{"id":32423,"date":"2022-02-12T21:42:35","date_gmt":"2022-02-12T13:42:35","guid":{"rendered":"https:\/\/swarma.org\/?p=32423"},"modified":"2022-02-12T21:42:35","modified_gmt":"2022-02-12T13:42:35","slug":"nat-comm-%e5%89%8d%e6%b2%bf%ef%bc%9a%e5%9f%ba%e4%ba%8e%e7%a5%9e%e7%bb%8f%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e7%9a%84%e5%a4%8d%e6%9d%82%e5%8a%a8%e5%8a%9b%e7%b3%bb%e7%bb%9f%e6%9c%80%e4%bc%98","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32423","title":{"rendered":"Nat. Comm. \u524d\u6cbf\uff1a\u57fa\u4e8e\u795e\u7ecf\u5e38\u5fae\u5206\u65b9\u7a0b\u7684\u590d\u6742\u52a8\u529b\u7cfb\u7edf\u6700\u4f18\u63a7\u5236"},"content":{"rendered":"
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AI Pontryagin or how artificial neural networks learn to control dynamical systems<\/span><\/p>\n

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\u5bf9\u4e8e\u7ebf\u6027\u7cfb\u7edf\uff0c\u57fa\u4e8e\u63a7\u5236\u77e9\u9635<\/span>\uff08controllability  matrix\uff09<\/span>\u7684\u79e9\uff0c\u53ef\u4ee5\u627e\u51fa\u53ef\u63a7\u7cfb\u7edf\u80fd\u5f97\u51fa\u89e3\u6790\u89e3\u7684\u6761\u4ef6\u3002\u800c\u57fa\u4e8e\u5df4\u62c9\u5df4\u897f2011\u5e74\u7684Nature\u8bba\u6587[1]\uff0c\u53ef\u4ee5\u5c06\u52a8\u529b\u7cfb\u7edf\u7684\u63a7\u5236\u95ee\u9898\uff0c\u8f6c\u6362\u4e3a\u7f51\u7edc\u4e2d\u5bfb\u627e\u4e8c\u90e8\u56fe\u6700\u5927\u5339\u914d\u7684\u95ee\u9898\u3002\u5f97\u5230\u7684\u89e3\u4f1a\u6307\u51fa\u5bf9\u7cfb\u7edf\u8fdb\u884c\u63a7\u5236\u7684\u6700\u5c0f\u8282\u70b9\u96c6\u5408\u3002<\/span><\/section>\n

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\u82cf\u8054\u6570\u5b66\u5bb6Pontryagin\u63d0\u51fa\u4e86\u6700\u4f18\u63a7\u5236\u95ee\u9898\u7684\u7ecf\u5178\u89e3\u51b3\u65b9\u6cd5\u2014\u2014Pontryagin\u6700\u5927\u5316\u539f\u7406\uff0c\u5728\u72b6\u6001\u6216\u8f93\u5165\u63a7\u4ef6\u6709\u9650\u5236\u6761\u4ef6\u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u627e\u5230\u5c06\u52a8\u529b\u7cfb\u7edf\u7531\u4e00\u4e2a\u72b6\u6001\u5230\u53e6\u4e00\u4e2a\u72b6\u6001\u7684\u6700\u4f18\u63a7\u5236\u4fe1\u53f7\u3002\u4e3a\u4e86\u5411Pontryagin\u81f4\u656c\uff0c\u65b0\u63d0\u51fa\u7684\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\u88ab\u547d\u540d\u4e3aAI Pontryagin\u3002<\/span><\/section>\n

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2. AI Pontryagin\u7684\u8bad\u7ec3\u65b9\u5f0f<\/strong><\/strong><\/p>\n<\/section>\n

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AI Pontryagin\u7684\u8bad\u7ec3\u8fc7\u7a0b\uff0c\u9996\u5148\u662f\u5728\u8fde\u7eed\u7684\u65f6\u95f4\u8f74\u4e0a\uff0c\u7ed9\u51fa\u79bb\u6563\u70b9\u5fae\u5206\u65b9\u7a0b\u7684\u8fd1\u4f3c\u89e3\uff0c\u5f53\u521d\u59cb\u6761\u4ef6\u4e0d\u540c\u65f6\uff0c\u7cfb\u7edf\u7684\u6f14\u5316\u4f1a\u5448\u73b0\u4e0d\u540c\u72b6\u6001\u3002<\/span><\/section>\n

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AI Pontryagin \u7684\u8fd0\u884c\u65b9\u5f0f\uff0c\u4e4b\u540e\u7684\u8bad\u7ec3\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u770b\u6210\u968f\u65f6\u95f4\u5c55\u5f00\u7684RNN\u3002a \u4f7f\u7528\u5e38\u5fae\u5206\u65b9\u7a0b\u8868\u793a\u672a\u53d7\u63a7\u5236\u7684\u7f51\u7edc\u52a8\u529b\u7cfb\u7edf\u7684\u793a\u4f8b\u3002b \u4f7f\u7528ANN\u5bf9\u7f51\u7edc\u7cfb\u7edf\u8fdb\u884c\u63a7\u5236\u7684\u57fa\u672c\u8981\u7d20\u3002c \u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u8bad\u7ec3ANN\u5b8c\u6210\u63a7\u5236\u4efb\u52a1\u3002<\/span><\/p>\n


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\u4e3a\u4e86\u9a8c\u8bc1AI Pontryagin\u7684\u51c6\u786e\u6027\uff0c\u4f5c\u8005\u9664\u4e86\u5728\u7ebf\u6027\u7cfb\u7edf\u4e4b\u5916\uff0c\u8fd8\u5728\u7531Kuramoto \u632f\u5b50\u7ec4\u6210\u7684\u4e8c\u7ef4\u6676\u683c\u975e\u7ebf\u6027\u7cfb\u7edf\u4e2d\uff0c\u4f7f\u7528AI Pontryagin\u8ba9\u7cfb\u7edf\u8fbe\u5230\u540c\u6b65\uff0c\u4e14\u76f8\u6bd4\u4e4b\u524d\u7684\u65b9\u6cd5\uff0c\u901f\u5ea6\u66f4\u5feb\u3002<\/span><\/section>\n

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AI Pontryagin \u662f\u4e00\u4e2a\u975e\u5e38\u901a\u7528\u7684\u63a7\u5236\u6846\u67b6\uff0c\u8865\u5145\u4e86\u73b0\u6709\u7684\u6700\u4f18\u63a7\u5236\u65b9\u6cd5\uff0c\u5e76\u89e3\u51b3\u4e86\u9ad8\u7ef4\u548c\u89e3\u6790\u68d8\u624b\u7684\u63a7\u5236\u95ee\u9898\u3002\u5b83\u53ef\u4ee5\u5728\u6ca1\u6709\u5173\u4e8e\u5f85\u63a7\u5236\u7cfb\u7edf\u5148\u9a8c\u77e5\u8bc6\uff0c\u4e5f\u6ca1\u6709\u88ab\u63d0\u524d\u544a\u77e5\u7406\u60f3\u7684\u89e3\u51b3\u65b9\u6848\u7684\u524d\u63d0\u4e0b\u3002\u5bf9\u4efb\u610f\u7cfb\u7edf\u7ed9\u51fa\u5de5\u7a0b\u4e0a\u53ef\u884c\u7684\u63a7\u5236\u65b9\u6848\u3002\u8fd9\u610f\u5473\u7740\u5176\u5e94\u7528\u8303\u56f4\u5e7f\u6cdb\uff0c\u57fa\u4e8e\u4eba\u5de5\u667a\u80fd<\/span> (AI) <\/span>\u7684\u63a7\u5236\u7cfb\u7edf\u53ef\u4ee5\u5e2e\u52a9\u4f18\u5316\u590d\u6742\u7684\u8fc7\u7a0b\uff0c\u4e5f\u53ef\u4ee5\u7528\u4e8e\u5f00\u53d1\u65b0\u7684\u5546\u4e1a\u6a21\u5f0f\u3002<\/span><\/section>\n

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\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u6ce2\u52a8\u80fd\u591f\u89e6\u53d1\u7ea7\u8054\u53cd\u5e94\u3002\u4e3a\u4e86\u907f\u514d\u6b64\u7c7b\u4e8b\u6545\u548c\u63d0\u9ad8\u5f39\u6027\uff0c\u7cfb\u7edf\u4e13\u5bb6\u8bbe\u8ba1\u4e86\u5404\u79cd\u5404\u6837\u7684\u63a7\u5236\u673a\u5236\u548c\u89c4\u7ae0\uff1b\u5178\u578b\u7684\u5e94\u7528\u5305\u62ec\u7535\u7f51\u7535\u538b\u63a7\u5236\uff0c\u91d1\u878d\u673a\u6784\u7684\u538b\u529b\u6d4b\u8bd5\u3002\u7136\u800c\uff0c\u901a\u8fc7\u4eba\u5de5\u5e72\u9884\u5e76\u4e0d\u603b\u662f\u80fd\u591f\u63a7\u5236\u590d\u6742\u7684\u52a8\u529b\u7cfb\u7edf\u3002\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u63a7\u5236\u65b9\u6cd5\uff0c\u53ef\u7528\u4e8e\u4fdd\u62a4\u7535\u7f51\u4e0d\u53d7\u6ce2\u52a8\u548c\u505c\u7535\u3001\u963b\u6b62\u6d41\u884c\u75c5\u4f20\u64ad\u4ee5\u53ca\u4f18\u5316\u4f9b\u5e94\u94fe\u7b49\u3002<\/span><\/section>\n

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\u4ee5\u4f9b\u5e94\u94fe\u4f18\u5316\u4e3a\u4f8b\uff0c\u5177\u4f53\u9610\u8ff0\u5982\u4f55\u4f7f\u7528AI Pontryagin\uff0c\u9996\u5148\u5fc5\u9700\u63d0\u4f9b\u5173\u4e8e\u76ee\u6807\u7cfb\u7edf\u52a8\u529b\u5b66\u7684\u4fe1\u606f\u3002\u5728\u4f9b\u5e94\u94fe\u4e2d\uff0c\u8fd9\u53ef\u80fd\u5305\u62ec\u53ef\u80fd\u7684\u4f9b\u5e94\u5546\u6570\u91cf\uff0c\u91c7\u8d2d\u6210\u672c\u548c\u5468\u8f6c\u65f6\u95f4\u3002\u8fd9\u4e9b\u4fe1\u606f\u7528\u4e8e\u786e\u5b9a\u54ea\u4e9b\u9886\u57df\u9700\u8981\u52a8\u529b\u5b66\u4f18\u5316\u3002\u8fd8\u5fc5\u987b\u63d0\u4f9b\u5173\u4e8e\u7cfb\u7edf\u521d\u59cb\u72b6\u6001\u7684\u4fe1\u606f\uff0c\u4f8b\u5982\u5f53\u524d\u5e93\u5b58\u6c34\u5e73\uff0c\u4ee5\u53ca\u671f\u671b\u7684<\/span> (\u76ee\u6807) <\/span>\u72b6\u6001\uff0c\u4f8b\u5982\u9700\u8981\u5c06\u5e93\u5b58\u8865\u5145\u5230\u67d0\u4e00\u6c34\u5e73\uff0c\u540c\u65f6\u5c3d\u91cf\u51cf\u5c11\u8d44\u6e90\u7684\u4f7f\u7528\u3002\u4e4b\u540e\u81ea\u8bad\u7ec3\u7684\u795e\u7ecf\u7f51\u7edc\uff0c\u5c31\u53ef\u4ee5\u7ed9\u51fa\u8981\u8fbe\u5230\u7279\u5b9a\u72b6\u6001\uff0c\u6240\u9700\u7684\u6700\u5c11\u5e72\u9884\u3002<\/span><\/section>\n

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AI Pontryagin\u7684\u51fa\u73b0\uff0c\u8bf4\u660e\u795e\u7ecf\u7f51\u7edc\u63a7\u5236\u65b9\u6cd5\uff0c\u5728\u77e5\u9053\u7cfb\u7edf\u52a8\u529b\u5b66\u3001\u521d\u59cb\u72b6\u6001\u3001\u76ee\u6807\u72b6\u6001\u8fd9\u4e09\u4e2a\u6761\u4ef6\u4e0b\uff0c\u901a\u8fc7\u81ea\u5b66\u4e60\u63a7\u5236\u90e8\u5206\u672a\u77e5\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u3002\u672a\u6765\u57fa\u4e8eAI Pontryagin \u7684\u53ef\u80fd\u7814\u7a76\u65b9\u5411\uff0c\u5305\u62ec\u4ee5\u4e0b\u4e09\u70b9\uff0c\u9996\u5148\u662f\u5e94\u7528\u5176\u89e3\u51b3\u590d\u6742\u7684\u91cf\u5b50\u63a7\u5236\u95ee\u9898\uff0c\u4ee5\u63d0\u9ad8\u91cf\u5b50\u7cfb\u7edf\u7684\u9c81\u68d2\u6027\uff1b\u5176\u6b21\u662f\u63a2\u7d22\u5176\u8ba1\u7b97\u6700\u4f18\u63a7\u5236\u7684\u80fd\u529b\uff0c\u4f8b\u5982\u5982\u4f55\u5728\u7ea7\u8054\u6545\u969c\u671f\u95f4\u4fdd\u6301\u53d1\u7535\u673a\u540c\u6b65\u6027\uff0c\u5e76\u6700\u7ec8\u907f\u514d\u505c\u7535\uff1b\u7b2c\u4e09\u70b9\u662f\u7ed3\u5408\u7269\u7406\u548c\u751f\u7269\u5b66\u7684\u5148\u9a8c\u77e5\u8bc6\uff0c\u4ee5\u5b8c\u6210\u590d\u6742\u7684\u63a7\u5236\u4efb\u52a1\u3002<\/span><\/section>\n

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\u53c2\u8003\u6587\u732e\uff1a<\/strong><\/span>
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[1] Liu, Y.-Y., Slotine, J.-J. & Barab\u00e1si, A.-L. Controllability of complex networks. Nature
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473, 167\u2013173 (2011).<\/span><\/section>\n
[2] Olshevsky, A. Minimal controllability problems. IEEE Trans. Control. Netw. Syst. 1, 249\u2013258 (2014).<\/span><\/section>\n
[3] Pasqualetti, F., Zampieri, S. & Bullo, F. Controllability metrics, limitations and algorithms for complex networks. IEEE Trans. Control. Netw. Syst. 1, 40\u201352 (2014).<\/span><\/section>\n
[4]Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S. & Bergstrom, C. T. Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PLoS ONE 7, e38398 (2012).<\/span><\/section>\n

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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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