09\u3002PPNN\u306e\u91cd\u307f\u306f\u3001\u7573\u307f\u8fbc\u307f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u5f62\u5f0f\u3067\u3042\u308a\u3001\u305d\u306e\u5024\u306e\u4e00\u90e8\u306f\u96e2\u6563\u5316\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u4e00\u90e8\u304cPPNN\u306e\u8a13\u7df4\u4e2d\u306b\u5b66\u7fd2\u3055\u308c\u3001\u4ed6\u306e\u90e8\u5206\u306fPDE\u306e\u96e2\u6563\u5316\u30b9\u30ad\u30fc\u30e0\u3092\u4fdd\u6301\u3059\u308b\u305f\u3081\u306b\u4e00\u5b9a\u306e\u307e\u307e\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3000\uff08\u56f3\uff14\u3092\u53c2\u7167\uff09\u3002<\/p>\n

\"\"<\/p>\n

\u56f3\uff14\uff0ePPNN-PDE\u3092\u4fdd\u6301\u3057\u305f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff08Liu et al., 2024). un<\/sup>\u306f\u3001\u7279\u5b9a\u306e\u30bf\u30a4\u30e0\u30b9\u30c6\u30c3\u30d7n \u3067\u306e\u7269\u7406\u91cf\u306e\u5024\u3092\u8868\u3057\u307e\u3059; un+1<\/sup>\u306f\u3001\u6b21\u306e\u30bf\u30a4\u30e0\u30b9\u30c6\u30c3\u30d7 n+1\u3067\u306e\u305d\u306e\u7269\u7406\u91cf\u306e\u4e88\u6e2c\u5024\u3067\u3001PPNN \u3068\u3044\u3046\u30c4\u30fc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059; \ud835\udf06\u306f\u3001\u79c1\u305f\u3061\u304c\u7814\u7a76\u3057\u3066\u3044\u308b\u73fe\u8c61\u304c\u8d77\u3053\u308b\u7279\u5b9a\u306e\u6761\u4ef6\u3092\u8a18\u8ff0\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u30d9\u30af\u30c8\u30eb\uff08\u30ea\u30b9\u30c8\uff09\u3067\u3059\u3002\ud835\udf06\u306f\u3001\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306b\u3088\u3063\u3066\u4e88\u6e2c\u3055\u308c\u308b\u7d50\u679c\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u307e\u3059\u3002\u53cd\u5fdc\u62e1\u6563\u65b9\u7a0b\u5f0f\u306e\u3088\u3046\u306a\u4f8b\u3067\u306f\u3001\u6642\u9593\u306e\u7d4c\u904e\u3068\u3068\u3082\u306b\u7269\u8cea\u304c\u3069\u306e\u3088\u3046\u306b\u5e83\u304c\u308a\u3001\u53cd\u5fdc\u3059\u308b\u304b\u3092\u898b\u3066\u3044\u307e\u3059\uff1au \u306f\u7269\u8cea\u306e\u6fc3\u5ea6\u3092\u610f\u5473\u3057\u307e\u3059; \ud835\udf06\u306b\u306f\u62e1\u6563\u4fc2\u6570D\u304c\u542b\u307e\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u3001\u3053\u308c\u306f\u7269\u8cea\u304c\u3069\u308c\u304f\u3089\u3044\u65e9\u304f\u3001\u3069\u306e\u3088\u3046\u306b\u5e83\u304c\u308b\u304b\u3092\u793a\u3057\u307e\u3059\u3002<\/h4>\n

PPNN\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306b\u3001\u53cd\u5fdc\u62e1\u6563\u65b9\u7a0b\u5f0f\u306e\u4f8b\u3092\u4f7f\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u3001\u7570\u306a\u308b\u7269\u8cea\u304c\u6642\u9593\u3068\u3068\u3082\u306b\u3069\u306e\u3088\u3046\u306b\u6df7\u3056\u308a\u5408\u3044\u3001\u53cd\u5fdc\u3059\u308b\u304b\u3092\u793a\u3057\u307e\u3059\u3002\u30c6\u30fc\u30d6\u30eb\u306e\u3088\u3046\u306a\u5e73\u9762\u3067\u3053\u308c\u304c\u8d77\u3053\u308b\u306e\u3092\u60f3\u50cf\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u304c\u79c1\u305f\u3061\u306e2\u6b21\u5143\u306e\u4f8b\u3067\u3059\u3002<\/p>\n

\u307e\u305a\u3001\u30c6\u30fc\u30d6\u30eb\u3092\u70b9\u306e\u30b0\u30ea\u30c3\u30c9\u306b\u5206\u5272\u3055\u308c\u305f\u3082\u306e\u3068\u8003\u3048\u307e\u3059\u3002\u5404\u70b9\u306f\u500b\u5225\u306b\u8abf\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b3\u3064\u306e\u56f3\u3092\u4f7f\u7528\u3057\u307e\u3059\uff1a<\/p>\n

\u56f31\u306f\u3001\u7269\u8cea\u304c\u30c6\u30fc\u30d6\u30eb\u4e0a\u3067\u3069\u306e\u3088\u3046\u306b\u6df7\u3056\u308a\u5408\u3044\u3001\u53cd\u5fdc\u3059\u308b\u304b\u306e\u57fa\u672c\u7684\u306a\u6982\u5ff5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002
\n\u56f32\u306f\u3001\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u3088\u308a\u5c0f\u3055\u306a\u30b9\u30c6\u30c3\u30d7\u306b\u5206\u89e3\u3057\u307e\u3059\uff08\u300c\u96e2\u6563\u5316\u300d\u3068\u547c\u3070\u308c\u307e\u3059\uff09\u3002\u3053\u308c\u306f\u3001\u5404\u7269\u8cea\u306e\u91cf\u304c\u6642\u9593\u3068\u7a7a\u9593\u306b\u308f\u305f\u3063\u3066\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u975e\u5e38\u306b\u8a73\u3057\u304f\u793a\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u3042\u308b\u77ac\u9593\u304b\u3089\u6b21\u306e\u77ac\u9593\u306b\u4f55\u304c\u8d77\u3053\u308b\u304b\u3092\u77e5\u308b\u305f\u3081\u306b\u3001\u5c0f\u3055\u306a\u6642\u9593\u30b9\u30c6\u30c3\u30d7\uff08\u0394t\uff09\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3042\u308b\u6642\u9593\u30b9\u30c6\u30c3\u30d7\u3067\u306e\u7269\u8cea\u306e\u6fc3\u5ea6\u3092\u898b\u3066\u3001\u6b21\u306e\u6642\u9593\u30b9\u30c6\u30c3\u30d7\u306e\u6fc3\u5ea6\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002
\n\u56f33\u306f\u3001\u30c6\u30fc\u30d6\u30eb\u5168\u4f53\u3067\u6fc3\u5ea6\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u628a\u63e1\u3059\u308b\u305f\u3081\u306e\u30c4\u30fc\u30eb\u3067\u3042\u308b\u7573\u307f\u8fbc\u307f\u30d5\u30a3\u30eb\u30bf\u30fc\u306e\u4f7f\u7528\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002
\n\u8981\u7d04\u3059\u308b\u3068\u3001PPNN\u306f\u7279\u5b9a\u306e\u6642\u70b9\u3067\u306e\u30b0\u30ea\u30c3\u30c9\u4e0a\u306e\u5404\u70b9\u306b\u304a\u3051\u308b\u7269\u8cea\u306e\u91cf\u3092\u898b\u3066\u3001\u305d\u308c\u304b\u3089CNN\u3092\u4f7f\u7528\u3057\u3066\u3053\u308c\u3089\u306e\u91cf\u304c\u3069\u306e\u3088\u3046\u306b\u5834\u6240\u304b\u3089\u5834\u6240\u3078\u5909\u5316\u3059\u308b\u304b\u3092\u628a\u63e1\u3057\u307e\u3059\u3002\u6700\u7d42\u7684\u306b\u3001PPNN\u306f\u6b21\u306e\u6642\u9593\u30b9\u30c6\u30c3\u30d7\u3067\u306e\u7269\u8cea\u306e\u91cf\u304c\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u304b\u3092\u4e88\u6e2c\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30c6\u30fc\u30d6\u30eb\u4e0a\u3067\u7269\u8cea\u304c\u3069\u306e\u3088\u3046\u306b\u6df7\u3056\u308a\u5408\u3044\u3001\u53cd\u5fdc\u3059\u308b\u304b\u3092\u7406\u89e3\u3057\u3001\u4e88\u6e2c\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002<\/p>\n

PPNN\u306f2\u3064\u306e\u7570\u306a\u308b\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u56f34\u53c2\u7167\uff09\uff1a<\/p>\n

\u8a13\u7df4\u53ef\u80fd\u306a\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff1aResNet\u3068\u547c\u3070\u308c\u308bCNN\u306e\u4e00\u7a2e\u3067\u3001\u6b21\u306e\u6642\u9593\u30b9\u30c6\u30c3\u30d7\u3067\u4f55\u304c\u8d77\u3053\u308b\u304b\u3092\u4e88\u6e2c\u3059\u308b\u3088\u3046\u306b\u8a2d\u8a08\u3055\u308c\u3066\u3044\u307e\u3059\u3002PPNN\u306e\u8a13\u7df4\u4e2d\u306b\u3001\u3053\u306e\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u5b66\u7fd2\u3057\u3001\u305d\u306e\u8a2d\u5b9a\uff08\u91cd\u307f\uff09\u3092\u8abf\u6574\u3057\u307e\u3059\u3002
\nPDE\u3092\u4fdd\u6301\u3059\u308b\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\uff1a\u305d\u306e\u8a2d\u5b9a\u304cPDE\u306e\u69cb\u9020\u306b\u5408\u308f\u305b\u3066\u56fa\u5b9a\u3055\u308c\u3001\u8a13\u7df4\u4e2d\u306b\u306f\u5909\u66f4\u3055\u308c\u306a\u3044\u5225\u306e\u30bf\u30a4\u30d7\u306eCNN\u3067\u3059\u3002
\n\u4ee5\u524d\u306b\u7d39\u4ecb\u3057\u305fPINN\u3068\u306f\u7570\u306a\u308a\u3001PPNN\u306f\u5b66\u7fd2\u3059\u308b\u305f\u3081\u306b\u7279\u5225\u306a\u7a2e\u985e\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u5fc5\u8981\u3067\u3059\u3002\u3053\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u306f\u3001\u30b0\u30ea\u30c3\u30c9\u5185\u306e\u7570\u306a\u308b\u70b9\u3067\u3001\u7279\u5b9a\u306e\u7269\u7406\u91cf\u304c\u6642\u9593\u3068\u3068\u3082\u306b\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u306b\u95a2\u3059\u308b\u60c5\u5831\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5909\u5316\u306f\u3001\u305d\u308c\u3089\u304c\u767a\u751f\u3059\u308b\u6761\u4ef6\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304c\u7269\u8cea\u304c\u6df7\u3056\u308a\u5408\u3063\u3066\u5e83\u304c\u308b\u53cd\u5fdc\uff08\u4e0a\u8a18\u306e\u53cd\u5fdc\u62e1\u6563\u65b9\u7a0b\u5f0f\u306e\u4f8b\u306e\u3088\u3046\u306b\uff09\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u7269\u8cea\u306e\u6fc3\u5ea6\u3068\u305d\u308c\u3089\u304c\u3069\u306e\u3088\u3046\u306b\u5e83\u304c\u308b\u304b\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u62e1\u6563\u4fc2\u6570\u3068\u547c\u3070\u308c\u308b\u3082\u306e\u3067\u5236\u5fa1\u3055\u308c\u307e\u3059\uff08\u56f31\u53c2\u7167\uff09\u3002<\/p>\n

PPNN\u3092\u3053\u306e\u62e1\u6563\u4fc2\u6570\u306e\u7570\u306a\u308b\u8a2d\u5b9a\u306e\u30c7\u30fc\u30bf\u3067\u8a13\u7df4\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u6761\u4ef6\u4e0b\u3067\u7269\u8cea\u306e\u6fc3\u5ea6\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u5b66\u3073\u307e\u3059\u3002\u4e00\u5ea6\u8a13\u7df4\u304c\u5b8c\u4e86\u3059\u308b\u3068\u3001\u65b0\u3057\u3044\u7570\u306a\u308b\u62e1\u6563\u4fc2\u6570\u306e\u8a2d\u5b9a\u3092\u4e0e\u3048\u3089\u308c\u3066\u3082\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u4ee5\u524d\u306b\u5b66\u7fd2\u3057\u305f\u5185\u5bb9\u306b\u57fa\u3065\u3044\u3066\u6fc3\u5ea6\u304c\u3069\u306e\u3088\u3046\u306b\u5909\u5316\u3059\u308b\u304b\u3092\u4e88\u6e2c\u3067\u304d\u308b\u3068\u3044\u3046\u8a33\u3067\u3059\u3002<\/p>\n

\u6587\u732e\uff1a<\/h2>\n

\u8ad6\u6587\uff1a<\/h3>\n

Liu X.-Y., Zhu M., Lu L., Sun H., Wang J.-X. (2024): Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics, Communications Physics volume 7, Article number: 31
\nSharma P., Chung W. T., Akoush B., Ihme M. (2023): A Review of Physics-Informed Machine Learning in Fluid Mechanics, Energies, 16, 2343.<\/p>\n

\u30a6\u30a7\u30d6\u30b5\u30a4\u30c8\uff1a<\/h3>\n

INTRODUCTION TO PHYSICS-INFORMED NEURAL NETWORKS – ecomott blog<\/a>
\nPDEs, Convolutions, and the Mathematics of Locality<\/a>
\nPartial Differential Equations (PDEs), Convolutions, and the Mathematics of Locality – video<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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