{"id":55084,"date":"2025-01-10T22:14:46","date_gmt":"2025-01-10T14:14:46","guid":{"rendered":"https:\/\/swarma.org\/?p=55084"},"modified":"2025-01-10T22:14:46","modified_gmt":"2025-01-10T14:14:46","slug":"%e9%9d%9e%e7%ba%bf%e6%80%a7%e5%8a%a8%e5%8a%9b%e5%ad%a6%e4%b8%adkoopman%e7%ae%97%e7%ac%a6%e7%9a%84%e5%ba%94%e7%94%a8-koopman%e5%88%86%e6%9e%90%e7%b3%bb%e5%88%97%e8%af%be%e7%a8%8b%e7%ac%ac%e5%9b%9b","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=55084","title":{"rendered":"\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2dKoopman\u7b97\u7b26\u7684\u5e94\u7528 | Koopman\u5206\u6790\u7cfb\u5217\u8bfe\u7a0b\u7b2c\u56db\u8bfe"},"content":{"rendered":"
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\u79d1\u5b66\u5bb6\u548c\u5de5\u7a0b\u5e08\u4e00\u76f4\u5728\u63a2\u7d22\u5982\u4f55\u901a\u8fc7\u6709\u6548\u7684\u6570\u5b66\u5de5\u5177\uff0c\u4ece\u590d\u6742\u7cfb\u7edf\u7684\u52a8\u6001\u884c\u4e3a\u4e2d\u63d0\u53d6\u6709\u610f\u4e49\u7684\u89c4\u5f8b\uff0c\u800cKoopman\u7b97\u7b26\u4f5c\u4e3a\u4e00\u79cd\u5f3a\u5927\u7684\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u5206\u6790\u65b9\u6cd5\uff0c\u4e3a\u6b64\u63d0\u4f9b\u4e86\u65b0\u7684\u89c6\u89d2\u548c\u89e3\u51b3\u65b9\u6848\u3002\u5728\u300aKoopman\u5206\u6790\u5728\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528\u300b\u7cfb\u5217\u8bfe\u7a0b<\/a>\u7b2c\u56db\u8282\u4e2d\uff0c\u5c06\u7531\u5170\u5cb3\u6052\u6559\u6388\u4e8e 1\u670811\u65e5\uff08\u5468\u516d\uff0914:00-16:00 \u5e26\u9886\u5927\u5bb6\uff0c\u805a\u7126 Koopman\u7b97\u7b26\u7684\u6570\u503c\u5b9e\u73b0\u4e0e\u672c\u5f81\u6a21\u6001\u7684\u6784\u5efa\uff0c\u6df1\u5165\u8bb2\u89e3\u5982\u4f55\u901a\u8fc7Arnoldi\u7b97\u6cd5\u548c\u52a8\u6001\u6a21\u5f0f\u5206\u89e3\uff08DMD\uff09\u63d0\u53d6\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u4e3b\u5bfc\u52a8\u6001\u6a21\u5f0f\uff0c\u4ee5\u53ca\u5982\u4f55\u7ed3\u5408\u672c\u5f81\u6a21\u6001\u63ed\u793a\u6d41\u4f53\u3001\u6620\u5c04\u7b49\u6df7\u6c8c\u4f53\u7cfb\u4e2d\u7684\u5173\u952e\u52a8\u6001\u7279\u6027\u3002\u6b64\u6b21\u8bfe\u7a0b\u5c06\u5e2e\u52a9\u6211\u4eec\u4ece\u7406\u8bba\u5230\u5e94\u7528\uff0c\u8fdb\u4e00\u6b65\u638c\u63e1Koopman\u7b97\u7b26\u5728\u5b9e\u9645\u95ee\u9898\u4e2d\u7684\u5f3a\u5927\u6f5c\u529b\u548c\u6838\u5fc3\u903b\u8f91\u3002<\/span><\/strong><\/p>\n<\/section>\n

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\u4e3b\u9898\uff1a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2dKoopman\u7b97\u7b26\u7684\u5e94\u7528<\/strong><\/span><\/h2>\n


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Koopman\u7b97\u7b26\u7528\u53e6\u4e00\u79cd\u65b9\u5f0f\u5c06\u7edf\u8ba1\u7269\u7406\u548c\u52a8\u529b\u5b66\u601d\u60f3\u7ed3\u5408\uff0c\u5c06\u6211\u4eec\u7684\u6ce8\u610f\u529b\u4ece\u5355\u6761\u8f68\u9053\u8f6c\u6362\u5230\u72b6\u6001\u7a7a\u95f4\u7684\u51fd\u6570\u53d8\u5316\uff0c\u8fd9\u6837\u975e\u7ebf\u6027\u95ee\u9898\u5c31\u53d8\u6210\u4e86\u51fd\u6570\u7a7a\u95f4\u4e2d\u7684\u7ebf\u6027\u95ee\u9898\u3002\u6211\u4eec\u53ef\u4ee5\u501f\u52a9\u672c\u5f81\u503c\u548c\u672c\u5f81\u51fd\u6570\u6765\u7814\u7a76\u4f53\u7cfb\u7684\u6027\u8d28\uff0c\u5b9a\u4e49\u52a8\u529b\u5b66\u6a21\u5f0f\uff0c\u5b9e\u73b0\u590d\u6742\u95ee\u9898\u7684\u5206\u89e3\uff0c\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u83b7\u5f97\u4e86\u7cfb\u7edf\u7684\u7ebf\u6027\u5316\u3002Koopman\u7b97\u7b26\u5b9e\u9645\u4e0a\u5305\u542b\u4e86\u4f53\u7cfb\u7684\u6240\u6709\u52a8\u529b\u5b66\u4fe1\u606f\uff0c\u4f46\u53ef\u4ee5\u7528\u4e0d\u540c\u7684\u89c2\u6d4b\u91cf\u8fdb\u884c\u7c97\u7c92\u5316\uff0c\u5341\u5206\u5951\u5408\u590d\u6742\u4f53\u7cfb\u7684\u5c42\u6b21\u5316\u7279\u5f81\u3002<\/span><\/section>\n

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\u672c\u6b21\u8bfe\u7a0b\u5c06\u91cd\u70b9\u8bb2\u89e3Koopman<\/strong>\u7b97\u7b26<\/strong>\u7684<\/strong>\u6027\u8d28\u3001<\/strong>\u6570\u503c\u5b9e\u73b0\u548c<\/strong>\u672c\u5f81<\/strong>\u6a21\u6001\u7684\u6784\u5efa\u8fc7\u7a0b<\/strong>\uff0c\u5305\u62ecArnoldi\u7b97\u6cd5\u548c\u52a8\u6001\u6a21\u5f0f\u5206\u89e3\uff08DMD\uff09\u7684\u57fa\u672c\u539f\u7406\u548c\u5e94\u7528\u65b9\u6cd5\u3002\u8bfe\u7a0b\u5185\u5bb9\u6db5\u76d6\u5982\u4f55\u4ece\u6709\u9650\u89c2\u6d4b\u6570\u636e\u4e2d\u63d0\u53d6Koopman\u7b97\u7b26\u7684\u672c\u5f81\u503c\u4e0e\u672c\u5f81\u6a21\u6001\uff0c\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u63cf\u8ff0\u590d\u6742\u7cfb\u7edf\u7684\u4e3b\u5bfc\u52a8\u6001\u7279\u6027\u3002\u7279\u522b\u5730\uff0c\u6211\u4eec\u5c06\u8ba8\u8bba\u5982\u4f55\u7ed3\u5408\u672c\u5f81\u6a21\u6001\u63ed\u793a\u6d41\u4f53\u6e4d\u6d41\u548c\u6df7\u6c8c\u7cfb\u7edf\u4e2d\u7684\u5173\u952e\u52a8\u6001\u6a21\u5f0f\uff0c\u5e76\u63a2\u7d22\u8fd9\u4e00\u5de5\u5177\u5728\u7269\u7406\u5b66\u548c\u5de5\u7a0b\u5b66\u4e2d\u7684\u5b9e\u9645\u5e94\u7528\u6f5c\u529b\u3002\u901a\u8fc7\u672c\u6b21\u8bfe\u7a0b\uff0c\u53c2\u4e0e\u8005\u5c06\u5b66\u4e60\u5982\u4f55\u7cfb\u7edf\u5730\u5229\u7528Koopman\u7b97\u7b26\u548c\u6570\u503c\u5de5\u5177\uff0c\u7b80\u5316\u590d\u6742\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7cfb\u7edf\u7684\u5206\u6790\uff0c\u5e76\u638c\u63e1\u76f8\u5173\u6280\u672f\u5728\u591a\u9886\u57df\u4e2d\u7684\u5e94\u7528\uff0c\u4e3a\u7814\u7a76\u548c\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u63d0\u4f9b\u65b0\u7684\u89c6\u89d2\u4e0e\u65b9\u6cd5\u3002<\/span><\/section>\n

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\u672c\u6b21\u8bfe\u7a0b\u65e8\u5728\u5e2e\u52a9\u5b66\u751f\u638c\u63e1Koopman\u7b97\u7b26\u5728\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528\uff0c\u7279\u522b\u662f\u5982\u4f55\u901a\u8fc7\u6570\u503c\u65b9\u6cd5\u63d0\u53d6\u590d\u6742\u7cfb\u7edf\u7684\u4e3b\u5bfc\u52a8\u6001\u6a21\u5f0f\u3002\u901a\u8fc7\u672c\u8bfe\u7a0b\uff0c\u5b66\u751f\u5c06\u4e86\u89e3Arnoldi\u7b97\u6cd5\u548c\u52a8\u6001\u6a21\u5f0f\u5206\u89e3\uff08DMD\uff09\u7684\u539f\u7406\uff0c\u5b66\u4e60\u4ece\u6709\u9650\u6570\u636e\u4e2d\u6784\u5efaKoopman\u7b97\u7b26\u7684\u672c\u5f81\u6a21\u6001\uff0c\u5e76\u5206\u6790\u5176\u5728\u7cfb\u7edf\u52a8\u6001\u63cf\u8ff0\u4e2d\u7684\u4f5c\u7528\u3002\u8bfe\u7a0b\u5c06\u91cd\u70b9\u4ecb\u7ecd\u5982\u4f55\u5229\u7528Koopman\u7b97\u7b26\u7684\u7ebf\u6027\u5316\u89c6\u89d2\u63ed\u793a\u590d\u6742\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u5168\u5c40\u7279\u6027\uff0c\u63a2\u8ba8\u672c\u5f81\u6a21\u6001\u5728\u6e4d\u6d41\u3001\u6df7\u6c8c\u7b49\u73b0\u8c61\u4e2d\u7684\u5e94\u7528\uff0c\u4ee5\u53ca\u5982\u4f55\u4ece\u4e2d\u63d0\u53d6\u91cd\u8981\u7684\u52a8\u529b\u5b66\u89c4\u5f8b\u3002\u901a\u8fc7\u672c\u8bfe\u7a0b\uff0c\u5b66\u751f\u5c06\u80fd\u591f\u7406\u89e3\u5e76\u5e94\u7528Koopman\u7b97\u7b26\u53ca\u76f8\u5173\u5de5\u5177\uff0c\u4e3a\u7814\u7a76\u590d\u6742\u7cfb\u7edf\u63d0\u4f9b\u65b0\u7684\u65b9\u6cd5\u548c\u601d\u8def\u3002<\/span><\/section>\n


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1. \u5f15\u8a00<\/span><\/strong><\/span><\/p>\n

a. \u8ba8\u8bba\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e0e\u7edf\u8ba1\u65b9\u6cd5\u4e2d\u9762\u4e34\u7684\u6311\u6218\uff0c\u4ee5\u53ca\u6784\u5efa\u6709\u6548\u7cfb\u7edf\u63cf\u8ff0\u9700\u8981\u8003\u8651\u7684\u5173\u952e\u56e0\u7d20\uff1b<\/span><\/p>\n

2. Koopman\u7b97\u7b26<\/span><\/strong><\/span><\/section>\n

a. \u4ecb\u7ecdKoopman\u7b97\u7b26\u7684\u6570\u5b66\u5b9a\u4e49\u53ca\u5176\u5982\u4f55\u5728\u89c2\u6d4b\u7a7a\u95f4\u4e2d\u5c06\u975e\u7ebf\u6027\u95ee\u9898\u7ebf\u6027\u5316\uff0c\u4ece\u800c\u63d0\u4f9b\u65b0\u7684\u5168\u5c40\u7cfb\u7edf\u63cf\u8ff0\u65b9\u6cd5\u3002<\/span><\/p>\n

b. \u9610\u8ff0Koopman\u7b97\u7b26\u901a\u8fc7\u672c\u5f81\u6a21\u6001\u548c\u76f8\u7a7a\u95f4\u5206\u533a\u63ed\u793a\u7cfb\u7edf\u4e2d\u7684\u4e0d\u53d8\u96c6\u548c\u52a8\u529b\u5b66\u6a21\u5f0f\u3002<\/span><\/p>\n

3. \u5e94\u7528<\/span><\/strong><\/span><\/section>\n

a. \u5229\u7528\u6807\u51c6\u6620\u5c04\u8fd9\u4e00\u7ecf\u5178\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u6a21\u578b\uff0c\u5c55\u793aKoopman\u7b97\u7b26\u5982\u4f55\u5206\u6790\u6df7\u6c8c\u884c\u4e3a\u548c\u4e0d\u53d8\u96c6\u7684\u7ed3\u6784\u3002<\/span><\/p>\n

b. \u901a\u8fc7\u6d41\u4f53\u6e4d\u6d41\u4e2d\u7684\u5b9e\u9645\u6848\u4f8b\uff0c\u5c55\u793aKoopman\u7b97\u7b26\u5982\u4f55\u63d0\u53d6\u4e3b\u5bfc\u6a21\u6001\uff0c\u63cf\u8ff0\u591a\u5c3a\u5ea6\u52a8\u6001\u7ed3\u6784\uff0c\u5206\u6790\u590d\u6742\u6da1\u65cb\u7684\u884c\u4e3a\u3002<\/span><\/p>\n

4. \u8bfe\u7a0b\u603b\u7ed3<\/span><\/strong><\/span><\/section>\n

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\u6d89\u53ca\u4e13\u4e1a\u672f\u8bed<\/strong><\/span><\/section>\n
Nonlinear Dynamics\uff08\u975e\u7ebf\u6027\u52a8\u529b\u5b66\uff09\u3001Dynamical Systems\uff08\u52a8\u529b\u5b66\u7cfb\u7edf\uff09\u3001Strong Nonlinearity\uff08\u5f3a\u975e\u7ebf\u6027\uff09\u3001Phase Space\uff08\u76f8\u7a7a\u95f4\uff09\u3001Invariant Set\uff08\u4e0d\u53d8\u96c6\uff09\u3001Morse Decomposition (\u6469\u5c14\u65af\u5206\u89e3)\u3001Poisson Bracket\uff08\u6cca\u677e\u62ec\u53f7\uff09\u3001Liouville Operator\uff08\u5218\u7ef4\u5c14\u7b97\u7b26\uff09\u3001Koopman Operator\uff08\u5e93\u666e\u66fc\u7b97\u7b26\uff09\u3001Spectral Decomposition\uff08\u8c31\u5206\u89e3\uff09\u3001Eigenmodes\uff08\u672c\u5f81\u6a21\u6001\uff09\u3001Krylov Subspace\uff08\u514b\u96f7\u6d1b\u592b\u5b50\u7a7a\u95f4\uff09\u3001Arnoldi Algorithm\uff08Arnoldi \u7b97\u6cd5\uff09\u3001Dynamic Mode Decomposition (DMD)\uff08\u52a8\u6001\u6a21\u5f0f\u5206\u89e3\uff09\u3001Reynolds Number\uff08\u96f7\u8bfa\u6570\uff09\u3001Turbulence\uff08\u6e4d\u6d41\uff09\u3001Mixing Zone\uff08\u6df7\u5408\u533a\uff09\u3001Resonant Zone\uff08\u5171\u632f\u533a\uff09\u3001Chaotic Behavior\uff08\u6df7\u6c8c\u884c\u4e3a\uff09\u3001Discrete Spectrum\uff08\u79bb\u6563\u8c31\uff09\u3001Continuous Spectrum\uff08\u8fde\u7eed\u8c31\uff09\u3001Observables\uff08\u89c2\u6d4b\u91cf\uff09\u3001Numerical Approximation\uff08\u6570\u503c\u8fd1\u4f3c\uff09<\/span><\/section>\n


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\u8bfe\u7a0b\u4e3b\u9898\uff1a\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2dKoopman\u7b97\u7b26\u7684\u5e94\u7528<\/span><\/p>\n

\u8bfe\u7a0b\u65f6\u95f4\uff1a2025\u5e741\u6708<\/strong>11<\/strong>\u65e5\uff08\u5468\u516d\uff09 14:00-16:00<\/strong><\/span><\/p>\n

\u8bfe\u7a0b\u5f62\u5f0f\uff1a\u817e\u8baf\u4f1a\u8bae\uff08\u4f1a\u8bae\u4fe1\u606f\u89c1\u7fa4\u5185\u901a\u77e5\uff09\uff1b\u96c6\u667a\u5b66\u56ed\u7f51\u7ad9\u5f55\u64ad\uff083\u4e2a\u5de5\u4f5c\u65e5\u5185\u4e0a\u7ebf\uff09<\/span><\/section>\n

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