{"id":23308,"date":"2026-03-19T15:30:22","date_gmt":"2026-03-19T06:30:22","guid":{"rendered":"https:\/\/www.ecomottblog.com\/?p=23308"},"modified":"2026-03-23T06:22:04","modified_gmt":"2026-03-22T21:22:04","slug":"physics-informed-neural-networks-%e3%81%ab%e3%81%8a%e3%81%91%e3%82%8b%e5%86%8d%e5%ad%a6%e7%bf%92%e3%82%92%e6%b8%9b%e3%82%89%e3%81%99%e6%96%b9%e6%b3%95","status":"publish","type":"post","link":"https:\/\/www.ecomottblog.com\/?p=23308","title":{"rendered":"Physics-Informed Neural Networks \u306b\u304a\u3051\u308b\u518d\u5b66\u7fd2\u3092\u6e1b\u3089\u3059\u65b9\u6cd5"},"content":{"rendered":"
\u3053\u3093\u306b\u3061\u306f\u3002AX\u7814\u7a76\u5ba4<\/span>\u306eRobert Hubacz\u3067\u3059\u3002\"\u7269\u7406\u6cd5\u5247\u3092\u8003\u616e\u3057\u305fPINN\u30e2\u30c7\u30eb\u306e\u5b66\u7fd2\u3092\u8c61\u5fb4\u3059\u308b\u30a4\u30e9\u30b9\u30c8\u3002\"<\/div>\n
Physics-Informed Neural Networks\uff08PINN\uff09\u306f\u3001\u7269\u7406\u73fe\u8c61\u306e\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u7528\u3044\u3089\u308c\u308b\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u4e00\u7a2e\u3067\u3059\u3002\u6a5f\u68b0\u5b66\u7fd2\u3068\u7269\u7406\u65b9\u7a0b\u5f0f\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u30c7\u30fc\u30bf\u3060\u3051\u3067\u306a\u304f\u3001\u7269\u7406\u6cd5\u5247\u304b\u3089\u3082\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/div>\n
\u3053\u306e\u305f\u3081\u3001PINN\u306f\u5229\u7528\u3067\u304d\u308b\u30c7\u30fc\u30bf\u304c\u5c11\u306a\u3044\u30c7\u30fc\u30bf\u3067\u3082\u7cbe\u5ea6\u3088\u304f\u5b66\u7fd2\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u7269\u7406\u6cd5\u5247\u306b\u53cd\u3059\u308b\u3088\u3046\u306a\u4e0d\u81ea\u7136\u306a\u7d50\u679c\u3092\u51fa\u3057\u306b\u304f\u3044\u3068\u3044\u3046\u5229\u70b9\u3082\u3042\u308a\u307e\u3059\u3002<\/div>\n
\u3057\u304b\u3057\u3001PINN\u306b\u306f\u91cd\u8981\u306a\u5236\u7d04\u3082\u3042\u308a\u307e\u3059\u3002\u307e\u305a\u3001PINN\u306e\u5b66\u7fd2\u306b\u306f\u6642\u9593\u304c\u304b\u304b\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u5f93\u6765\u578b\u306ePINN\u306f\u3001\u554f\u984c\u306e\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u5909\u5316\u3059\u308b\u3068\u3001\u901a\u5e38\u306f\u5b66\u7fd2\u3057\u76f4\u3055\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u3053\u3053\u3067\u3044\u3046\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u306f\u3001\u901f\u5ea6\u3001\u6e29\u5ea6\u3001\u6fc3\u5ea6\u3001\u3042\u308b\u3044\u306f\u554f\u984c\u3092\u89e3\u6790\u3059\u308b\u9818\u57df\u306e\u5927\u304d\u3055\u306e\u3088\u3046\u306a\u91cf\u3092\u6307\u3057\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u3042\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u6761\u4ef6\u3067\u5b66\u7fd2\u3057\u305fPINN\u306f\u3001\u5225\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u6761\u4ef6\u306b\u5bfe\u3059\u308b\u89e3\u3092\u305d\u306e\u307e\u307e\u4e88\u6e2c\u3059\u308b\u3053\u3068\u306f\u4e00\u822c\u306b\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/div>\n

<\/p>\n

\u3053\u306e\u70b9\u306f\u3001\u6d41\u4f53\u306e\u6d41\u308c\u3092\u4f8b\u306b\u3059\u308b\u3068\u308f\u304b\u308a\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002\u6d41\u4f53\u306e\u6d41\u308c\u306f Navier\u2013Stokes\u65b9\u7a0b\u5f0f<\/a>\u3067\u8868\u3055\u308c\u307e\u3059\u3002\u6570\u5024\u30b7\u30df\u30e5\u30ec\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u65b9\u7a0b\u5f0f\u306f\u3057\u3070\u3057\u3070\u3088\u308a\u7c21\u5358\u306a\u7121\u6b21\u5143\u5f62<\/a>\u306b\u66f8\u304d\u63db\u3048\u3089\u308c\u307e\u3059\u3002\u3053\u306e\u5f62\u3067\u306f\u3001\u91cd\u8981\u306a\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u306e1\u3064\u304c\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\uff08Re\uff09<\/a>\u3067\u3059\u3002\u3053\u306e\u6570\u306f\u3001\u6d41\u4f53\u306e\u6027\u8cea\u3001\u6d41\u901f\u3001\u5f62\u72b6\u306a\u3069\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6d41\u901f\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069\u3001\u3042\u308b\u3044\u306f\u5f62\u72b6\u304c\u5927\u304d\u304f\u306a\u308b\u307b\u3069\u3001\u4e00\u822c\u306b\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306f\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u591a\u304f\u306e\u5834\u5408\u3001\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u3060\u3051\u3067\u7570\u306a\u308b\u6d41\u308c\u6761\u4ef6\u3092\u533a\u5225\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/div>\n
\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u7a2e\u985e\u306e\u6d41\u308c\u304c\u751f\u3058\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u52a9\u3051\u306b\u306a\u308a\u307e\u3059\u3002\u6d41\u308c\u304c\u6ed1\u3089\u304b\u3067\u5b89\u5b9a\u3057\u305f\u5c64\u6d41<\/strong>\u306b\u306a\u308a\u3084\u3059\u3044\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u3088\u308a\u8907\u96d1\u3067\u4e71\u308c\u305f\u4e71\u6d41<\/strong>\u306b\u306a\u308a\u3084\u3059\u3044\u306e\u304b\u3092\u793a\u3057\u3066\u304f\u308c\u307e\u3059\u3002\u3042\u308b\u7a2e\u985e\u306e\u6d41\u308c\u306b\u5bfe\u3057\u3066\u3046\u307e\u304f\u50cd\u304f\u89e3\u6cd5\u304c\u3001\u5225\u306e\u7a2e\u985e\u306e\u6d41\u308c\u306b\u5bfe\u3057\u3066\u3082\u3046\u307e\u304f\u50cd\u304f\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002<\/div>\n
\u3057\u304b\u3057\u3001PINN\u306b\u306f\u3055\u3089\u306b\u91cd\u8981\u306a\u5236\u7d04\u304c\u3042\u308a\u307e\u3059\u3002\u6a19\u6e96\u7684\u306a PINN\u306f\u3001\u901a\u5e38\u3001\u3042\u308b1\u3064\u306e\u7279\u5b9a\u306e\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306b\u5bfe\u3057\u3066\u306e\u307f\u5b66\u7fd2\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6d41\u308c\u306e\u6027\u8cea\u304c\u305d\u308c\u307b\u3069\u5927\u304d\u304f\u5909\u308f\u3089\u306a\u3044\u5834\u5408\u3067\u3042\u3063\u3066\u3082\u3001\u3042\u308b\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u3067\u5b66\u7fd2\u3057\u305f\u30e2\u30c7\u30eb\u3092\u3001\u5225\u306e\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306b\u305d\u306e\u307e\u307e\u4f7f\u3046\u3053\u3068\u306f\u4e00\u822c\u306b\u306f\u3067\u304d\u307e\u305b\u3093\u3002<\/div>\n
\u305d\u306e\u305f\u3081\u3001\u591a\u304f\u306e\u5834\u5408\u3001PINN\u306f\u518d\u5b66\u7fd2\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/div>\n
 <\/div>\n
\u3064\u307e\u308a\u3001\u3053\u306e\u6295\u7a3f\u306e\u30dd\u30a4\u30f3\u30c8\u306f\u3001\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u5909\u308f\u308b\u305f\u3073\u306bPINN\u3092\u5b66\u7fd2\u3057\u76f4\u3055\u306a\u304f\u3066\u3088\u3044\u65b9\u6cd5\u304c\u3042\u308b\u306e\u304b\u3001\u3068\u3044\u3046\u70b9\u3067\u3059\u3002<\/div>\n
\u3053\u306e\u6295\u7a3f\u3067\u306f\u3001\u6b21\u306e 3 \u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u6bd4\u8f03\u3057\u307e\u3059\u3002<\/div>\n
    \n
  •  Traditional PINN<\/strong>\uff08\u5f93\u6765\u578bPINN\uff09\u2014 1\u3064\u306e\u30b1\u30fc\u30b9\u306b\u5bfe\u3057\u30661\u3064\u306e\u30e2\u30c7\u30eb<\/li>\n
  •  Parameterized PINN<\/strong>\uff08\u30d1\u30e9\u30e1\u30fc\u30bf\u5316PINN\uff09 \u2014 \u8907\u6570\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u306b\u5bfe\u3057\u30661\u3064\u306e\u30e2\u30c7\u30eb<\/li>\n
  •  Meta-learning PINN<\/strong>\uff08\u30e1\u30bf\u30e9\u30fc\u30cb\u30f3\u30b0PINN\uff09\u2014 \u65b0\u3057\u3044\u30b1\u30fc\u30b9\u306b\u3088\u308a\u901f\u304f\u9069\u5fdc\u3067\u304d\u308b\u30e2\u30c7\u30eb<\/li>\n<\/ul>\n
    \u3053\u306e\u6295\u7a3f\u306e\u76ee\u7684\u306f\u3001\u3053\u308c\u3089\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u3069\u306e\u3088\u3046\u306b\u7570\u306a\u308b\u306e\u304b\u3001\u305d\u3057\u3066\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u5909\u5316\u3057\u305f\u3068\u304d\u306b\u3001\u518d\u5b66\u7fd2\u3092\u5b8c\u5168\u306b\u56de\u907f\u3067\u304d\u308b\u306e\u304b\u3001\u305d\u308c\u3068\u3082\u5fc5\u8981\u306a\u518d\u5b66\u7fd2\u306e\u91cf\u3092\u6e1b\u3089\u3059\u3060\u3051\u306a\u306e\u304b\u3092\u8aac\u660e\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u3092\u308f\u304b\u308a\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\u3001\u4ee5\u4e0b\u3067\u306f\u3001\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u3092\u552f\u4e00\u306e\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u3057\u305f\u6d41\u4f53\u6d41\u308c\u4e88\u6e2c\u7528\u306ePINN\u3092\u4f8b\u3068\u3057\u3066\u7528\u3044\u307e\u3059\u3002<\/div>\n

     
    \n<\/p>\n

     \u65b9\u6cd51 \u2014 Traditional PINN<\/h2>\n

     <\/p>\n

    \"\u5bfe\u8c61\u3068\u306a\u308b\u73fe\u8c61\u306e\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u5909\u5316\u3059\u308b\u3068\u3001Traditional<\/div>\n
    \u56f31\u3002Traditional PINN\u3002\u3053\u3053\u3067\u3001x\u3068y\u306f\u7a7a\u9593\u5ea7\u6a19\u3001u\u3068p\u306fx\u3068y\u306b\u4f9d\u5b58\u3059\u308b\u901f\u5ea6\u3068\u5727\u529b\u306e\u5024\u3067\u3059\u3002<\/div>\n
     <\/div>\n
    \u6700\u3082\u5358\u7d14\u306a\u65b9\u6cd5\u306f\u3001\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u3054\u3068\u306b\u5225\u3005\u306e\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u5b66\u7fd2\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/div>\n
    \u4f8b\uff1a<\/div>\n
    \n
    \n
    “`PINN_100  \u2192 Re=100\u7528\u306b\u5b66\u7fd2<\/div>\n
    PINN_400  \u2192 Re=400\u7528\u306b\u5b66\u7fd2<\/div>\n
    PINN_800  \u2192 Re=800\u7528\u306b\u5b66\u7fd2<\/div>\n
    “`<\/div>\n
     <\/div>\n<\/div>\n<\/div>\n
    \u3053\u306e\u30e2\u30c7\u30eb\u306f\u3001\u3042\u308b\u56fa\u5b9a\u3055\u308c\u305fRe\u306e\u5024\u306b\u5bfe\u3057\u3066\u306e\u307f\u3001\u6d41\u901f\u3068\u5727\u529b\u304c\u4f4d\u7f6e\u306b\u3069\u3046\u4f9d\u5b58\u3059\u308b\u304b\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/div>\n
    “`<\/div>\n
    (x, y) \u2192 (u, p)<\/div>\n
    “`<\/div>\n
     <\/div>\n
    \u5404\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u30011\u3064\u306e\u7279\u5b9a\u306e\u30b1\u30fc\u30b9<\/strong>\u306b\u5bfe\u3059\u308bNavier\u2013Stokes\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001Re\u306e\u5024\u304c\u5909\u308f\u308b\u3068\u3001PINN\u306f\u518d\u5b66\u7fd2\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002<\/div>\n
     <\/div>\n
     \u5229\u70b9<\/strong><\/div>\n
    \u2714 \u5b9f\u88c5\u304c\u7c21\u5358<\/div>\n
    \u2714 \u5b89\u5b9a\u3057\u3066\u3044\u3066\u9ad8\u3044\u7cbe\u5ea6\u304c\u5f97\u3089\u308c\u3084\u3059\u3044<\/div>\n
     <\/div>\n
    \u6b20\u70b9<\/strong><\/div>\n
    \u274c \u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u3054\u3068\u306b\u518d\u5b66\u7fd2\u304c\u5fc5\u8981<\/div>\n
    \u274c \u8a08\u7b97\u30b3\u30b9\u30c8\u304c\u9ad8\u3044<\/div>\n
    \u274c \u3042\u308b\u6d41\u308c\u6761\u4ef6\u3067\u5f97\u305f\u77e5\u8b58\u3092\u3001\u5225\u306e\u6d41\u308c\u6761\u4ef6\u306b\u6d3b\u304b\u305b\u306a\u3044<\/div>\n

     <\/p>\n

     \u65b9\u6cd52 \u2014 Parameterized PINN<\/h2>\n

    \"Parameterized<\/p>\n

    \u56f32\u3002Parameterized PINN\u3002\u3053\u3053\u3067\u3001x\u3068y\u306f\u7a7a\u9593\u5ea7\u6a19\u3001Re\u306f\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u3001u\u3068p\u306f x\u3001y\u3001Re\u306b\u4f9d\u5b58\u3059\u308b\u901f\u5ea6\u3068\u5727\u529b\u306e\u5024\u3067\u3059\u3002<\/div>\n
     <\/div>\n
    Parameterized PINN\u3068\u306f\u3001\u7570\u306a\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u5024\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u8907\u6570\u306e\u95a2\u9023\u3059\u308b\u7269\u7406\u554f\u984c\u306b\u5bfe\u3057\u3066\u30011\u3064\u306e\u30e2\u30c7\u30eb\u3067\u89e3\u3092\u4e88\u6e2c<\/strong>\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/div>\n
    \u5f93\u6765\u578b\u306e PINN\u3067\u306f\u7a7a\u9593\u5ea7\u6a19\u3060\u3051\u3092\u5165\u529b\u3057\u307e\u3059\u304c\u3001Parameterized PINN\u3067\u306f\u3001\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306e\u3088\u3046\u306a\u7269\u7406\u30d1\u30e9\u30e1\u30fc\u30bf\u3082\u5165\u529b\u306b\u52a0\u3048\u307e\u3059\u3002<\/div>\n
    \u4f8b\uff1a<\/div>\n
    “`<\/div>\n
    Input:  (x, y, Re)<\/div>\n
    Output: (u, p)<\/div>\n
    “`<\/div>\n
     <\/div>\n
    \u3053\u306e\u3088\u3046\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u306f\u901f\u5ea6\u3068\u5727\u529b\u304c\u4f4d\u7f6e\u3060\u3051\u3067\u306a\u304fRe\u306e\u5024\u306b\u3088\u3063\u3066\u3069\u3046\u5909\u308f\u308b\u304b\u3082\u5b66\u7fd2\u3067\u304d\u307e\u3059\u3002<\/div>\n
    “`<\/div>\n
    (x, y, Re) \u2192 (u, p)<\/div>\n
    “`<\/div>\n

     \u5b66\u7fd2\u3068\u4f7f\u3044\u65b9<\/h3>\n
    Parameterized PINN\u3067\u306f\u3001\u30e2\u30c7\u30eb\u306fRe=100\u3001Re=400\u3001Re=800\u306e\u3088\u3046\u306a\u7570\u306a\u308b\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u8907\u6570\u306e\u6d41\u308c\u30b1\u30fc\u30b9\u3092\u7528\u3044\u3066\u5b66\u7fd2\u3055\u308c\u307e\u3059\u3002<\/div>\n
    \u305d\u306e\u305f\u3081\u3001\u5b66\u7fd2\u5f8c\u306b\u306f\u3001\u305f\u3068\u3048\u3070 Re=500\u306e\u3088\u3046\u306a\u5b66\u7fd2\u7bc4\u56f2\u5185\u306e\u65b0\u3057\u3044\u5024\u306b\u5bfe\u3057\u3066\u3001\u8ffd\u52a0\u5b66\u7fd2\u306a\u3057\u3067\u4e88\u6e2c\u3067\u304d\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/div>\n
    \u3064\u307e\u308a\u3001Parameterized PINN\u306f\u3001\u5b66\u7fd2\u3057\u305f\u7bc4\u56f2\u5185\u3067\u3042\u308c\u3070\u518d\u5b66\u7fd2\u3092\u884c\u308f\u305a\u306b\u4f7f\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/div>\n

     \u9650\u754c<\/h3>\n
    \u305f\u3060\u3057\u3001\u5b66\u7fd2\u3057\u305f\u7bc4\u56f2\u306e\u5916\u306b\u3042\u308b\u5024\u3067\u306f\u3001\u4e88\u6e2c\u7cbe\u5ea6\u304c\u4f4e\u4e0b\u3059\u308b\u3053\u3068\u304c\u4e00\u822c\u7684\u3067\u3059\u3002<\/div>\n
    \u307e\u305f\u3001\u5b66\u7fd2\u3057\u305f\u30b1\u30fc\u30b9\u3068\u5927\u304d\u304f\u7570\u306a\u308b\u6d41\u308c\u306b\u306f\u3001\u305d\u306e\u307e\u307e\u5bfe\u5fdc\u3067\u304d\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3068\u3048\u3070\u3001\u6ed1\u3089\u304b\u306a\u6d41\u308c\u3060\u3051\u3067\u5b66\u7fd2\u3057\u305f\u30e2\u30c7\u30eb\u306f\u3001\u3088\u308a\u8907\u96d1\u306a\u6d41\u308c\u3092\u6b63\u78ba\u306b\u4e88\u6e2c\u3067\u304d\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/div>\n
     <\/div>\n
    \u5229\u70b9<\/strong><\/div>\n
    \u2714 1\u3064\u306e\u30e2\u30c7\u30eb\u3067\u8907\u6570\u306e\u6d41\u308c\u6761\u4ef6\u3092\u6271\u3048\u308b<\/div>\n
    \u2714 \u5b66\u7fd2\u7bc4\u56f2\u5185\u3067\u306f\u3001\u518d\u5b66\u7fd2\u3092\u5b8c\u5168\u306b\u56de\u907f\u3067\u304d\u308b\u3053\u3068\u304c\u591a\u3044<\/div>\n
    \u2714 \u7570\u306a\u308b\u6d41\u308c\u540c\u58eb\u306e\u95a2\u4fc2\u3092\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304c\u5b66\u7fd2\u3067\u304d\u308b<\/div>\n
     <\/div>\n
     \u6b20\u70b9<\/strong><\/div>\n
    \u274c \u5b66\u7fd2\u304c\u3088\u308a\u96e3\u3057\u304f\u306a\u308b<\/div>\n
    \u274c \u5b66\u7fd2\u7bc4\u56f2\u306e\u5916\u3067\u306f\u7cbe\u5ea6\u304c\u4f4e\u4e0b\u3057\u3084\u3059\u3044<\/div>\n
    \u274c \u8ffd\u52a0\u306e\u30c7\u30fc\u30bf\u304c\u5fc5\u8981\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308b<\/div>\n

     \u65b9\u6cd53 \u2014 Meta-Learning PINN<\/h2>\n
    Parameterized PINN\u306f\u30011\u3064\u306e\u30e2\u30c7\u30eb\u3067\u306e\u7570\u306a\u308b\u6761\u4ef6\u306b\u5bfe\u5fdc\u3059\u308b\u89e3\u3092\u76f4\u63a5\u4e88\u6e2c\u3057\u3088\u3046\u3068\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/div>\n
    \u4e00\u65b9\u3001Meta-learning PINN\u306f\u3001\u65b0\u3057\u3044\u6761\u4ef6\u306b\u5bfe\u3057\u3066\u5c11\u306a\u3044\u8ffd\u52a0\u5b66\u7fd2\u3067\u7d20\u65e9\u304f\u9069\u5fdc\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/div>\n
    \u3064\u307e\u308a\u3001\u518d\u5b66\u7fd2\u3092\u5b8c\u5168\u306b\u306a\u304f\u3059\u65b9\u6cd5\u3067\u306f\u306a\u304f\u3001\u5b66\u7fd2\u3057\u76f4\u3057\u3092\u901f\u304f\u3059\u308b\u65b9\u6cd5<\/strong>\u3067\u3059\u3002<\/div>\n
    \u4ee3\u8868\u7684\u306a\u30e1\u30bf\u30e9\u30fc\u30cb\u30f3\u30b0\u624b\u6cd5\u3068\u3057\u3066\u3001MAML\u3068Reptile\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306f\u30011\u3064\u306e\u6700\u7d42\u7684\u306a\u89e3\u305d\u306e\u3082\u306e\u3092\u5b66\u7fd2\u3059\u308b\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u4ee3\u308f\u308a\u306b\u3001PINN\u304c\u65b0\u3057\u3044\u985e\u4f3c\u554f\u984c\u306b\u3059\u3070\u3084\u304f\u9069\u5fdc\u3067\u304d\u308b\u3088\u3046\u306a\u826f\u3044\u521d\u671f\u91cd\u307f\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/div>\n
    \u7c21\u5358\u306b\u8a00\u3048\u3070\u3001\u30e2\u30c7\u30eb\u306f\u300c\u65b0\u3057\u3044\u304c\u4f3c\u305f\u554f\u984c\u3092\u3001\u3088\u308a\u901f\u304f\u5b66\u7fd2\u3057\u59cb\u3081\u308b\u65b9\u6cd5\u300d\u3092\u5b66\u3073\u307e\u3059\u3002<\/div>\n

     \u5b66\u7fd2\u30d7\u30ed\u30bb\u30b9<\/h3>\n
    \u30e2\u30c7\u30eb\u306f\u3001\u591a\u6570\u306e\u95a2\u9023\u30bf\u30b9\u30af\u3067\u5b66\u7fd2\u3055\u308c\u307e\u3059\u3002\u5404\u30bf\u30b9\u30af\u306f\u3001\u305f\u3068\u3048\u3070Re=100\u3001Re=400\u3001Re=800\u3068\u3044\u3063\u305f\u7570\u306a\u308b\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u30bf\u30b9\u30af\u306f\u8907\u6570\u3042\u308a\u307e\u3059\u304c\u3001\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u81ea\u4f53\u306f1\u3064\u3067\u3042\u308a\u3001\u305d\u306e\u521d\u671f\u91cd\u307f\u306e\u30bb\u30c3\u30c8\u30821\u3064\u3060\u3051\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u91cd\u307f\u306f\u3059\u3079\u3066\u306e\u30bf\u30b9\u30af\u3067\u5171\u6709\u3055\u308c\u307e\u3059\u3002<\/div>\n
    \u5404\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c1\u3064\u306e\u30bf\u30b9\u30af\u3092\u9078\u3073\u3001\u305d\u306e\u30bf\u30b9\u30af\u3067\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u77ed\u6642\u9593\u3060\u3051\u5b66\u7fd2\u3055\u305b\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u5171\u6709\u3055\u308c\u305f\u521d\u671f\u91cd\u307f\u3092\u66f4\u65b0\u3057\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u4f55\u5ea6\u3082\u7e70\u308a\u8fd4\u3059\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u306f\u3001\u65b0\u3057\u3044\u985e\u4f3c\u554f\u984c\u306b\u5bfe\u3057\u3066 PINN \u304c\u3059\u3070\u3084\u304f\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u308b\u3088\u3046\u306a\u521d\u671f\u91cd\u307f\u3092\u5b66\u7fd2\u3057\u307e\u3059\u3002<\/div>\n

     <\/p>\n

    \"\u30d6\u30ed\u30b0\u672c\u6587\u3067\u3082\u7c21\u6f54\u306b\u8aac\u660e\u3057\u3066\u3044\u308b\u3001Meta-Learning<\/div>\n
    \u56f33\u3002\u7c21\u7565\u5316\u3057\u305fMeta-Learning PINN\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3002<\/div>\n

    \u30e2\u30c7\u30eb\u306e\u4f7f\u3044\u65b9<\/h3>\n
    \u65b0\u3057\u3044\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u304c\u73fe\u308c\u305f\u3068\u304d\u306f\u3001\u6b21\u306e\u3088\u3046\u306b\u4f7f\u3044\u307e\u3059\u3002 <\/div>\n
     <\/div>\n
    “`<\/div>\n
    \u5b66\u7fd2\u6e08\u307f\u306e\u521d\u671f\u91cd\u307f\u304b\u3089\u958b\u59cb \u2192  \u5c11\u6570\u30b9\u30c6\u30c3\u30d7\u306e\u8ffd\u52a0\u5b66\u7fd2\u3092\u884c\u3046 \u2192  \u65b0\u3057\u3044\u30ec\u30a4\u30ce\u30eb\u30ba\u6570\u306b\u5bfe\u3059\u308b\u89e3\u3092\u4e88\u6e2c\u3059\u308b<\/div>\n
    “`<\/div>\n
     <\/div>\n
    \u3064\u307e\u308a\u3001Meta-learning PINN \u3067\u306f\u3001\u65b0\u3057\u3044\u6761\u4ef6\u306b\u5bfe\u3057\u3066\u8ffd\u52a0\u5b66\u7fd2\u306f\u5fc5\u8981\u3067\u3059\u3002<\/div>\n
    \u305f\u3060\u3057\u3001\u30bc\u30ed\u304b\u3089\u9577\u6642\u9593\u5b66\u7fd2\u3059\u308b\u4ee3\u308f\u308a\u306b\u3001\u5c11\u6570\u306e\u8ffd\u52a0\u5b66\u7fd2\u30b9\u30c6\u30c3\u30d7\u3067\u6e08\u3080\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002<\/div>\n
     <\/div>\n
    \u5229\u70b9<\/strong><\/div>\n
    \u2714 \u65b0\u3057\u3044\u6761\u4ef6\u3078\u306e\u9069\u5fdc\u304c\u901f\u3044<\/div>\n
    \u2714 \u5fc5\u8981\u306a\u5b66\u7fd2\u53cd\u5fa9\u56de\u6570\u3092\u6e1b\u3089\u305b\u308b\u5834\u5408\u304c\u3042\u308b<\/div>\n
    \u2714 \u591a\u6570\u306e\u985e\u4f3c PDE \u554f\u984c\u3092\u6271\u3046\u3068\u304d\u306b\u6709\u7528<\/div>\n
     <\/div>\n
     \u6b20\u70b9<\/strong><\/div>\n
    \u274c \u5b66\u7fd2\u624b\u9806\u304c\u3088\u308a\u8907\u96d1<\/div>\n
    \u274c \u591a\u6570\u306e\u5b66\u7fd2\u30bf\u30b9\u30af\u304c\u5fc5\u8981<\/div>\n
    \u274c \u8ffd\u52a0\u5b66\u7fd2\u306f\u4f9d\u7136\u3068\u3057\u3066\u5fc5\u8981<\/div>\n

     \u3069\u306e\u65b9\u6cd5\u304c\u518d\u5b66\u7fd2\u3092\u6700\u3082\u6e1b\u3089\u305b\u308b\u306e\u304b\uff1f<\/h2>\n
    \u3053\u306e 3 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u518d\u5b66\u7fd2\u306e\u6e1b\u3089\u3057\u65b9\u304c\u305d\u308c\u305e\u308c\u7570\u306a\u308a\u307e\u3059\u3002<\/div>\n
     <\/div>\n\n\n\n\n\n\n\n
    \u65b9\u6cd5<\/th>\n\u518d\u5b66\u7fd2\u306f\u5fc5\u8981\u304b\uff1f<\/th>\n\u57fa\u672c\u30a2\u30a4\u30c7\u30a2<\/th>\n<\/tr>\n<\/thead>\n
    Traditional PINN<\/td>\n\u306f\u3044<\/td>\n\u30b1\u30fc\u30b9\u3054\u3068\u306b\u65b0\u3057\u3044\u30e2\u30c7\u30eb\u3092\u5b66\u7fd2\u3059\u308b<\/td>\n<\/tr>\n
    Parameterized PINN<\/td>\n\u591a\u304f\u306e\u5834\u5408\u4e0d\u8981<\/td>\n\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u5165\u529b\u306b\u542b\u3081\u308b<\/td>\n<\/tr>\n
    Meta-learning PINN<\/td>\n\u5c11\u91cf\u306a\u3089\u5fc5\u8981<\/td>\n\u3059\u3070\u3084\u304f\u9069\u5fdc\u3067\u304d\u308b\u521d\u671f\u72b6\u614b\u3092\u5b66\u3076<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
     <\/div>\n
    Parameterized PINN\u3068Meta-learning PINN\u306e\u9055\u3044\u306f\u30b7\u30f3\u30d7\u30eb\u3067\u3059\u3002<\/div>\n