{"id":59174,"date":"2025-05-09T18:24:28","date_gmt":"2025-05-09T10:24:28","guid":{"rendered":"https:\/\/swarma.org\/?p=59174"},"modified":"2025-05-09T18:24:28","modified_gmt":"2025-05-09T10:24:28","slug":"%e3%80%8aaixscience%e5%8d%81%e5%a4%a7%e5%89%8d%e6%b2%bf%e8%a7%82%e5%af%9f%e3%80%8b8%ef%bc%9a%e7%a7%91%e5%ad%a6%e5%90%af%e5%8f%91%e7%9a%84ai%e6%96%b0%e6%9e%b6%e6%9e%84","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=59174","title":{"rendered":"\u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b8\uff1a\u79d1\u5b66\u542f\u53d1\u7684AI\u65b0\u67b6\u6784"},"content":{"rendered":"
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    \u50a8\u5907\u6c60\u8ba1\u7b97\uff08RC\uff09\u5219\u5229\u7528\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u5bf9\u8f93\u5165\u6570\u636e\u8fdb\u884c\u9ad8\u7ef4\u6620\u5c04\uff0c\u7279\u522b\u9002\u5408\u5904\u7406\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u3002RC\u7684\u56fa\u5b9a\u7684\u968f\u673a\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf\u975e\u5e38\u9002\u5408\u4e8e\u7279\u6b8a\u8bbe\u8ba1\u7684\u9ad8\u80fd\u6548\u786c\u4ef6\u67b6\u6784\uff0c\u8fd9\u4f7f\u5f97RC\u5728\u5b9e\u73b0\u9ad8\u6548\u4fe1\u606f\u5904\u7406\u65b9\u9762\u5177\u6709\u5de8\u5927\u6f5c\u529b\u3002<\/span><\/span><\/p>\n<\/li>\n

  • \n

    \u673a\u68b0\u795e\u7ecf\u7f51\u7edc<\/span>\uff08MNN\uff09<\/span>\u662f\u4e00\u79cd\u6a21\u4eff\u751f\u7269\u795e\u7ecf\u7cfb\u7edf\u7ed3\u6784\u548c\u529f\u80fd\u7684\u7269\u7406\u7cfb\u7edf\uff0c\u901a\u8fc7\u7279\u5b9a\u6750\u6599\u548c\u51e0\u4f55\u7ed3\u6784\u8bbe\u8ba1\uff0c\u80fd\u591f\u50cf\u795e\u7ecf\u7f51\u7edc\u4e00\u6837\u5904\u7406\u548c\u4f20\u9012\u4fe1\u606f\uff0c\u5177\u6709\u81ea\u9002\u5e94\u548c\u54cd\u5e94\u5916\u90e8\u523a\u6fc0\u7684\u80fd\u529b\uff0c\u4e3b\u8981\u5e94\u7528\u4e8e\u67d4\u6027\u673a\u5668\u4eba\u3001\u667a\u80fd\u6750\u6599\u548c\u4eff\u751f\u5de5\u7a0b\u9886\u57df\u3002<\/span><\/span><\/p>\n<\/li>\n

  • \n

    \u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50<\/span>\uff08FNO\uff09<\/span>\u5f00\u521b\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u79d1\u5b66AI\u8303\u5f0f\uff0c\u901a\u8fc7\u5728\u9891\u57df\u7a7a\u95f4\u5b66\u4e60\u7b97\u5b50\u6620\u5c04\uff0c\u5b9e\u73b0\u4e86\u5206\u8fa8\u7387\u65e0\u5173\u7684\u5feb\u901f\u4eff\u771f\uff0c\u7279\u522b\u9002\u5408\u5904\u7406\u7531\u504f\u5fae\u5206\u65b9\u7a0b\u63cf\u8ff0\u7684\u7269\u7406\u7cfb\u7edf\u3002<\/span><\/span><\/p>\n<\/li>\n<\/ul>\n


    <\/span><\/h2>\n

    \n
    \n
    \n
    \n
    \n

    <\/span><\/section>\n

    <\/span><\/section>\n
    \n
    <\/section>\n<\/section>\n<\/section>\n
    \n

    \u7814\u7a76\u8fdb\u5c55<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

    \n

    <\/span><\/section>\n

    <\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


    <\/span><\/p>\n

    \n

    \u8fdb\u5c55\u76ee\u5f55<\/span><\/span><\/p>\n

      \n
    1. \n

      Komogorov Arnold Networks (KAN)<\/span><\/span><\/p>\n<\/li>\n

    2. \n

      \u8109\u51b2\u795e\u7ecf\u7f51\u7edc<\/span><\/span><\/p>\n<\/li>\n

    3. \n

      \u50a8\u5907\u6c60\u8ba1\u7b97<\/span><\/span><\/p>\n<\/li>\n

    4. \n

      \u673a\u68b0\u795e\u7ecf\u7f51\u7edc<\/span><\/span><\/p>\n<\/li>\n

    5. \n

      \u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n<\/blockquote>\n

      Komogorov Arnold Networks (KAN)<\/span><\/span><\/h3>\n

      \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong>KAN\u662f\u4e00\u79cd\u53d7\u6570\u5b66\u7406\u8bba\u542f\u53d1\u7684\u5168\u65b0\u6df1\u5ea6\u5b66\u4e60\u67b6\u6784\uff0c\u53ef\u4ee5\u66ff\u4ee3\u4e00\u822c\u7684\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff0c\u5177\u6709\u8868\u793a\u80fd\u529b\u66f4\u5f3a\u3001\u66f4\u5bb9\u6613\u8fdb\u884c\u590d\u6742\u51fd\u6570\u62df\u5408\u3001\u66f4\u9002\u5408\u79d1\u5b66\u8ba1\u7b97\u7b49\u4f18\u70b9\uff1b<\/span><\/span>\u7531\u96c6\u667a\u793e\u533a\u6210\u5458<\/span><\/span><\/span>\u3001<\/span><\/span><\/span>\u96c6\u667a\u79d1\u5b66\u5bb6\u5218\u5b50\u9e23\u4e3a\u9996\u7684<\/span><\/span><\/span>\u9ebb\u7701\u7406\u5de5\u5b66\u9662<\/span><\/span><\/span>\u79d1\u7814\u56e2\u961f\u5f00\u53d1\u3002<\/span><\/span><\/span><\/p>\n

      Komogorov Arnold Networks<\/span> (KAN)<\/span> [1][2]\u7684\u6838\u5fc3\u601d\u8def\u6e90\u81ea\u4e00\u4e2a\u6570\u5b66\u7406\u8bba\uff0c\u5373<\/span><\/span>\u79d1\u5c14\u83ab\u6208\u7f57\u592b-\u963f\u8bfa\u5fb7\uff08Kolmogorov-Arnold\uff09\u5b9a\u7406<\/span><\/span><\/strong>\u3002\u8be5\u5b9a\u7406\u8868\u660e\uff0c\u4efb\u4f55\u590d\u6742\u7684\u591a\u53d8\u91cf\u51fd\u6570\u90fd\u53ef\u4ee5\u901a\u8fc7\u4e00\u7cfb\u5217\u7b80\u5355\u51fd\u6570\u7684\u7ec4\u5408\u6765\u8868\u793a\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5728\u7406\u8bba\u4e0a\uff0c\u5373\u4f7f\u662f\u9ad8\u5ea6\u590d\u6742\u7684\u5173\u7cfb\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u5c06\u5176\u62c6\u89e3\u6210\u4e00\u7ec4\u7b80\u5355\u51fd\u6570\u53e0\u52a0\u7684\u5f62\u5f0f\uff0c\u4ece\u800c\u8fdb\u884c\u5efa\u6a21\u548c\u9884\u6d4b\u3002<\/span><\/span><\/p>\n

      KAN\u5c06\u4e0a\u8ff0\u5b9a<\/span><\/span>\u7406\u63cf\u8ff0\u7684\u5355\u5c42\u7f51\u7edc\u53e0\u52a0\u4e3a\u591a\u5c42\u7684\u6df1\u5ea6\u7f51\u7edc\u3002<\/span><\/span>\u4e0e\u4f20\u7edf\u591a\u5c42\u524d\u9988\u795e\u7ecf\u7f51\u7edc<\/span>\uff08MLP\uff09<\/span>\u76f8\u6bd4\uff0cKAN\u7684\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u5c06MLP\u4e2d\u76f8\u5bf9\u56fa\u5b9a\u7684\u6fc0\u6d3b\u51fd\u6570\u66ff\u6362\u4e3a\u66f4\u52a0\u4e30\u5bcc\u7684\u6570\u5b66\u51fd\u6570\u96c6\u3002\u8fd9\u79cd\u8bbe\u8ba1\u4f7f\u5176\u80fd\u591f\u4ee5\u66f4\u7b80\u6d01\u7684\u7f51\u7edc\u7ed3\u6784\u5efa\u6a21\u590d\u6742\u51fd\u6570\u5173\u7cfb\uff0c\u663e\u8457\u63d0\u5347\u4e86\u6a21\u578b\u8868\u8fbe\u80fd\u529b\u3002<\/span><\/span><\/span>\u8fd9\u4e0d\u4ec5\u80fd\u591f\u63d0\u9ad8\u6a21\u578b\u7684\u533a\u95f4\u5916\u63d2\u503c\u80fd\u529b\uff0c<\/span><\/span>\u5728\u7279\u5b9a\u95ee\u9898\u4e0a<\/span><\/span><\/span>\u589e\u5f3a\u4e86<\/span><\/span><\/span>\u5206\u5e03\u5916\u6cdb\u5316\u80fd\u529b<\/span><\/span><\/span>\uff0c\u540c<\/span><\/span>\u65f6\u8fd8\u589e\u52a0\u4e86\u6a21\u578b\u7684\u6613\u7406\u89e3\u6027\uff0c\u66f4\u9002\u4e8e\u5728\u79d1\u5b66\u8ba1\u7b97\u4e2d\u5e94\u7528\u3002<\/span><\/span><\/p>\n

      <\/section>\n

      \u4f20\u7edf\u591a\u5c42\u611f\u77e5\u673a\uff08MLP\uff09\u7ed3\u6784\u548cKAN\u7ed3\u6784\u7684\u5bf9\u6bd4 [1]<\/span><\/span><\/em><\/p>\n

      KAN \u7684\u67b6\u6784\u901a\u8fc7\u4e00\u4e2a\u79f0\u4e3a\u201c\u9690\u85cf\u51fd\u6570\u201d\u7684\u5c42\u5c06\u8f93\u5165\u6570\u636e\u8f6c\u5316\uff0c\u7136\u540e\u901a\u8fc7\u591a\u4e2a\u7b80\u5355\u51fd\u6570\u7684\u7ec4\u5408\u8f93\u51fa\u7ed3\u679c\u3002\u8fd9\u79cd\u65b9\u5f0f\u4f7f\u5f97\u5b83\u6bd4\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\u66f4\u5177\u89e3\u91ca\u6027\u548c\u53ef\u63a7\u6027\uff0c\u56e0\u4e3a\u6211\u4eec\u80fd\u591f\u6e05\u6670\u5730\u770b\u5230\u6bcf\u4e2a\u7b80\u5355\u51fd\u6570\u5728\u6574\u4f53\u67b6\u6784\u4e2d\u7684\u4f5c\u7528\uff0c\u800c\u4e0d\u9700\u8981\u4f9d\u8d56\u5927\u91cf\u7684\u53c2\u6570\u8bad\u7ec3\u3002<\/span><\/span><\/p>\n

      \u8109\u51b2\u795e\u7ecf\u7f51\u7edc<\/span><\/span><\/h3>\n

      \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong>\u76f8\u6bd4\u5f53\u524d\u4e3b\u6d41AI\u7684\u6280\u672f\u5b9e\u73b0\uff0c\u4eba\u8111\u5728\u9ad8\u6548\u3001\u4f4e\u529f\u8017\u548c\u5b9e\u65f6\u5904\u7406\u80fd\u529b\u7b49\u65b9\u9762\u90fd\u8868\u73b0\u51fa\u65e0\u4ee5\u4f26\u6bd4\u7684\u4f18\u52bf\u3002\u8109\u51b2\u795e\u7ecf\u7f51\u7edc<\/span><\/span>\uff08<\/span><\/span>Spiking Neural Networks\uff0cSNN<\/span><\/span><\/span>\uff09<\/span><\/span>\u662f\u4e00\u79cd\u6a21\u4eff\u751f\u7269\u5927\u8111\u795e\u7ecf\u7cfb\u7edf\u7ed3\u6784\u548c\u529f\u80fd\u7684\u8ba1\u7b97\u65b9\u6cd5\uff0c\u6709\u671b\u89e3\u9664AI\u5728\u8017\u80fd\u3001\u5b9e\u65f6\u9ad8\u6548\u4fe1\u606f\u5904\u7406\u7b49\u65b9\u9762\u7684\u53d1\u5c55\u5236\u7ea6\u3002<\/span><\/span><\/p>\n

      \u8109\u51b2\u795e\u7ecf\u7f51\u7edc\u88ab\u79f0\u4e3a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc[3]<\/span><\/span>\uff0c<\/span><\/span>\u6a21\u4eff<\/span><\/span><\/span>\u4e86<\/span><\/span><\/span>\u751f\u7269<\/span><\/span><\/span>\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u8109\u51b2\u53d1\u653e\u65b9\u5f0f\u3002\u76f8\u6bd4\u4f20\u7edf\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc<\/span>\uff08ANN\uff09<\/span>\uff0cSNN\u901a\u8fc7\u79bb\u6563\u7684\u8109\u51b2<\/span><\/span>\uff08<\/span><\/span><\/span>S<\/span><\/span><\/span>pike\uff09<\/span><\/span><\/span>\u8fdb\u884c<\/span><\/span>\u4fe1\u606f\u4f20\u9012\uff0c\u4ece\u800c\u6709\u6548\u964d\u4f4e\u8ba1\u7b97\u80fd\u8017\uff0c\u80fd\u66f4\u9ad8\u6548\u5730\u6a21\u62df\u751f\u7269\u795e\u7ecf\u7cfb\u7edf\u7684\u65f6\u95f4\u548c\u7a7a\u95f4\u7279\u6027\u3002SNN\u901a\u5e38\u91c7\u7528\u4e8b\u4ef6\u9a71\u52a8\u673a\u5236\uff0c\u4ec5\u5728\u6709\u4e8b\u4ef6\u89e6\u53d1\u65f6\u6fc0\u6d3b\u795e\u7ecf\u5143\uff0c\u53ef\u6709\u6548\u964d\u4f4e\u80fd\u8017\u3002\u6b64\u5916\uff0cSNN\u8fd8\u53ef\u6a21\u62df\u7a81\u89e6\u53ef\u5851\u6027\uff0c\u901a\u8fc7\u6a21\u62df\u5927\u8111\u7684\u5b66\u4e60\u673a\u5236\uff0c\u4f7f\u5f97\u7f51\u7edc\u80fd\u591f\u5728\u52a8\u6001\u73af\u5883\u4e2d\u5b9e\u73b0\u5b9e\u65f6\u5b66\u4e60\u3002<\/span><\/span><\/p>\n

      <\/section>\n

      \u4ece\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff08ANN\uff09\u8f6c\u6362\u5230 \u8109\u51b2\u795e\u7ecf\u7f51\u7edc\uff08SNN\uff09[3]<\/span><\/span><\/em><\/p>\n

      \u76f8\u6bd4\u4f20\u7edf\u7684\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\uff0c\u91c7\u7528\u8109\u51b2<\/span><\/span>\uff08<\/span><\/span><\/span>S<\/span><\/span><\/span>pike\uff09<\/span><\/span><\/span>\u4f20\u9012\u4fe1<\/span><\/span>\u606f\uff0c\u4e8b\u4ef6\u9a71\u52a8\u7684SNN\u5728\u80fd\u6548\u6bd4\u548c\u8ba1\u7b97\u8d44\u6e90\u6d88\u8017\u65b9\u9762\u5177\u6709\u660e\u663e\u4f18\u52bf\u3002SNN\u80fd\u591f\u5728\u6570\u636e\u53d1\u751f\u53d8\u5316\u65f6\u624d\u8fdb\u884c\u8ba1\u7b97\uff0c\u8fd9\u79cd\u8ba1\u7b97\u6a21\u5f0f\u5bf9\u4e8e\u5b9e\u65f6\u5904\u7406\u548c\u54cd\u5e94\u662f\u975e\u5e38\u6709<\/span><\/span>\u4ef7\u503c\u7684\u3002SN<\/span><\/span>N\u53ef\u4ee5\u4e0e\u4e13\u95e8\u4e3aSNN\u8bbe\u8ba1\u7684\u795e\u7ecf\u5f62\u6001\u786c\u4ef6<\/span>\uff08\u5982IBM\u7684TrueNorth\u3001Intel\u7684Loihi\uff09<\/span>\u66f4\u7d27\u5bc6\u5730\u96c6\u6210\uff0c\u5b9e\u73b0\u66f4\u9ad8\u7684\u80fd\u6548\u548c\u5e76\u884c\u5904\u7406\u80fd\u529b\u3002\u6b64\u5916\uff0cSNN\u6a21\u4eff\u751f\u7269\u5927\u8111\u7684\u5de5\u4f5c\u65b9\u5f0f\uff0c\u4f7f\u5f97\u5b83\u4eec\u5728\u9700\u8981\u4e0e\u751f\u7269\u7cfb\u7edf\u63a5\u53e3\u7684\u5e94<\/span><\/span>\u7528\u4e2d<\/span><\/span>\uff08\u5982\u8111\u673a\u63a5\u53e3\uff09<\/span>\u66f4\u4e3a\u6709\u6548<\/span><\/span><\/span>\u3002<\/span><\/span><\/p>\n

      \u50a8\u5907\u6c60\u8ba1\u7b97<\/span><\/span><\/h3>\n

      \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong>\u50a8\u5907\u6c60\u8ba1\u7b97<\/span>\uff08Reservoir Computing\uff0c RC\uff09<\/span>\u662f\u4e00\u79cd\u53ef\u4ee5\u66ff\u4ee3\u4f20\u7edf\u5faa\u73af\u795e\u7ecf\u7f51\u7edc<\/span>\uff08RNN\uff09<\/span>\u7684\u65b0\u578bAI\u6a21\u578b\uff0c\u66f4\u64c5\u957f\u4e8e\u4ece\u65f6\u95f4\u5e8f\u5217\u4e2d\u5b66\u4e60\u590d\u6742\u7684\u52a8\u529b\u5b66\u3002\u76f8\u6bd4\u8f83\u666e\u901a\u7684RNN\uff0c\u50a8\u5907\u6c60\u8ba1\u7b97\u5177\u6709\u8bad\u7ec3\u6548\u7387\u66f4\u9ad8\u3001\u66f4\u5bb9\u6613\u7528\u4f4e\u6210\u672c\u786c\u4ef6\u5b9e\u73b0\u7b49\u7279\u70b9\u3002<\/span><\/span><\/p>\n

      \u50a8\u5907\u6c60\u8ba1\u7b97\u7684\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u975e\u7ebf\u6027\u52a8\u529b\u7cfb\u7edf<\/span>\uff08\u5373\u201c\u50a8\u5907\u6c60\u201d\uff09<\/span>\u5bf9\u8f93\u5165\u6570\u636e\u8fdb\u884c\u9ad8\u7ef4\u975e\u7ebf\u6027\u6620\u5c04\uff0c\u4f7f\u5f97\u6570\u636e\u7684\u7279\u5f81\u66f4\u5bb9\u6613\u88ab\u7ebf\u6027\u5206\u79bb\u3002\u5b83\u662f\u4e00\u79cd\u7279\u6b8a\u7684RNN\u5f62\u5f0f\uff0c\u901a\u5e38\u4f7f\u7528\u7ed3\u6784\u56fa\u5b9a\u7684\u968f\u673a\u8fde\u63a5\u7f51\u7edc\u4f5c\u4e3a\u201c\u50a8\u5907\u6c60\u201d<\/span>\uff08Reservoir\uff09<\/span>\uff0c\u50a8\u5907\u6c60\u540e\u9762\u8fde\u63a5\u6709\u53ef\u8bad<\/span><\/span>\u7ec3\u7684<\/span><\/span>\u8f93\u51fa\u5c42<\/span><\/span><\/span>\uff0c\u4ece\u800c<\/span><\/span><\/span>\u5c06\u5185\u90e8<\/span><\/span><\/span>\u72b6\u6001<\/span><\/span>\u7ebf\u6027\u6620\u5c04\u56de\u4f4e\u7ef4\u7684\u8f93\u51fa\u53d8\u91cf\u3002\u7531\u4e8e\u50a8\u5907\u6c60\u7f51\u7edc\u7ed3\u6784\u548c\u53c2\u6570\u5747\u56fa\u5b9a\uff0c\u56e0\u6b64\u65e0\u9700\u5bf9\u5176\u8bad\u7ec3\uff0c\u800c\u53ea\u9700\u8981\u8bad\u7ec3\u8f93\u51fa\u5c42\u5373\u53ef\u3002\u8fd9\u4e0d\u4ec5\u53ef\u4ee5\u5927\u5927\u63d0\u9ad8\u50a8\u5907\u6c60\u6a21\u578b\u7684\u8bad\u7ec3\u6548\u7387\uff0c\u66f4\u4e3a\u7814\u53d1\u76f8\u5e94\u7684\u4e13\u6709\u786c\u4ef6\u63d0\u4f9b\u4e86\u4fbf\u5229\u3002\u50a8\u5907\u6c60\u8ba1\u7b97\u901a\u8fc7\u8f93\u5165\u9a71\u52a8\u50a8\u5907\u6c60\u5185\u90e8\u7684\u795e\u7ecf\u6d3b\u52a8\uff0c\u5e76\u5229\u7528\u8f93\u51fa\u7684\u7ebf\u6027\u6216\u975e\u7ebf\u6027\u7ec4\u5408\u6620\u5c04\u5230\u4f4e\u7ef4\u7684\u8f93\u51fa\u53d8\u91cf\u6765\u5b8c\u6210\u4efb\u52a1[4][5]\u3002\u56e0\u4e3a\u50a8\u5907\u6c60\u672c\u8eab\u5c31\u662f\u4e00\u4e2a\u9ad8\u7ef4\u7684\u52a8\u529b\u7cfb\u7edf\uff0c\u56e0\u6b64\u5b83\u66f4\u9002\u5408\u62df\u5408\u65f6\u95f4\u5e8f\u5217\u4e2d\u7684\u590d\u6742\u9ad8\u7ef4\u52a8\u529b\u5b66\u3002<\/span><\/span><\/p>\n

      <\/section>\n

      \u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff0c\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\uff0c\u4ee5\u53ca\u50a8\u5907\u6c60\u8ba1\u7b97\u7684\u5173\u7cfb[10]<\/span><\/span><\/em><\/p>\n

      \u50a8\u5907\u6c60\u8ba1\u7b97\u7684\u53d1\u5c55\u5206\u4e3a\u4e09\u4e2a\u9636<\/span><\/span>\u6bb5\uff1a<\/span><\/span>1)<\/span><\/span><\/span>\uff09<\/span><\/span><\/span>2001\u5e74\u63d0\u51fa\u539f\u578b\uff1a\u56de\u58f0\u72b6\u6001\u7f51\u7edc<\/span>\uff08Echo State Network\uff0c ESO\uff09<\/span>\uff0c\u524d\u5341\u5e74\u4e3b\u8981\u7814\u7a76\u5168\u6570\u5b57\u7b97\u6cd5\uff1b2<\/span><\/span><\/span>\uff09<\/span><\/span><\/span>\u968f\u540e\u5341\u5e74\u63a2\u7d22\u6570\u6a21\u6df7\u5408\u5b9e\u73b0\uff0c\u5305\u62ec\u4e0d\u540c\u67b6\u6784\u548c\u6a21\u62df\u57df\u7684\u7269\u7406\u8282\u70b9\uff1b3<\/span><\/span><\/span>\uff09<\/span><\/span><\/span>\u6700\u8fd1\u51e0\u5e74\u8f6c\u5411\u5168\u6a21\u62df\u7cfb\u7edf\uff0c<\/span><\/span><\/span>\u4f7f\u7528\u6a21\u62df\u578b\u5fc6\u963b\u5668\u9635\u5217\u964d\u4f4e\u529f\u8017\u548c\u6210\u672c<\/span><\/span>[6]\u3002<\/span><\/span><\/p>\n

      <\/section>\n

      \u50a8\u5907\u6c60\u8ba1\u7b97\u7684\u53d1\u5c55\u8109\u7edc\u4e0e\u673a\u9047 [6]<\/span><\/span><\/em><\/p>\n

      \u50a8\u5907\u6c60\u8ba1\u7b97\u4e3b\u8981\u7528\u4e8e\u5904\u7406\u65f6\u95f4\u5e8f\u5217\u6570\u636e\u7684\u4efb\u52a1\uff0c\u5982\u8bed\u97f3\u8bc6\u522b\u3001\u91d1\u878d\u9884\u6d4b\u3001\u673a\u5668\u4eba\u63a7\u5236\u7b49<\/span><\/span>\u3002<\/span><\/span>\u5176\u7ed3\u6784\u7b80\u5355<\/span><\/span><\/span>\u3001<\/span><\/span><\/span>\u8bad\u7ec3\u6548\u7387\u9ad8<\/span><\/span><\/span>\uff0c\u5c24\u5176<\/span><\/span>\u9002\u5408\u5b9e\u73b0\u4f4e\u6210\u672c\u7684\u5d4c\u5165\u5f0f\u7cfb\u7edf\u3002\u76ee\u524d\uff0c\u7269\u7406\u50a8\u5907\u6c60\u8ba1\u7b97\u6b63\u5feb\u901f\u53d1\u5c55\uff0c\u5176\u539f\u7406\u548c\u53ef\u884c\u6027\u5df2\u88ab\u9a8c\u8bc1\uff0c\u672a\u6765\u5728\u591a\u4e2a\u65b9\u9762\u6709\u5de8\u5927\u6f5c\u529b\uff0c\u6027\u80fd\u548c\u5e94\u7528\u9886\u57df\u5c06\u8fdb\u4e00\u6b65\u6269\u5c55\u3002<\/span><\/span><\/p>\n

      \u673a\u68b0\u795e\u7ecf\u7f51\u7edc<\/span><\/span><\/h3>\n

      \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong>\u673a\u68b0\u795e\u7ecf\u7f51\u7edc<\/span>\uff08Mechanical Neural Networks\uff0c MNN\uff09<\/span>\u80fd\u591f\u5728\u4e0d\u4f9d\u8d56\u7535\u5b50\u7cfb\u7edf\u7684\u60c5\u51b5\u4e0b\uff0c\u901a\u8fc7\u6750\u6599\u672c\u8eab\u7684\u7269\u7406\u7279\u6027\u5b9e\u73b0\u4fe1\u606f\u5904\u7406\u548c\u667a\u80fd\u54cd\u5e94\uff0c\u80fd\u591f\u5b9e\u73b0\u4fe1\u606f\u5904\u7406\u3001\u81ea\u9002\u5e94\u548c\u667a\u80fd\u54cd\u5e94\uff0c\u540c\u65f6\u5177\u6709\u6bd4\u4f20\u7edf\u7535\u5b50\u795e\u7ecf\u7f51\u7edc\u66f4\u9ad8\u7684\u67d4\u6027\u3001\u751f\u7269\u76f8\u5bb9\u6027\u548c\u73af\u5883\u9002\u5e94\u6027\u3002<\/span><\/span><\/p>\n

      \u673a\u68b0\u795e\u7ecf\u7f51\u7edc\u662f\u4e00\u79cd\u57fa\u4e8e\u7269\u7406\u5b66\u539f\u7406\u7684\u673a\u5668\u5b66\u4e60\u67b6\u6784\uff0c\u901a\u8fc7\u8282\u70b9\u4e4b\u95f4\u7684\u673a\u68b0\u8fde\u63a5\u5b9e\u73b0\u4fe1\u606f\u7684\u5904\u7406\u548c\u5b58\u50a8\u3002\u5176\u6838\u5fc3\u8bbe\u8ba1\u601d\u8def\u662f\u5c06\u8ba1\u7b97\u64cd\u4f5c\u6620\u5c04\u5230\u7269\u7406\u884c\u4e3a\u4e0a\uff0c\u4ee5\u8282\u70b9\u4e4b\u95f4\u7684\u5f39\u7c27\u8fde\u63a5\u4e3a\u57fa\u7840\uff0c\u5c06\u529b\u4e0e\u4f4d\u79fb\u4e4b\u95f4\u7684\u54cd\u5e94\u5173\u7cfb\u6a21\u62df\u4e3a\u795e\u7ecf\u5143\u4e4b\u95f4\u7684\u6fc0\u6d3b\u4e0e\u4f20\u64ad\u8fc7\u7a0b\u3002\u8282\u70b9\u7684\u7a7a\u95f4\u4f4d\u7f6e\u5728\u65bd\u52a0\u5916\u529b\u65f6\u53d1\u751f\u53d8\u5316\uff0c\u901a\u8fc7\u7269\u7406\u8fde\u63a5\u8fdb\u884c\u4fe1\u53f7\u4f20\u8f93\uff0c\u8f93\u51fa\u8282\u70b9\u7684\u4f4d\u79fb\u4ee3\u8868\u7f51\u7edc\u7684\u8f93\u51fa\u7ed3\u679c\u3002\u8fd9\u79cd\u673a\u5236\u4e0e\u4f20\u7edf\u7684\u8ba1\u7b97\u673a\u795e\u7ecf\u7f51\u7edc\u7c7b\u4f3c\uff0c\u4f46\u4f9d\u8d56\u4e8e\u7269\u7406\u8fc7\u7a0b\u800c\u975e\u7535\u5b50\u8ba1\u7b97\u3002<\/span><\/span><\/p>\n

      MNNs \u7684\u4e3b\u8981\u67b6\u6784\u7531\u8282\u70b9<\/span>\uff08\u673a\u68b0\u795e\u7ecf\u5143\uff09<\/span>\u3001\u5f39\u7c27<\/span>\uff08\u8fde\u63a5\u6743\u91cd\uff09<\/span>\u548c\u8f93\u5165\u8f93\u51fa\u8282\u70b9<\/span>\uff08\u529f\u80fd\u7c7b\u4f3c\u4e8e\u611f\u77e5\u5668\u7684\u8f93\u5165\u548c\u8f93\u51fa\u5c42\uff09<\/span>\u7ec4\u6210\u3002\u65bd\u52a0\u5230\u8f93\u5165\u8282\u70b9\u7684\u529b\u88ab\u89c6\u4e3a\u8f93\u5165\u4fe1\u53f7\uff0c\u8282\u70b9\u5728\u529b\u7684\u4f5c\u7528\u4e0b\u53d1\u751f\u4f4d\u79fb\uff0c\u8868\u793a\u6fc0\u6d3b\u7a0b\u5ea6\u3002\u8fd9\u4e9b\u529b\u901a\u8fc7\u5f39\u7c27\u4f20\u9012\u5230\u5176\u4ed6\u8282\u70b9\uff0c\u51b3\u5b9a\u4e86\u8f93\u51fa\u8282\u70b9\u7684\u6700\u7ec8\u4f4d\u79fb\u3002\u8f93\u5165\u8282\u70b9\u7684\u529b\u548c\u8f93\u51fa\u8282\u70b9\u7684\u4f4d\u79fb\u90fd<\/span><\/span>\u662f<\/span><\/span>\u77e2\u91cf<\/span><\/span><\/span>\uff0c<\/span><\/span>\u4f7f\u5f97 MNNs \u80fd\u591f\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u5e76\u884c\u5904\u7406\u590d\u6742\u4efb\u52a1\u3002<\/span><\/span><\/p>\n

      <\/section>\n

      \u4f7f\u7528Polyjet\u6a61\u80f6\u7c7b\u6750\u6599Agilus30\u76843D\u6253\u5370\u673a\u68b0\u795e\u7ecf\u7f51\u7edc[11]<\/span><\/span><\/em><\/p>\n

      \u4e0e\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\u4e0d\u540c\uff0cMNNs \u5177\u6709\u591a\u79cd\u72ec\u7279\u4f18\u52bf\uff1a<\/span><\/span><\/p>\n

        \n
      1. \n

        \u9ad8\u80fd\u6548\u4e0e\u8282\u80fd\u6027\uff1a<\/span><\/span><\/strong> \u7531\u4e8e\u8ba1\u7b97\u8fc7\u7a0b\u57fa\u4e8e\u7269\u7406\u8fd0\u52a8\uff0cMNNs \u7684\u8ba1\u7b97\u80fd\u8017\u6781\u4f4e\uff0c\u5c24\u5176\u9002\u5408\u5728\u80fd\u6e90\u53d7\u9650\u7684\u73af\u5883\u4e2d\u8fd0\u884c\u3002<\/span><\/span><\/p>\n<\/li>\n

      2. \n

        \u7ed3\u6784\u7b80\u5355\uff0c\u786c\u4ef6\u5b9e\u73b0\u6210\u672c\u4f4e\uff1a<\/span><\/span><\/strong> MNNs \u4f9d\u8d56\u4e8e\u7b80\u5355\u7684\u673a\u68b0\u7ed3\u6784\uff0c\u51cf\u5c11\u4e86\u5bf9\u590d\u6742\u7535\u8def\u548c\u96c6\u6210\u82af\u7247\u7684\u9700\u6c42\u3002<\/span><\/span><\/p>\n<\/li>\n

      3. \n

        \u9c81\u68d2\u6027\u4e0e\u81ea\u9002\u5e94\u6027\uff1a<\/span><\/span><\/strong> \u7531\u4e8e\u529b\u548c\u4f4d\u79fb\u7684\u7269\u7406\u7279\u6027\uff0cMNNs \u5728\u7535\u78c1\u73af\u5883\u590d\u6742\u6216\u566a\u58f0\u5e72\u6270\u5f3a\u7684\u73af\u5883\u4e2d\u5177\u6709\u5929\u7136\u4f18\u52bf\u3002<\/span><\/span><\/p>\n<\/li>\n

      4. \n

        \u53ef\u6269\u5c55\u6027\u4e0e\u6a21\u5757\u5316\uff1a<\/span><\/span><\/strong> \u4e0d\u540c\u7ed3\u6784\u548c\u8282\u70b9\u5e03\u5c40\u7684 MNNs \u53ef\u4ee5\u901a\u8fc7\u8c03\u6574\u5f39\u7c27\u5e38\u6570\u548c\u8fde\u63a5\u62d3\u6251\u6765\u9002\u914d\u591a\u79cd\u4efb\u52a1\u9700\u6c42\u3002<\/span><\/span><\/p>\n<\/li>\n<\/ol>\n

        \u8fd9\u4e9b\u7279\u70b9\u4f7f MNNs \u6210\u4e3a\u672a\u6765\u7269\u7406\u795e\u7ecf\u7f51\u7edc\u786c\u4ef6\u5e73\u53f0\u7684\u6f5c\u5728\u6838\u5fc3\u6280\u672f\uff0c\u6709\u671b\u5728\u667a\u80fd\u6750\u6599\u3001\u673a\u5668\u4eba\u548c\u81ea\u9002\u5e94\u8bbe\u5907\u7b49\u5e94\u7528\u9886\u57df\u4e2d\u53d1\u6325\u91cd\u8981\u4f5c\u7528\u3002<\/span><\/span><\/p>\n

        \u4e00\u7bc7\u6700\u65b0\u7684\u5de5\u4f5c[11]\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u4f34\u968f\u53d8\u91cf\u6cd5<\/span>\uff08Adjoint Variable Method\uff09<\/span>\u7684\u201c\u539f\u4f4d\u53cd\u5411\u4f20\u64ad\u201d<\/span>\uff08In-situ Backpropagation\uff09<\/span>\u65b9\u6cd5\uff0c\u5f00\u521b\u6027\u5730\u89e3\u51b3\u4e86 MNNs \u7684\u68af\u5ea6\u8ba1\u7b97\u4e0e\u53c2\u6570\u66f4\u65b0\u96be\u9898\u3002\u4f20\u7edf\u7684\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u4f9d\u8d56\u4e8e\u8ba1\u7b97\u673a\u4e0a\u7684\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\uff0c\u800c\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u53c2\u6570\u66f4\u65b0\u4e00\u76f4\u53d7\u5230\u7cbe\u5ea6\u548c\u64cd\u4f5c\u590d\u6742\u5ea6\u7684\u9650\u5236\u3002\u8be5\u7814\u7a76\u63d0\u51fa\u4e86\u4e00\u79cd\u80fd\u591f\u5728\u7269\u7406\u73af\u5883\u4e2d\u76f4\u63a5\u8ba1\u7b97\u68af\u5ea6\u7684\u65b9\u6cd5\uff0c\u5927\u5927\u63d0\u5347\u4e86 MNNs \u7684\u8bad\u7ec3\u6548\u7387\u548c\u53ef\u6269\u5c55\u6027\u3002\u7814\u7a76\u8005\u6210\u529f\u89e3\u51b3\u4e86\u4eff\u771f\u4e0e\u5b9e\u9645\u7269\u7406\u7ed3\u6784\u4e4b\u95f4\u7684\u8bef\u5dee\u95ee\u9898\uff0c\u4e3a\u672a\u6765\u7684\u673a\u68b0\u795e\u7ecf\u7f51\u7edc\u7814\u7a76\u63d0\u4f9b\u4e86\u53ef\u9760\u7684\u6280\u672f\u8def\u5f84\u3002<\/span><\/span><\/p>\n

        \u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50<\/span><\/span><\/h3>\n

        \u63a8\u8350\u7406\u7531:<\/span><\/span><\/strong> \u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50<\/span>\uff08Fourier neural operator\uff0c FNO\uff09<\/span>[12]\u5f00\u521b\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u79d1\u5b66AI\u8303\u5f0f\uff0c\u901a\u8fc7\u5728\u9891\u57df\u7a7a\u95f4\u5b66\u4e60\u7b97\u5b50\u6620\u5c04\uff0c\u5b9e\u73b0\u4e86\u5206\u8fa8\u7387\u65e0\u5173\u7684\u5feb\u901f\u4eff\u771f\uff0c\u7279\u522b\u9002\u5408\u5904\u7406\u7531\u504f\u5fae<\/span><\/span>\u5206\u65b9\u7a0b\u63cf\u8ff0\u7684\u7269\u7406\u7cfb\u7edf\u3002<\/span><\/span>\u672c\u65b9\u6cd5\u7531\u96c6\u667a\u793e\u533a\u6210\u5458\u3001\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u535a\u58eb\u751f\u674e\u5b97\u5b9c\u7b49\u4eba\u63d0\u51fa\u3002<\/span><\/span><\/span><\/p>\n

        \u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50<\/span> (FNO) <\/span>\u7684\u6838\u5fc3\u521b\u65b0\u5728\u4e8e\u5b83\u5f7b\u5e95\u6539\u53d8\u4e86\u795e\u7ecf\u7f51\u7edc\u5904\u7406\u7269\u7406\u95ee\u9898\u7684\u65b9\u5f0f\u3002\u8fd9\u662f\u4e00\u79cd\u65b0\u7684\u6df1\u5ea6\u5b66\u4e60\u67b6\u6784\uff0c\u80fd\u591f\u5b66\u4e60\u65e0\u9650\u7ef4\u51fd\u6570\u7a7a\u95f4\u4e2d\u7684\u6620\u5c04\u3002\u5982\u4e0b\u56fe\u6240\u793a\uff1a<\/span><\/span><\/p>\n

        <\/section>\n

        \u5085\u7acb\u53f6\u795e\u7ecf\u7b97\u5b50\u7684\u7f51\u7edc\u67b6\u6784 | \u6765\u6e90\uff1aLi Z\uff0c Kovachki N B\uff0c Azizzadenesheli K\uff0c et al. Fourier Neural Operator for Parametric Partial Differential Equations. <\/span><\/span>International Conference on Learning Representations. <\/span><\/span><\/em><\/span><\/p>\n

        FNO\u7684\u5904\u7406\u6d41\u7a0b\u4e3b\u8981\u5206\u4e3a<\/span><\/span>\u4e09\u6b65\uff1a<\/span><\/span>1.<\/span><\/span><\/span><\/span>\u901a\u8fc7\u7ebf\u6027\u5c42\u8fdb\u884c\u5347\u7ef4\uff1b2.<\/span><\/span><\/span><\/span>\u5e94\u7528\u56db\u5c42\u79ef\u5206\u7b97\u5b50\u548c\u6fc0\u6d3b\u51fd\u6570\uff1b3.<\/span><\/span><\/span><\/span>\u518d\u5c06\u8f93\u51fa\u7279\u5f81\u6295\u5f71\u56de\u76ee\u6807\u7ef4\u5ea6\u3002<\/span><\/span><\/span>\u5176\u4e2d\u5085\u7acb<\/span><\/span>\u53f6\u5c42\u5bf9\u7279\u5f81\u8fdb\u884c\u5085\u91cc\u53f6\u53d8\u6362\uff0c\u7136\u540e\u5bf9\u4f4e\u9891\u90e8\u5206\u8fdb\u884c\u7ebf\u6027\u53d8\u6362\u518d\u5e94\u7528\u53cd\u5085\u7acb\u53f6\u53d8\u6362\uff1b\u800c\u5bf9\u9ad8\u9891\u90e8\u5206\uff0c\u5219\u8fdb\u884c\u5c40\u90e8\u7ebf\u6027\u53d8\u6362\uff0c\u5e76\u5c06\u9ad8\u9891\u4fe1\u606f\u548c\u4f4e\u9891\u4fe1\u606f\u76f8\u52a0\u8f93\u5165\u6fc0\u6d3b\u51fd\u6570\uff0c\u518d\u8fdb\u884c\u53cd\u5085\u91cc\u53f6\u53d8\u6362\u3002\u8fd9\u79cd\u8bbe\u8ba1\u65e2\u4fdd\u6301\u4e86\u7269\u7406\u91cf\u7684\u5b88\u6052\u6027\uff0c\u53c8\u80fd\u663e\u8457\u63d0\u5347\u8ba1\u7b97\u6548\u7387\u3002<\/span><\/span><\/p>\n

        FNO \u5df2\u7ecf\u88ab\u5e94\u7528\u4e8e\u8bb8\u591a\u91cd\u8981\u7684\u79d1\u5b66\u9886\u57df\uff0c\u5176\u4e2d\u5728\u5929\u6c14\u9884\u62a5\u9886\u57df\uff0c\u57fa\u4e8eFNO\u63d0\u51fa\u7684FourCastNet[13]\u4f7f<\/span><\/span>\u7528<\/span><\/span>T<\/span><\/span><\/span>ransformer\u6a21\u578b<\/span><\/span><\/span>\uff0c\u642d<\/span><\/span>\u5efa\u4e86\u4eba\u5de5\u667a\u80fd\u548c\u7269\u7406\u5b66\u4e4b\u95f4\u7684\u6865\u6881\uff0c\u5e76\u53d6\u5f97\u4e86\u7a81\u7834\u6027\u7684\u6210\u679c\u3002\u5b83\u6bd4\u4f20\u7edf\u7684\u6570\u503c\u5929\u6c14\u9884\u62a5<\/span>\uff08NWP\uff09<\/span>\u6a21\u578b\u5feb\u7ea645000\u500d\u3002\u5728\u8bad\u7ec3\u65f6\uff0c\u4e0eNWP\u6a21\u578b\u4e2d\u7684\u6807\u6746\u2014\u2014\u6b27\u6d32\u7efc\u5408\u9884\u62a5\u7cfb\u7edf\u76f8\u6bd4\uff0cFourCastNet\u9884\u6d4b\u5929\u6c14\u6240\u9700\u7684\u80fd\u8017\u51cf\u5c11\u4e8612000\u500d\u3002\u66f4\u4ee4\u4eba\u5174\u594b\u7684\u662f\u5176\u5728\u78b3\u6355\u96c6\u4e0e\u5c01\u5b58<\/span> (CCS) <\/span>\u9886\u57df\u7684\u5e94\u7528 – Nested FNO[14]\u5c06\u590d\u6742\u7684\u5730\u8d28\u6d41\u52a8\u9884\u6d4b\u52a0\u901f\u4e86\u8fd170\u4e07\u500d\uff0c\u4e3a\u5927\u89c4\u6a21CCS\u6280\u672f\u7684\u5de5\u4e1a\u90e8\u7f72\u626b\u6e05\u4e86\u8ba1\u7b97\u74f6\u9888\u3002<\/span><\/span><\/p>\n

        \u8fd9\u4e9b\u6210\u529f\u6848\u4f8b\u8868\u660e\uff0cFNO\u4e0d\u4ec5\u662f\u4e00\u4e2a\u7406\u8bba\u7a81\u7834\uff0c\u66f4\u662f\u4e00\u4e2a\u80fd\u591f\u89e3\u51b3\u5b9e\u9645\u5de5\u7a0b\u95ee\u9898\u7684\u5f3a\u5927\u5de5\u5177\uff0c\u4e5f\u5728\u6d41\u4f53\u52a8\u529b\u5b66\u3001\u6750\u6599\u79d1\u5b66\u3001\u5730\u7403\u79d1\u5b66\u3001\u751f\u7269\u533b\u5b66\u5de5\u7a0b\u7b49\u9886\u57df\u53d1\u6325\u4e86\u91cd\u8981\u7684\u4f5c\u7528[15]\u3002<\/span><\/span><\/p>\n


        <\/span><\/h2>\n

        \n
        \n
        \n
        \n
        \n

        <\/span><\/section>\n

        <\/span><\/section>\n
        \n
        <\/section>\n<\/section>\n<\/section>\n
        \n

        \u6311\u6218\u4e0e\u5c55\u671b<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

        \n

        <\/span><\/section>\n

        <\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


        <\/span><\/p>\n

        KAN\u53ef\u4ee5\u88ab\u5f52\u7c7b\u4e3a\u7269\u7406\u5f15\u5bfc\u7684\u673a\u5668\u5b66\u4e60<\/span>\uff08Physics-Informed Machine Learning\uff0c PIML\uff09<\/span>\u3002\u4f5c\u4e3a\u6b63\u5728\u53d1\u5c55\u7684\u65b0\u578bAI\u67b6\u6784\uff0c\u5728\u6c14\u5019\u6a21\u62df\u3001\u6750\u6599\u79d1\u5b66\u548c\u751f\u7269\u533b\u5b66\u4e2d\u5177\u6709\u5e7f\u9614\u524d\u666f[7]\u3002PIML\u7684\u4e3b\u8981\u4f18\u52bf\u5728\u4e8e\u53ef\u4ee5\u51cf\u5c11\u5bf9\u5927\u91cf\u6570\u636e\u7684\u4f9d\u8d56\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u6570\u636e\u7a00\u7f3a\u6216\u6602\u8d35\u7684\u9886\u57df\u3002PIML\u9762\u4e34\u7684\u6311\u6218\u4e3b\u8981\u5728\u4e8e\u5982\u4f55\u6709\u6548\u5d4c\u5165\u7269\u7406\u7ea6\u675f\uff0c\u63d0\u5347\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u8ba1\u7b97\u6548\u7387\u548c\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u3002\u6b64\u5916\uff0cPIML\u6a21\u578b\u7684\u6709\u6548\u6027\u548c\u7cbe\u5ea6\u5f80\u5f80\u4f9d\u8d56\u4e8e\u7269\u7406\u6a21\u578b\u7684\u51c6\u786e\u6027\uff0c\u56e0\u6b64\u5728\u7269\u7406\u6a21\u578b\u4e0d\u591f\u5b8c\u5584\u65f6\u53ef\u80fd\u5f71\u54cd\u7ed3\u679c\u7684\u53ef\u9760\u6027\u3002<\/span><\/span><\/p>\n

        PIML\u4e3b\u8981\u805a\u7126\u4e8eAI\u7b97\u6cd5\u5c42\u9762\u7684\u4f18\u5316\uff0c\u800c\u7c7b\u8111\u8ba1\u7b97\u5219\u901a\u8fc7\u786c\u4ef6\u67b6\u6784\u9769\u65b0<\/span>\uff08\u5982\u795e\u7ecf\u5f62\u6001\u82af\u7247\uff09<\/span>\u4e0e\u8f6f\u4ef6\u6808\u91cd\u6784<\/span>\uff08\u6db5\u76d6\u64cd\u4f5c\u7cfb\u7edf\u3001\u7b97\u6cd5\u8bbe\u8ba1\u7b49\uff09<\/span>\uff0c\u6784\u5efa\u8d77\u5b8c\u5168\u4e0d\u540c\u4e8e\u4f20\u7edf\u4f53\u7cfb\u7684\u8ba1\u7b97\u8303\u5f0f\u3002<\/span><\/span><\/span>\u7c7b<\/span><\/span>\u8111\u8ba1\u7b97\u4ee5\u5927\u8111\u8303\u5f0f\u4e3a\u6307\u5bfc\uff0c\u590d\u5236\u751f\u7269\u795e\u7ecf\u7cfb\u7edf\u7684\u7279\u5f81\u6216\u529f\u80fd\uff0c\u7528\u4e8e\u63a2\u7d22\u795e\u7ecf\u79d1\u5b66\u548c\u52a0\u901f\u667a\u80fd\u4efb\u52a1\u3002\u6b64\u5916\uff0c\u878d\u5408\u7c7b\u8111\u8ba1\u7b97\u548c\u4f20\u7edf\u8ba1\u7b97\u673a\u56fa\u6709\u7684\u8ba1\u7b97\u8303\u5f0f\uff0c\u53ef\u4ee5\u9ad8\u6548\u3001\u7075\u6d3b\u5730\u5904\u7406\u66f4\u5e7f\u6cdb\u7684\u901a\u7528\u4efb\u52a1\u3002<\/span><\/span><\/p>\n

        <\/section>\n

        \u7c7b\u8111\u8ba1\u7b97\u7684\u6311\u6218\u5728\u4e8e\u5b9e\u73b0\u8ba1\u7b97\u7684\u901a\u7528\u6027<\/span><\/span>\uff0c<\/span><\/span>\u6709<\/span><\/span><\/span>\u4e09\u79cd\u53ef\u80fd\u7684\u5b9e\u73b0\u7b56\u7565<\/span><\/span><\/span>\uff1a\u5e94\u7528\u7ea7<\/span><\/span>\u6a21\u5f0f\u901a\u7528\u5316\u3001\u786c\u4ef6\u7ea7\u7ed3\u6784\u901a\u7528\u5316\u548c\u8f6f\u4ef6\u7ea7\u7cfb\u7edf\u901a\u7528\u5316\u3002\u7c7b\u4f3cSNN\u7b49\u6280\u672f\u6700\u521d\u662f\u4e3a\u9ad8\u6548\u8fd0\u884c\u7279\u5b9a\u7b97\u6cd5\u800c\u8bbe\u8ba1\u7684\uff0c\u4f46\u8d8a\u6765\u8d8a\u591a\u7684\u7cfb\u7edf\u88ab\u8bbe\u8ba1\u4e3a\u53ef\u540c\u65f6\u652f\u6301ANN\u548cSNN\u8ba1\u7b97\uff0c\u6269\u5927\u4e86\u7cfb\u7edf\u53ef\u652f\u6301\u7684\u5e94\u7528\u8303\u56f4\uff0c\u4ece\u800c\u4e3a\u6700\u7ec8\u8fbe\u5230\u901a\u7528\u76ee\u7684\u63d0\u4f9b\u4e86\u53ef\u80fd[8]\u3002<\/span><\/span><\/p>\n

        \u50a8\u5907\u6c60\u8ba1\u7b97<\/span>\uff08RC\uff09<\/span>\u5c55\u73b0\u51fa\u5229\u7528\u65b0\u5174\u7535\u5b50\u6280\u672f\u5b9e\u73b0\u9ad8\u6548\u4fe1\u606f\u5904\u7406\u7684\u6f5c\u529b\uff0c\u5176\u672a\u6765\u53d1\u5c55\u5c06\u62d3\u5c55\u81f3\u7535\u5b50\u3001\u5149\u5b66\u53ca\u673a\u68b0\u7cfb\u7edf\u7684\u591a\u7269\u7406\u5b9e\u73b0\uff0c\u4ece\u800c\u6784\u5efa\u80fd\u6548\u7a81\u7834\u4f20\u7edf\u67b6\u6784\u7684\u65b0\u578b\u8ba1\u7b97\u5e73\u53f0\u3002<\/span><\/span><\/span>\u8fd9\u7c7b<\/span><\/span>\u7cfb\u7edf\u53ef\u5b9e\u73b0\u4f4e\u529f\u8017\u548c\u5b9e\u65f6\u6570\u636e\u5904\u7406\uff0c\u5c24\u5176\u9002\u5408\u795e\u7ecf\u5f62\u6001\u8ba1\u7b97\u3002RC\u9762\u4e34\u7684\u6311\u6218\u4e3b\u8981\u5305\u62ec\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u3001\u9002\u5e94\u6027\u4ee5\u53ca\u5982\u4f55\u63d0\u9ad8\u5176\u5728\u590d\u6742\u4efb\u52a1\u4e0b\u7684\u6cdb\u5316\u80fd\u529b\u548c\u8ba1\u7b97\u7cbe\u5ea6\u7b49\u95ee\u9898\u3002<\/span><\/span><\/p>\n

        \u5173\u4e8e\u673a\u68b0\u795e\u7ecf\u7f51\u7edc<\/span>\uff08MNN\uff09<\/span>\u7684\u6700\u65b0\u7814\u7a76<\/span><\/span>[11]<\/span><\/span>\u4e3a<\/span><\/span><\/span>\u5176<\/span><\/span><\/span>\u5f00\u53d1<\/span><\/span><\/span>\u548c\u90e8\u7f72\u94fa<\/span><\/span>\u5e73\u4e86\u9053\u8def\uff0c\u63d0\u51fa\u4e86\u673a\u68b0\u7f51\u7edc\u5728\u667a\u80fd\u6750\u6599\u3001\u8f6f\u4f53\u673a\u5668\u4eba\u548c\u81ea\u9002\u5e94\u673a\u68b0\u8bbe\u5907\u4e2d\u7684\u5e7f\u6cdb\u5e94\u7528\u524d\u666f\u3002\u7814\u7a76\u8868\u660e\uff0c\u672a\u6765\u53ef\u901a\u8fc7\u6539\u8fdb\u5f39\u7c27\u5e38\u6570\u7684\u52a8\u6001\u8c03\u6574\u673a\u5236\u8fdb\u4e00\u6b65\u6269\u5c55\u8be5\u6280\u672f\uff0c\u8bbe\u8ba1\u5177\u6709\u9ad8\u5ea6\u81ea\u52a8\u5316\u548c\u81ea\u4e3b\u5b66\u4e60\u80fd\u529b\u7684\u6750\u6599\u4e0e\u8bbe\u5907\u3002\u6b64\u5916\uff0c\u901a\u8fc7\u7814\u7a76\u975e\u7ebf\u6027\u6750\u6599\u7684\u54cd\u5e94\uff0c\u63a2\u7d22\u66f4\u590d\u6742\u7684\u6570\u636e\u96c6\u5904\u7406\u548c\u51b3\u7b56\u4efb\u52a1\uff0c\u5c06\u6210\u4e3a\u672a\u6765\u7684\u7814\u7a76\u91cd\u70b9\u3002\u8fd9\u4e9b\u521b\u65b0\u4e3a\u5c06\u673a\u5668\u5b66\u4e60\u4e0e\u7269\u7406\u6750\u6599\u79d1\u5b66\u878d\u5408\u5f00\u8f9f\u4e86\u65b0\u7684\u7814\u7a76\u65b9\u5411\uff0c\u6216\u5c06\u5728\u65b0\u4e00\u4ee3\u8282\u80fd\u8ba1\u7b97\u786c\u4ef6\u548c\u667a\u80fd\u7cfb\u7edf\u7684\u5f00\u53d1\u4e2d\u53d1\u6325\u5173\u952e\u4f5c\u7528\u3002<\/span><\/span><\/p>\n

        \u53c2\u8003\u6587\u732e<\/span><\/span><\/h2>\n

        [1] Liu\uff0c Ziming\uff0c et al. “Kan: Kolmogorov-arnold networks.” <\/span><\/span>arXiv preprint arXiv:2404.19756<\/span><\/span><\/em> (2024).<\/span><\/span><\/p>\n

        https:\/\/arxiv.org\/abs\/2404.19756<\/span><\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86\u591a\u5c42\u611f\u77e5\u5668\uff08MLPs\uff09\u7684\u66ff\u4ee3\u65b9\u6848KAN\uff0c\u901a\u8fc7\u5728\u8fb9\u7f18\uff08\u800c\u975e\u8282\u70b9\uff09\u4e0a\u8bbe\u7f6e\u53ef\u5b66\u4e60\u7684\u6fc0\u6d3b\u51fd\u6570\uff0c\u5e76\u7528\u6837\u6761\u53c2\u6570\u5316\u7684\u5355\u53d8\u91cf\u51fd\u6570\u66ff\u6362\u4f20\u7edf\u7684\u7ebf\u6027\u6743\u91cd\uff0c\u4ece\u800c\u5728\u51c6\u786e\u6027\u548c\u53ef\u89e3\u91ca\u6027\u65b9\u9762\u8d85\u8d8aMLPs\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [2] Liu\uff0c Ziming\uff0c et al. “Kan 2.0: Kolmogorov-arnold networks meet science.” <\/span><\/span>arXiv preprint arXiv:2408.10205<\/span><\/span><\/em> (2024).<\/span><\/span><\/p>\n

        https:\/\/arxiv.org\/abs\/2408.10205<\/span><\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86KAN 2.0\uff0c\u5728KAN\u7684\u57fa\u7840\u4e0a\u5f15\u5165\u4e86\u4e58\u6cd5\u8282\u70b9\u3001kanpiler\u7f16\u8bd1\u5668\u548c\u6811\u5f62Transformer\u67b6\u6784\uff0c\u589e\u5f3a\u4e86\u6a21\u578b\u7684\u8868\u8fbe\u529b\u3001\u5b9e\u7528\u6027\u548c\u53ef\u89e3\u91ca\u6027\uff0c\u5e76\u62d3\u5c55\u4e86\u5176\u5728\u79d1\u5b66\u53d1\u73b0\u9886\u57df\u7684\u5e94\u7528\u8303\u56f4\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [3] Hu\uff0c Yangfan\uff0c et al. “Toward Large-scale Spiking Neural Networks: A Comprehensive Survey and Future Directions.” <\/span><\/span>arXiv preprint arXiv:2409.02111<\/span><\/span><\/em> (2024).<\/span><\/span><\/p>\n

        https:\/\/arxiv.org\/abs\/2409.02111<\/span><\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u63d0\u4f9b\u4e86\u5bf9\u5927\u89c4\u6a21\u5c16\u5cf0\u795e\u7ecf\u7f51\u7edc\uff08SNN\uff09\u7684\u5168\u9762\u7efc\u8ff0\uff0c\u5e76\u63a2\u8ba8\u4e86\u672a\u6765\u7684\u53d1\u5c55\u65b9\u5411\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [4] Jaeger\uff0c H. (2001). \u201cThe \u201cecho state\u201d approach to analysing and training recurrent neural networks.\u201d <\/span><\/span>Technical report\uff0c GMD German National Research Institute for Computer Science<\/span><\/span><\/em>.<\/span><\/span><\/p>\n

        https:\/\/www.ai.rug.nl\/minds\/uploads\/EchoStatesTechRep.pdf<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u4ecb\u7ecd\u4e86\u201c\u56de\u58f0\u72b6\u6001\u201d\u65b9\u6cd5\uff0c\u8fd9\u662f\u4e00\u79cd\u5206\u6790\u548c\u8bad\u7ec3\u9012\u5f52\u795e\u7ecf\u7f51\u7edc\uff08RNNs\uff09\u7684\u6280\u672f\uff0c\u5b83\u901a\u8fc7\u4fdd\u6301\u7f51\u7edc\u7684\u72b6\u6001\u6765\u6355\u6349\u65f6\u95f4\u52a8\u6001\uff0c\u5e76\u5c06\u5b66\u4e60\u4efb\u52a1\u7b80\u5316\u4e3a\u8f93\u51fa\u6743\u91cd\u7684\u8c03\u6574\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [5] Maass\uff0c W.\uff0c Natschlager\uff0c T.\uff0c & Markram\uff0c H. (2002). \u201cReal-time computing without stable states: A new framework for neural computation based on perturbations.\u201d <\/span><\/span>Neural Computation<\/span><\/span><\/em>.<\/span><\/span><\/p>\n

        https:\/\/ieeexplore.ieee.org\/abstract\/document\/6789852<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u65b0\u7684\u795e\u7ecf\u8ba1\u7b97\u6846\u67b6\uff0c\u5373\u201c\u5b9e\u65f6\u8ba1\u7b97\u65e0\u9700\u7a33\u5b9a\u72b6\u6001\u201d\uff0c\u5b83\u57fa\u4e8e\u9ad8\u7ef4\u52a8\u6001\u7cfb\u7edf\u7684\u539f\u7406\u548c\u7edf\u8ba1\u5b66\u4e60\u7406\u8bba\uff0c\u53ef\u4ee5\u5728\u901a\u7528\u7684\u9012\u5f52\u7535\u8def\u4e0a\u5b9e\u73b0\u5b9e\u65f6\u5904\u7406\u65f6\u95f4\u53d8\u5316\u7684\u8f93\u5165\uff0c\u800c\u4e0d\u9700\u8981\u7a33\u5b9a\u7684\u5185\u90e8\u72b6\u6001\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [6] Liang\uff0c Xiangpeng\uff0c et al. “Physical reservoir computing with emerging electronics.” <\/span><\/span>Nature Electronics<\/span><\/span><\/em> 7.3 (2024): 193-206.<\/span><\/span><\/p>\n

        https:\/\/www.nature.com\/articles\/s41928-024-01133-z<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u7cfb\u7edf\u68b3\u7406\u4e86\u57fa\u4e8e\u65b0\u578b\u7535\u5b50\u5668\u4ef6\u7684\u7269\u7406\u50a8\u5907\u6c60\u8ba1\u7b97\u7684\u8d77\u6e90\u3001\u53d1\u5c55\u4e0e\u672a\u6765\u5c55\u671b\uff0c\u5e76\u91cd\u70b9\u5206\u6790\u4e86\u50a8\u5907\u6c60\u67b6\u6784\u3001\u7269\u7406\u8282\u70b9\u3001\u8f93\u51fa\u5c42\u7b49\u6784\u7b51\u4e00\u4e2a\u5b8c\u6574\u7269\u7406\u50a8\u5907\u6c60\u7cfb\u7edf\u7684\u5173\u952e\u6280\u672f\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [7] Karniadakis\uff0c G. E.\uff0c et al. \u201cPhysics-informed Machine Learning.\u201d <\/span><\/span>Nature Reviews Physics<\/span><\/span><\/em>\uff0c 2021.<\/span><\/span><\/p>\n

        https:\/\/www.osti.gov\/pages\/servlets\/purl\/2282016<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u7cfb\u7edf\u5730\u8c03\u67e5\u5e76\u603b\u7ed3\u4e86\u7269\u7406\u4fe1\u606f\u673a\u5668\u5b66\u4e60\u9886\u57df\uff0c\u63a2\u8ba8\u4e86\u5982\u4f55\u5c06\u7269\u7406\u5148\u9a8c\u77e5\u8bc6\uff08\u5982PDEs\/ODEs\/SDEs\u3001\u5bf9\u79f0\u6027\u7ea6\u675f\u548c\u76f4\u89c2\u7269\u7406\uff09\u5d4c\u5165\u5230\u673a\u5668\u5b66\u4e60\u6a21\u578b\u7684\u4e0d\u540c\u90e8\u5206\uff08\u6570\u636e\u3001\u67b6\u6784\u3001\u635f\u5931\u51fd\u6570\u3001\u4f18\u5316\u65b9\u6cd5\u548c\u63a8\u7406\u7b97\u6cd5\uff09\uff0c\u5e76\u8be6\u7ec6\u5448\u73b0\u4e86\u73b0\u6709\u65b9\u6cd5\u3001\u6311\u6218\u548c\u672a\u6765\u65b9\u5411\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [8] Zhang\uff0c Weihao\uff0c et al. “The development of general-purpose brain-inspired computing.” <\/span><\/span>Nature Electronics<\/span><\/span><\/em> (2024): 1-12.<\/span><\/span><\/p>\n

        https:\/\/www.nature.com\/articles\/s41928-024-01277-y<\/span><\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u63a2\u8ba8\u4e86\u901a\u7528\u8111\u542f\u53d1\u8ba1\u7b97\u7684\u53d1\u5c55\uff0c\u6d89\u53ca\u795e\u7ecf\u5f62\u6001\u7535\u5b50\u7cfb\u7edf\u3001\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u7684\u5927\u8111\u76f8\u4f3c\u6027\u3001\u89c6\u89c9\u4f20\u611f\u5668\u6280\u672f\u3001\u5927\u89c4\u6a21\u795e\u7ecf\u6a21\u62df\u4ee5\u53ca\u76f8\u5173\u786c\u4ef6\u548c\u8f6f\u4ef6\u5de5\u5177\u7684\u8fdb\u6b65\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [9] Fan\uff0c Feng-Lei\uff0c et al. “On interpretability of artificial neural networks: A survey.” <\/span><\/span>IEEE Transactions on Radiation and Plasma Medical Sciences<\/span><\/span><\/em> 5.6 (2021): 741-760.<\/span><\/span><\/p>\n

        https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC9105427\/<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u8fd9\u7bc7\u8bba\u6587\u662f\u4e00\u9879\u5173\u4e8e\u4eba\u5de5\u795e\u7ecf\u7f51\u7edc\u53ef\u89e3\u91ca\u6027\u7684\u7efc\u8ff0\u7814\u7a76\uff0c\u63d0\u51fa\u4e86\u4e00\u4e2a\u5168\u9762\u7684\u53ef\u89e3\u91ca\u6027\u5206\u7c7b\u4f53\u7cfb\uff0c\u7cfb\u7edf\u56de\u987e\u4e86\u63d0\u9ad8\u795e\u7ecf\u7f51\u7edc\u53ef\u89e3\u91ca\u6027\u7684\u6700\u65b0\u7814\u7a76\uff0c\u8ba8\u8bba\u4e86\u53ef\u89e3\u91ca\u6027\u5728\u533b\u5b66\u7b49\u9886\u57df\u7684\u5e94\u7528\uff0c\u5e76\u63a2\u8ba8\u4e86\u672a\u6765\u7814\u7a76\u65b9\u5411\uff0c\u5982\u4e0e\u6a21\u7cca\u903b\u8f91\u548c\u8111\u79d1\u5b66\u7684\u5173\u8054\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [10] Cucchi\uff0c Matteo\uff0c et al. “Hands-on reservoir computing: a tutorial for practical implementation.” <\/span><\/span>Neuromorphic Computing and Engineering<\/span><\/span><\/em> 2.3 (2022): 032002.<\/span><\/span><\/p>\n

        https:\/\/iopscience.iop.org\/article\/10.1088\/2634-4386\/ac7db7\/meta<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u672c\u6587\u65e8\u5728\u4e3a\u6750\u6599\u79d1\u5b66\u3001\u5316\u5b66\u548c\u7535\u5b50\u5b66\u7b49\u9886\u57df\u7684\u8bfb\u8005\u63d0\u4f9b\u5b9e\u65bd\u6c34\u5e93\u8ba1\u7b97\uff08RC\uff09\u5b9e\u9a8c\u7684\u6982\u89c8\u3002RC\u4e3a\u5229\u7528\u6750\u6599\u7cfb\u7edf\u7684\u975e\u7ebf\u6027\u884c\u4e3a\u548c\u77ed\u671f\u8bb0\u5fc6\u8bbe\u8ba1\u65b0\u578b\u8ba1\u7b97\u8303\u5f0f\u63d0\u4f9b\u4e86\u6846\u67b6\uff0c\u907f\u514d\u4e86\u4f20\u7edf\u524d\u9988\u795e\u7ecf\u7f51\u7edc\u5728\u786c\u4ef6\u4e0a\u5b9e\u73b0\u65f6\u7684\u95ee\u9898\u3002\u672c\u6587\u5f3a\u8c03\u4e86RC\u5728\u786c\u4ef6\u795e\u7ecf\u7f51\u7edc\u4e2d\u7684\u6f5c\u529b\u3001\u4f18\u52bf\u53ca\u5b9e\u65bd\u969c\u788d\uff0c\u5e76\u5e0c\u671b\u964d\u4f4e\u79d1\u5b66\u5bb6\u5229\u7528\u975e\u7ebf\u6027\u7cfb\u7edf\u8fdb\u884c\u673a\u5668\u5b66\u4e60\u548c\u4eba\u5de5\u667a\u80fd\u4efb\u52a1\u7684\u95e8\u69db\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [11] Li\uff0c Shuaifeng\uff0c and Xiaoming Mao. “Training all-mechanical neural networks for task learning through in situ backpropagation.” <\/span><\/span>arXiv preprint arXiv:2404.15471<\/span><\/span><\/em> (2024).<\/span><\/span><\/p>\n

        https:\/\/arxiv.org\/abs\/2404.15471<\/span><\/span><\/p>\n\n\n\n
        \n

        \u63a8\u8350\u7406\u7531\uff1a<\/span><\/span><\/strong><\/span>\u672c\u6587\u63d0\u51fa\u4e86\u4e00\u79cd\u5168\u65b0\u7684\u673a\u68b0\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u65b9\u6cd5\u2014\u2014\u539f\u4f4d\u53cd\u5411\u4f20\u64ad\uff0c\u901a\u8fc7\u5c40\u90e8\u4fe1\u606f\u9ad8\u6548\u8ba1\u7b97\u68af\u5ea6\uff0c\u5b9e\u73b0\u884c\u4e3a\u5b66\u4e60\u548c\u673a\u5668\u5b66\u4e60\u4efb\u52a1\u3002\u5b9e\u9a8c\u8bc1\u660e\uff0c\u8be5\u65b9\u6cd5\u5728\u56de\u5f52\u548c\u5206\u7c7b\u4efb\u52a1\u4e2d\u8fbe\u5230\u9ad8\u7cbe\u5ea6\uff0c\u5c55\u73b0\u4e86\u673a\u68b0\u5b66\u4e60\u786c\u4ef6\u7684\u6f5c\u529b\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [12] Li\uff0c Zongyi\uff0c et al. “Fourier Neural Operator for Parametric Partial Differential Equations.” International Conference on Learning Representations\uff0c 2021.<\/span><\/span><\/p>\n

        https:\/\/arxiv.org\/abs\/2010.08895<\/span><\/span><\/p>\n\n\n\n
        \n

        \u8be5\u8bba\u6587\u63d0\u51fa\u7684\u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50\u5f00\u521b\u4e86\u9891\u57df\u5b66\u4e60\u7684\u65b0\u8303\u5f0f,\u5728\u79d1\u5b66\u8ba1\u7b97\u9886\u57df\u4ea7\u751f\u4e86\u91cd\u8981\u5f71\u54cd\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [13] Pathak\uff0c Jaideep\uff0c et al. “FourCastNet: A Global Data-driven High-resolution Weather Model Using Adaptive Fourier Neural Operators.” Nature\uff0c vol. 614\uff0c no. 7947\uff0c 2023\uff0c pp. 474-481.<\/span><\/span><\/p>\n

        https:\/\/www.nature.com\/articles\/s41586-023-05847-6<\/span><\/span><\/p>\n\n\n\n
        \n

        \u8be5\u8bba\u6587\u5c06\u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50\u5e94\u7528\u4e8e\u5168\u7403\u5929\u6c14\u9884\u62a5,\u5b9e\u73b0\u4e86\u663e\u8457\u7684\u8ba1\u7b97\u52a0\u901f\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [14] Wen\uff0c Guannan\uff0c et al. “Real-time High-resolution CO2 Geological Storage Prediction Using Nested Fourier Neural Operators.” Energy & Environmental Science\uff0c vol. 16\uff0c no. 4\uff0c 2023\uff0c pp. 1732-1741.<\/span><\/span><\/p>\n

        https:\/\/doi.org\/10.1039\/D2EE03266A<\/span><\/span><\/p>\n\n\n\n
        \n

        \u8be5\u5de5\u4f5c\u5c06\u5d4c\u5957\u5085\u91cc\u53f6\u795e\u7ecf\u7b97\u5b50\u5e94\u7528\u4e8e\u5730\u8d28\u50a8\u5b58\u9884\u6d4b,\u663e\u8457\u63d0\u5347\u4e86\u9884\u6d4b\u6548\u7387\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

        [15] Azizzadenesheli\uff0c Kamyar\uff0c et al. “Neural Operators for Accelerating Scientific Simulations and Design.” Nature Reviews Physics\uff0c 2024\uff0c pp. 1-9.<\/span><\/span><\/p>\n

        https:\/\/www.nature.com\/articles\/s42254-024-00712-5<\/span><\/span><\/p>\n\n\n\n
        \n

        \u8be5\u7efc\u8ff0\u5168\u9762\u603b\u7ed3\u4e86\u795e\u7ecf\u7b97\u5b50\u5728\u79d1\u5b66\u4eff\u771f\u4e0e\u8bbe\u8ba1\u4e2d\u7684\u5e94\u7528\u8fdb\u5c55\u3002<\/span><\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n


        <\/span><\/strong><\/p>\n

        \n

        \u51fa\u54c1<\/span><\/span><\/strong>\uff1a\u6f06\u8fdc\u3001\u5434\u529b\u6ce2\u3001\u5f20\u6c5f<\/span><\/span><\/span><\/p>\n

        \u8fd0\u8425<\/span><\/span><\/strong>\uff1a\u5b5f\u664b\u5b87\u3001\u738b\u5a77<\/span><\/span><\/p>\n

        \u64b0\u7a3f<\/span><\/span><\/strong>\uff1a\u5f20\u6c5f\u3001\u6768\u71d5\u9752\u3001\u738b\u5a77\u3001\u738b\u671d\u4f1a\u3001\u5341\u4e09\u7ef4\u3001\u5468\u8389\u3001\u6881\u91d1\u3001\u8881\u51b0\u3001\u6c5f\u5343\u6708\u3001\u5218\u5fd7\u6bc5<\/span><\/span><\/p>\n

        \u9e23\u8c22<\/span><\/span><\/strong>\uff08\u6309\u59d3\u6c0f\u62fc\u97f3\u987a\u5e8f\uff0c\u6392\u540d\u4e0d\u5206\u5148\u540e\uff09\uff1a<\/span><\/span><\/p>\n

        \u66f9\u98ce\u96f7 \u3001\u9648\u5c0f\u6768 \u3001\u7a0b\u8fdc\u3001\u675c\u6c85\u5c82 \u3001\u6bb5\u90c1\u3001\u65b9\u69af\u6977 \u3001\u4ed8\u5f66\u4f1f\u3001 \u9ad8\u60a6\u3001\u9ec4\u67ef\u946b\u3001\u674e\u660a\u3001\u5218\u5723\u8d85\u3001\u8c2d\u4f1f\u654f\u3001\u5434\u6cf0\u9716\u3001\u5434\u8273\u73b2\u3001\u5411\u7ea2\u519b\u3001\u5f20\u9aa5\u3001\u5f20\u8273\u3001\u6731\u601d\u8bed<\/span><\/span><\/p>\n<\/blockquote>\n


        <\/span><\/p>\n


        <\/span><\/p>\n

        <\/section>\n


        <\/span><\/p>\n

        \n
        \n
        \n
        \n

        AI+Science \u8bfb\u4e66\u4f1a<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

        \n


        <\/span><\/span><\/p>\n<\/section>\n

        <\/span><\/section>\n

        \"\u56fe\u7247\"<\/span><\/a><\/p>\n

        <\/span><\/p>\n

        <\/span><\/section>\n
        \u8be6\u60c5\u8bf7\u89c1\uff1a<\/span><\/span><\/span><\/section>\n
        \u4eba\u5de5\u667a\u80fd\u548c\u79d1\u5b66\u53d1\u73b0\u76f8\u4e92\u8d4b\u80fd\u7684\u65b0\u8303\u5f0f\uff1aAI+Science \u8bfb\u4e66\u4f1a\u542f\u52a8<\/a><\/span><\/span><\/span><\/section>\n

        <\/span><\/section>\n

        <\/span><\/section>\n
        \u63a8\u8350\u9605\u8bfb<\/span><\/span><\/strong><\/strong><\/strong><\/section>\n
        <\/strong><\/section>\n
        1. \u300aAI X Science\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b\u53d1\u5e03\uff1a35\u4e2a\u7814\u7a76\u524d\u6cbf\uff0c\u5f00\u542f\u79d1\u5b66\u53d1\u73b0\u7684\u9ec4\u91d1\u65f6\u4ee3<\/span><\/a><\/span><\/strong>
        <\/span><\/strong><\/span><\/section>\n
        2. \u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b1\uff1a\u57fa\u4e8eLLM\u7684\u79d1\u5b66\u7814\u7a76<\/span><\/a><\/span><\/strong>
        <\/span><\/strong><\/span><\/section>\n
        3. \u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b2\uff1a\u5782\u76f4\u9886\u57df\u79d1\u5b66\u5927\u6a21\u578b<\/span><\/a><\/span><\/strong><\/section>\n
        4. \u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b3\uff1a\u878d\u5165\u5148\u9a8c\u77e5\u8bc6\u7684AI\u6a21\u578b<\/span><\/a><\/span><\/strong><\/section>\n
        5. \u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b4\uff1aAI\u79d1\u5b66\u5bb6<\/span><\/a><\/span><\/strong><\/section>\n
        6. \u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b5\uff1a\u590d\u6742\u4e16\u754c\u7684\u591a\u667a\u80fd\u4f53\u5efa\u6a21<\/span><\/a><\/span><\/strong><\/section>\n
        7. \u300aAI\u00d7SCIENCE\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b6\uff1aAI \u4eff\u771f\u4e0e\u7cfb\u7edf\u6a21\u62df<\/span><\/a><\/span><\/strong><\/span><\/section>\n
        <\/strong><\/section>\n
        8. <\/span><\/strong><\/span>\u6e38\u620f\u5316\u79d1\u7814\u2014\u2014\u8ba9\u6211\u4eec\u7a81\u7834\u5185\u5377\u3001\u5171\u7814\u6d8c\u73b0<\/a><\/span><\/strong><\/strong><\/span><\/section>\n
        <\/strong>9. <\/span><\/strong>\u63a2\u7d22\u8005\u8ba1\u5212 | \u96c6\u667a\u4ff1\u4e50\u90e82025\u5185\u5bb9\u56e2\u961f\u62db\u52df\uff08\u5168\u804c&\u517c\u804c\uff09<\/a><\/span><\/strong><\/span><\/section>\n

        10. \u52a0\u5165\u96c6\u667a\uff0c\u73a9\u8f6c\u590d\u6742\uff0c\u5171\u521b\u6591\u56fe\uff01\u96c6\u667a\u4ff1\u4e50\u90e8\u7ebf\u4e0b\u5fd7\u613f\u8005\u62db\u52df<\/span><\/a><\/span><\/strong>
        <\/span><\/strong><\/span><\/p>\n


        <\/span><\/p>\n


        <\/span><\/span><\/p>\n

        \u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/span><\/section>\n<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

        \u5bfc\u8bed \u4e0a\u6d77\u79d1\u5b66\u667a\u80fd\u7814\u7a76\u9662\u3001\u96c6\u667a\u79d1\u5b66\u7814\u7a76\u4e2d\u5fc3\u548c\u963f\u91cc\u4e91\u8054\u5408\u53d1\u5e03\u4e86\u300aAI \u00d7 Science\u5341\u5927\u524d\u6cbf\u89c2\u5bdf\u300b\uff0c\u68b3\u7406\u51fa35\u4e2a\u7814\u7a76\u524d\u6cbf\uff0c\u6765\u63a8\u52a8\u79d1\u5b66\u53d1\u5c55\u7684\u9ec4\u91d1\u65f6\u4ee3\u5230\u6765\u3002\u672c\u7bc7\u4e3a\u524d\u6cbf\u89c2\u5bdf8\uff0c\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\uff0c\u53ef\u83b7\u5f97\u5b8c\u6574\u7248\u4e0b\u8f7d\u5730\u5740\u3001\u5feb\u901f\u94fe\u63a5\u8bba\u6587\u539f\u6587\u3002 \u626b\u63cf\u4e8c\u7ef4\u7801 \u4e0b\u8f7d\u5b8c\u6574\u62a5\u544a \u79d1\u5b66\u542f\u53d1\u7684 AI \u65b0\u67b6\u6784 \u80cc\u666f\u4ecb\u7ecd \u968f\u7740\u5927\u578b…<\/p>\n","protected":false},"author":1,"featured_media":59161,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/59174"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=59174"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/59174\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/59161"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=59174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=59174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=59174"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=59174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}