{"id":1670,"date":"2018-06-05T01:00:00","date_gmt":"2018-06-04T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%swarma-paper%\/"},"modified":"2018-12-06T15:09:30","modified_gmt":"2018-12-06T07:09:30","slug":"%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%e8%83%bd%e5%90%a6%e7%a0%b4%e8%a7%a3%e6%b7%b7%e6%b2%8c%ef%bc%9f-prl%e8%ae%ba%e6%96%87%e8%af%a6%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=1670","title":{"rendered":"\u673a\u5668\u5b66\u4e60\u80fd\u5426\u7834\u89e3\u6df7\u6c8c\uff1f| PRL\u8bba\u6587\u8be6\u89e3"},"content":{"rendered":"
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1. \u5bfc\u8bed<\/strong><\/span><\/p>\n

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\u524d\u4e0d\u4e45\uff0cQuanta Magazine \u62a5\u9053\u4e86\u9a6c\u91cc\u5170\u5927\u5b66\u7684\u7814\u7a76\u8005\u5229\u7528\u673a\u5668\u5b66\u4e60\u89e3\u51b3\u6df7\u6c8c\u7cfb\u7edf\u7684\u9884\u6d4b\u95ee\u9898\uff08\u53c2\u89c1\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u8bd1\u6587<\/span>\u4e0b\u4e00\u79d2\u706b\u7130\u5982\u4f55\u71c3\u70e7\uff1f\u673a\u5668\u5b66\u4e60\u6210\u529f\u9884\u6d4b\u6df7\u6c8c<\/strong><\/a><\/span>\uff09\u3002\u5176\u4e2d\u7684\u4e00\u7bc7\u7814\u7a76\u6210\u679c\uff0c\u9898\u4e3a\u300aModel-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach\u300b\uff0c\u53d1\u8868\u5728\u4e86\u7269\u7406\u5b66\u9876\u7ea7\u671f\u520a Physical Review Letters \u4e0a\uff0c\u4e0b\u9762\u662f\u5bf9\u8bba\u6587\u7684\u89e3\u8bfb\u3002<\/span><\/p>\n


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\u62c9\u666e\u62c9\u65af\u66fe\u65ad\u8a00\uff1a\u53ea\u8981\u77e5\u9053\u5b87\u5b99\u4e2d\u6bcf\u4e2a\u539f\u5b50\u786e\u5207\u7684\u4f4d\u7f6e\u548c\u52a8\u91cf\uff0c\u4fbf\u80fd\u6839\u636e\u725b\u987f\u5b9a\u5f8b\u9884\u6d4b\u4efb\u4f55\u65f6\u523b\u7684\u60c5\u51b5\u3002\u8fd9\u79cd\u601d\u60f3\u88ab\u79f0\u4e3a\u201c\u51b3\u5b9a\u8bba\u201d\u3002\u7136\u800c\uff0c20 \u4e16\u7eaa\u7684\u4e24\u5927\u53d1\u73b0\u5f7b\u5e95\u7c89\u788e\u4e86\u8fd9\u4e00\u68a6\u60f3\u3002\u6d77\u68ee\u5821\u6d4b\u4e0d\u51c6\u539f\u7406\u6307\u51fa\uff1a\u4e00\u4e2a\u7c92\u5b50\u7684\u4f4d\u7f6e\u548c\u52a8\u91cf\u4e0d\u53ef\u80fd\u540c\u65f6\u7cbe\u786e\u786e\u5b9a\u3002\u800c\u6df7\u6c8c\u7406\u8bba\u5219\u6307\u51fa\u4e86\u6df7\u6c8c\u7cfb\u7edf\u7684\u521d\u503c\u654f\u611f\u6027\uff0c\u4e5f\u5c31\u662f\u719f\u77e5\u7684\u201c\u8774\u8776\u6548\u5e94\u201d\uff1a\u521d\u503c\u7684\u5fae\u5c0f\u53d8\u5316\uff0c\u4f1a\u5bfc\u81f4\u6574\u4e2a\u7cfb\u7edf\u7684\u957f\u671f\u7684\u5de8\u5927\u7684\u8fde\u9501\u53cd\u5e94\u3002<\/span><\/p>\n


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\u8fd9\u7bc7\u8bba\u6587\u60f3\u89e3\u51b3\u7684\u95ee\u9898\u5c31\u662f\uff1a\u5982\u4f55\u9884\u6d4b\u5927\u578b\u65f6\u7a7a\u6df7\u6c8c\u7cfb\u7edf\u7684\u6f14\u5316\uff1f\u5bf9\u4e00\u4e2a\u52a8\u529b\u5b66\u7cfb\u7edf\u5efa\u7acb\u516c\u5f0f\u5316\u7684\u63cf\u8ff0\u662f\u56f0\u96be\u7684\uff0c\u4f46\u83b7\u5f97\u8be5\u7cfb\u7edf\u957f\u65f6\u95f4\u3001\u9ad8\u7cbe\u5ea6\u7684\u89c2\u6d4b\u6570\u636e\u5374\u662f\u5bb9\u6613\u7684\u3002\u6211\u4eec\u81ea\u7136\u5e0c\u671b\u673a\u5668\u80fd\u591f\u4ece\u6570\u636e\u4e2d\u5b66\u4e60\u5230\u7cfb\u7edf\u7684\u6f14\u5316\u89c4\u5f8b\uff0c\u65b9\u4fbf\u6211\u4eec\u505a\u9884\u6d4b\u3002<\/span><\/p>\n

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\"\u96c6\u667a\"<\/p>\n

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2. \u65b9\u6cd5\uff1aReservoir Computing<\/strong><\/span><\/p>\n

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\u50a8\u5c42\u8ba1\u7b97<\/strong><\/span><\/strong><\/strong><\/p>\n

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


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\u8fd9\u7bc7\u8bba\u6587\u4e2d\u7528\u5230\u7684\u65b9\u6cd5\u79f0\u4e3a Reservoir Computing\uff0cGoodfellow \u7684\u300a\u6df1\u5ea6\u5b66\u4e60\u300b\u4e2d\u6587\u7248\u4e00\u4e66\u4e2d\u5c06\u5176\u7ffb\u8bd1\u6210\u201c\u50a8\u5c42\u8ba1\u7b97\u201d\u3002\u8fd9\u91cc\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e0b Reservoir Computing \u7684\u5386\u53f2\u3002
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\u5faa\u73af\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u662f\u56f0\u96be\u7684\uff0c\u5b58\u5728\u7740\u8ba1\u7b97\u91cf\u5927\u3001\u6536\u655b\u6162\u3001\u68af\u5ea6\u6d88\u5931\u7b49\u96be\u70b9\u3002\u4e3a\u4e86\u514b\u670d\u4e0a\u8ff0\u96be\u70b9\uff0c\u4e00\u79cd\u89e3\u51b3\u529e\u6cd5\u662f\uff1a\u53ef\u4ee5\u53ea\u521d\u59cb\u5316\u9690\u85cf\u5c42\u800c\u4e0d\u53bb\u8bad\u7ec3\u5b83\uff0c\u53ea\u53bb\u5b66\u4e60\u9690\u85cf\u5c42\u5230\u8f93\u51fa\u7684\u6743\u91cd\uff0c\u8fd9\u6837\uff0c\u95ee\u9898\u5c31\u53ef\u4ee5\u7b80\u5316\u6210\u4e00\u4e2a\u56de\u5f52\u95ee\u9898\u3002<\/span><\/p>\n


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\u57fa\u4e8e\u4e0a\u8ff0\u60f3\u6cd5\uff0cJaeger \u548c Maass \u5206\u522b\u72ec\u7acb\u63d0\u51fa\u4e86 Echo State Network\uff08\u56de\u58f0\u72b6\u6001\u7f51\u7edc\uff09\u548c Liquid State Machine\uff08\u6d41\u4f53\u72b6\u6001\u673a\uff09\u3002\u540e\u6765,\u8fd9\u4e24\u79cd\u65b9\u6cd5\u88ab\u7edf\u79f0\u4e3a Reservoir Computing\u3002<\/span><\/p>\n


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\"\u96c6\u667a\"<\/p>\n

\u56fe 1: Reservoir computing \u793a\u610f\u56fe\u3002<\/strong><\/span><\/p>\n

(a)\u8bad\u7ec3\u9636\u6bb5\uff1b(b)\u9884\u6d4b\u9636\u6bb5\u3002<\/strong><\/span><\/p>\n

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\u56fe\u7247\u6765\u6e90: <\/span><\/p>\n

https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.120.024102<\/span><\/p>\n<\/blockquote>\n


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\u4e0b\u9762\u4ecb\u7ecd Reservoir Computing\u3002\u5148\u4ecb\u7ecd\u63a5\u4e0b\u6765\u9700\u8981\u7528\u5230\u7684\u7b26\u53f7\uff1a\u5bf9\u4e8e\u65f6\u95f4\u5e8f\u5217 u\uff0c\u8f93\u5165\u4e3a u \u5728 t \u65f6\u523b\u7684 Din \u7ef4\u5411\u91cf u(t)\uff0c\u8f93\u51fa\u662f Dout \u7ef4\u5411\u91cf v(t)\uff0c\u9690\u85cf \u5c42\u72b6\u6001\u7528 Dr \u7ef4\u5411\u91cf r(t) \u8868\u793a\u3002<\/span><\/p>\n


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\u8f93\u5165\u4e3a u(t) \u65f6\uff0c\u9996\u5148\u53ef\u4ee5\u5f97\u5230\u4e0b\u4e00\u65f6\u523b\uff08t + \u2206t \u65f6\u523b\uff09\u9690\u85cf\u5c42\u7684\u72b6\u6001\uff1a<\/span><\/p>\n


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\"\u96c6\u667a\"<\/p>\n


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\u5176\u4e2d\uff0cWin \u662f\u4e00\u4e2a Dr \u00d7 Din \u7ef4\u77e9\u9635\uff08\u77e9\u9635\u5143\u7d20\u4ece [\u2212\u03c3, \u03c3] \u7684\u5747\u5300\u5206\u5e03\u62bd\u6837\uff09\uff0cA \u662f\u9690\u85cf\u5c42\uff08reservoir\uff09\u7684\u90bb\u63a5\u77e9\u9635\uff08Dr\u00d7Dr \u7ef4\uff09\uff0c\u4e14\u6ee1\u8db3\u56de\u58f0\u72b6\u6001\u6027\u8d28\uff08\u7b80\u5355\u5730\u8bf4, \u5c31\u662f\u7f51\u7edc\u5f53\u524d\u65f6\u523b\u7684\u72b6\u6001 r(t) \u7531\u7f51\u7edc\u4ece\u521d\u59cb\u5230\u5f53\u524d\u7684\u8f93\u5165\u552f\u4e00\u51b3\u5b9a\uff1b\u6570\u5b66\u4e0a\uff0c\u6ee1\u8db3\u77e9\u9635 A \u7684\u8c31\u534a\u5f84 \u03c1 < 1\u3002\u5173\u4e8e\u56de\u58f0\u72b6\u6001\u6027\u8d28\u7684\u8be6\u7ec6<\/span>\u8bf4\u660e\uff0c\u53ef\u53c2\u8003 The\u201cecho state\u201dapproach to analysing and training recurrent neural networks \u2013with an Erratum note\uff09\u3002<\/span><\/p>\n


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t + \u2206t \u65f6\u523b\u9690\u85cf\u5c42\u7684\u9884\u6d4b\u8f93\u51fa\u4e3a\uff1a<\/span><\/p>\n


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\"\u96c6\u667a\"<\/p>\n


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P1\u3001P2 \u90fd\u662f Dout \u00d7 Dr \u7ef4\u77e9\u9635\u3002\u7531\u4e8e t + \u2206t \u65f6\u523b\u7684\u771f\u5b9e\u503c\u662f\u65f6\u95f4\u5e8f\u5217\u4e2d\u7684 u(t + \u2206t)\uff0c\u56e0\u6b64\u8bad\u7ec3\u7684\u76ee\u6807\u662f\u627e\u5230\u5408\u9002\u7684 P1\u3001P2\uff0c\u4f7f\u5f97 v(t + \u2206t) \u5c3d\u53ef\u80fd\u63a5\u8fd1 u(t + \u2206t) \u3002<\/span><\/p>\n


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\u5728\u8bad\u7ec3\u9636\u6bb5\uff0c\u5c06 \u2212T \u2264 t \u2264 0 \u65f6\u95f4\u7684 u(t) \u4f9d\u6b21\u8f93\u5165\u7f51\u7edc\uff0c\u5219\u635f\u5931\u51fd\u6570\u53ef\u5199\u4f5c\uff1a<\/span><\/p>\n

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\"\u96c6\u667a\"<\/div>\n


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\u7b49\u53f7\u53f3\u8fb9\u7b2c\u4e00\u9879\u4e3a\u6b63\u5e38\u7684\u635f\u5931\u51fd\u6570\u9879\uff0c\u7b2c\u4e8c\u9879\u4e3a\u6b63\u5219\u9879\u3002<\/span><\/p>\n


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\u5728\u7b97\u51fa P1\u3001P2 \u4e4b\u540e\uff0c\u5c31\u53ef\u4ee5\u505a\u9884\u6d4b\u4e86\u3002\u5728\u9884\u6d4b\u9636\u6bb5\uff0c\u6bcf\u4e00\u65f6\u523b\u7684\u8f93\u5165\u90fd\u662f\u5f53\u524d\u65f6\u523b\u7684\u8f93\u51fa\u503c\uff0c\u5373 u(t) = v(t)\u3002\u4f46\u7531\u4e8e\u6df7\u6c8c\u7cfb\u7edf\u7684\u6307\u6570\u5206\u79bb\u7279\u6027\uff08exponential separation of trajectories\uff09\uff0c\u5f88\u5feb v(t) \u5c31\u4f1a\u5f7b\u5e95\u504f\u79bb\u771f\u5b9e\u7684 u(t)\u3002\u56e0\u6b64,\u5f53\u9884\u6d4b\u67d0\u4e00\u672a\u6765\u65f6\u523b \u03b8 > 0 \u7684\u72b6\u6001\uff0c\u9700\u8981\u5229\u7528 \u03b8 \u4e4b\u524d\u7684\u4e00\u5c0f\u6bb5\u65f6\u95f4 (\u03b8 \u2212 \u03b5 \u2264 t \u2264 \u03b8) \u6839\u636e\u516c<\/span>\u5f0f (1) \u91cd\u65b0<\/span>\u521d\u59cb\u5316 r(\u03b8)\uff0c\u518d\u53bb\u505a\u9884\u6d4b\u3002<\/span>
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3. \u5c0f\u8bd5\u725b\u5200\uff1aKS \u65b9\u7a0b<\/strong><\/span><\/p>\n

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

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\u5229\u7528\u4e0a\u8ff0\u65b9\u6cd5,\u6587\u7ae0\u4f5c\u8005\u5728\u4e00\u4e2a\u53eb\u505a Kuramoto-Sivashinsky(KS) \u65b9\u7a0b\u7684\u65f6\u7a7a\u6df7\u6c8c\u7cfb\u7edf\u4e0a\u5c0f\u8bd5\u725b\u5200\u3002KS \u65b9\u7a0b\u4e3a\uff1a<\/span><\/p>\n

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\"\u96c6\u667a\"<\/div>\n


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\u6807\u51c6\u7684 KS \u65b9\u7a0b\u65e0\u6700\u540e\u7684\u7a7a\u95f4\u4e0d\u5747\u9879\u3002\u65b9\u7a0b\u6ee1\u8db3\u5468\u671f\u8fb9\u754c\u6761\u4ef6 y(x, t) = y(x + L, t)\uff0c\u65b9\u7a0b\u7684\u89e3\u7531\u7cfb\u7edf\u5927\u5c0f L \u548c\u521d\u59cb\u6761\u4ef6 y(x, 0) \u51b3\u5b9a\u3002\u5173\u4e8e KS \u65b9\u7a0b\u7684\u8be6\u7ec6\u4ecb\u7ecd\uff0c\u53ef\u53c2<\/span>\u8003<\/span><\/p>\n

Kuramoto-Sivashinsky: an investigation of spatiotemporal \u201cturbulence\u201d\u3002<\/span><\/p>\n


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\u5728\u4e00\u4e2a L = 22\uff0c\u683c\u70b9\u6570\uff08\u8f93\u5165\u5411\u91cf\u7ef4\u5ea6\uff09Q = 64\uff0c\u03bc = 0 \u7684\u7cfb\u7edf\u4e0a\u7684\u9884\u6d4b\u7ed3\u679c\u5982<\/span>\u56fe(3)<\/span>\u6240\u793a\u3002\uff08a\uff09\u662f\u771f\u5b9e\u6570\u636e\uff0c\uff08b\uff09\u662f\u9884\u6d4b\u503c\uff0c\uff08c\uff09\u662f\u4e24\u8005\u7684\u8bef\u5dee\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u5728 6 \u4e2a\u674e\u96c5\u666e\u8bfa\u592b\u65f6\u95f4\u5185\uff0c\u6a21\u578b\u7684\u9884\u6d4b\u4e0e\u5b9e\u9645\u6570\u636e\u7b26\u5408\u7684\u76f8\u5f53\u597d\u3002<\/span><\/p>\n


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\"\u96c6\u667a\"<\/p>\n

\u56fe 2: Kuramoto-Sivashinsky(KS) equation \u7684\u793a\u610f\u56fe\u3002<\/strong><\/span><\/p>\n


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\"\u96c6\u667a\"<\/div>\n

\u56fe 3: L = 22 \u5c3a\u5ea6\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c<\/span><\/strong><\/span><\/p>\n

Q = 64\uff0cDr = 5000\uff0c\u03bc = 0\u3002<\/span><\/strong><\/span><\/p>\n


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\u56fe\u7247\u6765\u6e90:<\/span><\/p>\n

https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.120.024102<\/span><\/p>\n<\/blockquote>\n

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4. \u5982\u4f55\u5904\u7406\u5927\u578b\u65f6\u7a7a\u6df7\u6c8c\u7cfb\u7edf\uff1f<\/strong><\/span><\/p>\n

\u591a\u4e2a reservoir \u5e76\u884c\u8ba1\u7b97<\/strong><\/span><\/p>\n

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


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\u5bf9\u4e8e\u4e0a\u9762 L = 22 \u7684\u7cfb\u7edf\uff0c\u9690\u85cf\u5c42\uff08reservoir\uff09\u7684\u5927\u5c0f\u5df2\u7ecf\u8fbe\u5230\u4e86 Dr = 5000\u3002\u5bf9\u4e8e\u66f4\u5927\u7a7a\u95f4\u5c3a\u5ea6\u7684\u7cfb\u7edf\u800c\u8a00\uff0c\u9690\u85cf\u5c42\u7684\u5927\u5c0f\u4f1a\u6025\u5267\u589e\u52a0\uff0c\u6b64\u65f6\u518d\u5229\u7528\u5355\u4e2a reservoir \u8fdb\u884c\u9884\u6d4b\u6709\u70b9\u4e0d\u5207\u5b9e\u9645\u3002\u8fd9\u7bc7\u8bba\u6587\u4e3a\u7684\u4eae\u70b9\u4fbf\u5728\u4e8e\uff1a\u63d0\u51fa\u4e86\u591a\u4e2areservoir \u5e76\u884c\u5904\u7406\u7684\u6846\u67b6\u3002<\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe 4: \u591a\u4e2a reservoir \u5e76\u884c\u5904\u7406\u793a\u610f\u56fe\u3002<\/strong><\/span><\/p>\n

\u8fd9\u91cc q = 2\uff0cl = 1\u3002
<\/strong><\/span><\/p>\n


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

\u5177\u4f53\u5730\uff0c\u6211\u4eec\u4f9d\u7136\u8003\u8651\u7a7a\u95f4\u683c\u70b9\u6570(\u8f93\u5165\u5411\u91cf\u7ef4\u5ea6)\u4e3a Q\uff0c\u4f46\u662f\u5c06\u8f93\u5165\u5411 \u91cf u(t) \u6309\u7167\u7ef4\u6570\u5e73\u5747\u5206\u6210 g \u7ec4\uff0c\u6bcf\u7ec4\u7684\u7ef4\u6570\u662f q\u3002<\/span><\/p>\n


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

\u6bcf\u7ec4\u5411\u91cf\u8bb0\u4e3a\uff1a<\/span><\/p>\n

\"\u96c6\u667a\"
<\/p>\n

\"\u96c6\u667a\"
<\/div>\n


<\/p>\n

\u8fd9\u6837\u5c31\u76f8\u5f53\u4e8e\u5c06\u539f\u6765\u7684\u9ad8\u7ef4\u5411\u91cf\u5e73\u5747\u5207\u5206\u6210 g \u4e2a\u4f4e\u7ef4\u5411\u91cf\u3002\u4e00\u4e2a\u7b80\u5355\u7684\u5e76\u884c\u5904\u7406\u7684\u60f3\u6cd5\u662f\uff1a\u8bbe\u7f6e g \u4e2a reservoir\uff0c\u7b2c i \u4e2a reservoir \u7684\u8f93\u5165\u4e3a\uff1a<\/span><\/p>\n

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

\"\u96c6\u667a\"<\/p>\n

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

\u8fd9\u6837\u53ef\u4ee5\u5b9e\u73b0 g \u4e2a reservoir \u7684\u5e76\u884c\u5904\u7406\u3002\u7136\u800c\uff0c\u8fd9\u6837\u505a\u53ea\u662f\u5355\u7eaf\u628a\u4e00\u4e2a\u5927\u7684\u6df7\u6c8c\u7cfb\u7edf\u770b\u505a g \u4e2a\u5f7c\u6b64\u72ec\u7acb\u7684\u5b50\u7cfb\u7edf\u3002\u8bba\u6587\u4e2d\u7684\u505a\u6cd5\u662f:\u540c\u6837\u662f\u8bbe\u7f6e g \u4e2a reservoir\uff0c\u8f93\u5165\u4e0d\u518d\u662f gi(t)\uff0c\u800c\u662f gi(t) \u52a0\u4e0a\u548c\u5b83\u5de6\u53f3\u76f8\u90bb\u7684 l \u4e2a\u70b9\u7684\u503c\uff0c\u5373\u8f93\u5165\u662f\u4e00\u4e2aq + 2l \u7ef4\u5411\u91cf:<\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n


<\/p>\n

\u8fd9\u6837\u505a\u7684\u76ee\u7684\u662f\u4e3a\u4e86\u5c3d\u53ef\u80fd\u5229\u7528\u5230\u6df7\u6c8c\u7cfb\u7edf\u7684\u5c40\u90e8\u76f8\u4e92\u4f5c\u7528\u7279\u6027\u3002<\/span><\/p>\n

\u6211\u4eec\u5199\u51fa\u7b2c i \u4e2a reservoir \u7684\u6240\u6709\u65b9\u7a0b:<\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n


<\/p>\n

\u4e0b\u9762\u662f L = 200 \u7684 KS \u65b9\u7a0b\u7684\u9884\u6d4b\u7ed3\u679c\u3002\u8fd9\u91cc\u7684\u53c2\u6570\u8bbe\u7f6e\u4e3a Dr = 5000\uff0cT = 70000\uff0c\u03c1 = 0.6\uff0c\u03c3 = 1.0\uff0cl = 6\uff0c\u5e76\u5c06\u9700\u8981\u9884\u6d4b\u7684\u672a\u6765\u5e73\u5747\u5206\u6210 K = 30 \u4e2a\u65f6\u95f4\u95f4\u9694 \u03b8k \u2264 t \u2264 \u03b8k + \u03c4 \uff0c\u03c4 = 1000 \u65f6\u95f4\u6b65\u3002<\/span><\/p>\n


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

\u9884\u6d4b\u9636\u6bb5,\u5728\u5bf9\u6bcf\u4e2a\u65f6\u95f4\u95f4\u9694 \u03b8k \u2264t\u2264\u03b8k +\u03c4 \u7684\u9884\u6d4b\u5f00\u59cb\u524d\uff0c\u90fd\u9700\u8981\u521d\u59cb\u5316 ri =0\uff0c\u518d\u5229\u7528 \u03b8k \u2212\u03b5\u2264t\u2264\u03b8k\uff0c\u03b5 = 10 \u65f6\u95f4\u6b65\u7684\u6570\u636e\uff0c\u6839<\/span>\u636e \u5f0f(7) \u66f4\u65b0 ri \u3002\u9884\u6d4b\u7ed3\u679c\u5982 \u56fe(5) <\/span>\u6240\u793a\uff0c(a)\u662f\u771f\u5b9e\u6570\u636e\uff0c(b)\u662f\u9884\u6d4b\u503c\uff0c(c)\u662f\u4e24\u8005\u7684\u8bef\u5dee\uff0c(d)\u662f\u5c06 t = 0 \u65f6\u7684\u9884\u6d4b\u503c y(x, 0) \u4f5c\u4e3a\u521d\u59cb\u6761\u4ef6\u7684\u6570\u503c\u89e3\u548c\u771f\u5b9e\u6570\u636e\u7684\u8bef\u5dee\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u56fe(c) \u7684\u7ed3\u679c\u53ea\u6bd4 \u56fe(d) \u5dee\u4e00\u70b9\u70b9\uff0c\u8bf4\u660e reservoir computing \u7684\u65b9\u6cd5\u80fd\u591f\u5f88\u597d\u7684\u5b66\u5230\u7cfb\u7edf\u7684\u771f\u5b9e\u52a8\u529b\u5b66\uff0c\u5176\u6548\u679c\u53ef\u4ee5\u5ab2\u7f8e\u6570\u503c\u65b9\u6cd5\u3002<\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\u56fe 5: L = 200 \u5c3a\u5ea6\u7684\u5b9e\u9a8c\u7ed3\u679c\uff0c<\/span><\/strong><\/span><\/p>\n

Q = 512\uff0cDr = 5000\uff0c\u03bc = 0.01\u3002<\/span><\/strong><\/span><\/p>\n

\n

\u56fe\u7247\u6765\u6e90:<\/span><\/p>\n

https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.120.024102<\/span><\/p>\n<\/blockquote>\n

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


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

5. \u5c55\u671b<\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n


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

\u4e00\u65b9\u9762\uff0c\u8fd9\u7bc7\u8bba\u6587\u5411\u6211\u4eec\u5c55\u793a\u4e86\u673a\u5668\u5b66\u4e60\u9884\u6d4b\u5927\u578b\u65f6\u7a7a\u6df7\u6c8c\u7cfb\u7edf\u7684\u5f3a\u5927\u80fd\u529b\uff1b\u53e6\u4e00\u65b9\u9762\uff0c\u4e3a\u4f55 Reservoir Computing \u7684\u6548\u679c\u5982\u6b64\u4e4b\u597d\uff0c\u5b83\u7684\u5185\u90e8\u5b66\u4e60\u673a\u5236\u662f\u4ec0\u4e48\uff0c\u4ecd\u6709\u5f85\u7814\u7a76\u3002<\/span><\/p>\n


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

\u6b64\u5916\uff0c\u901a\u8fc7\u524d\u9762\u7684\u8bb2\u89e3\u4e0d\u96be\u53d1\u73b0\uff0cReservoir Computing \u672c\u8d28\u4e0a\u8bb2\u4f9d\u7136\u662f\u4f20\u7edf\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u3002\u90a3\u4e48\uff0c\u5f53\u4e0b\u524d\u6cbf\u7684\u6df1\u5ea6\u5b66\u4e60\u6280\u672f\u80fd\u5426\u5904\u7406\u7c7b\u4f3c\u7684\u6df7\u6c8c\u9884\u6d4b\u4e5f\u662f\u4e00\u4e2a\u503c\u5f97\u7814\u7a76\u7684\u95ee\u9898\u3002<\/span><\/p>\n


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

\n

\u4f5c\u8005\uff1a\u5218\u6676<\/span><\/p>\n

\u5ba1\u6821\uff1a\u9ad8\u98de<\/span><\/p>\n

\u7f16\u8f91\uff1a\u5c0f\u98ce
<\/span><\/p>\n

\u8bba\u6587\u5730\u5740\uff1a<\/span><\/p>\n

https:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.120.024102<\/span><\/p>\n<\/blockquote>\n


<\/p>\n

\n
\n
<\/p>\n

\u63a8\u8350\u9605\u8bfb<\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n


<\/p>\n

\u4e0b\u4e00\u79d2\u706b\u7130\u5982\u4f55\u71c3\u70e7\uff1f\u673a\u5668\u5b66\u4e60\u6210\u529f\u9884\u6d4b\u6df7\u6c8c<\/strong><\/span><\/a>
<\/p>\n

 \u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01\u96c6\u667a\u4ff1\u4e50\u90e8\u56e2\u961f\u62db\u65b0\u5566\uff01<\/a><\/strong><\/strong>
<\/p>\n


<\/p>\n

\n
\n

\"\u96c6\u667a\"
<\/p>\n

\n
\n
\n
\n
\n
\n

\u96c6\u667aQQ\u7fa4\uff5c292641157
\u5546\u52a1\u5408\u4f5c\uff5czhangqian@swarma.org
\u6295\u7a3f\u8f6c\u8f7d\uff5cwangting@swarma.org<\/span><\/strong><\/span><\/p>\n

\n

\u25c6 <\/span>\u25c6 <\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/span><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/strong><\/span><\/p>\n


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

\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/strong><\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n<\/section>\n

\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/p>\n

\"\u96c6\u667a\"<\/div>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n

\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff1a \u96c6\u667a\u4ff1\u4e50\u90e8 <\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

1. \u5bfc\u8bed \u524d\u4e0d\u4e45\uff0cQuanta Magazine \u62a5\u9053\u4e86\u9a6c\u91cc\u5170\u5927\u5b66\u7684\u7814\u7a76\u8005\u5229\u7528\u673a\u5668\u5b66\u4e60\u89e3\u51b3\u6df7\u6c8c\u7cfb\u7edf\u7684\u9884\u6d4b\u95ee\u9898\uff08\u53c2\u89c1\u96c6\u667a\u4ff1\u4e50\u90e8\u7684\u8bd1\u6587\u4e0b\u4e00\u79d2\u706b\u7130\u5982\u4f55\u71c3\u70e7\uff1f\u673a\u5668\u5b66\u4e60\u6210\u529f\u9884\u6d4b\u6df7\u6c8c\uff09\u3002\u5176\u4e2d\u7684\u4e00\u7bc7\u7814\u7a76\u6210\u679c\uff0c\u9898\u4e3a\u300aModel-Free Prediction of Large Spatiotempora…<\/p>\n","protected":false},"author":1,"featured_media":1671,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[19],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/1670"}],"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=1670"}],"version-history":[{"count":1,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/1670\/revisions"}],"predecessor-version":[{"id":1695,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/1670\/revisions\/1695"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/1671"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1670"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1670"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1670"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=1670"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}