{"id":54522,"date":"2024-12-19T19:46:31","date_gmt":"2024-12-19T11:46:31","guid":{"rendered":"https:\/\/swarma.org\/?p=54522"},"modified":"2024-12-19T19:46:31","modified_gmt":"2024-12-19T11:46:31","slug":"%e7%90%86%e8%a7%a3%e5%a4%8d%e6%9d%82%e7%b3%bb%e7%bb%9f%e7%9a%84%e7%ac%ac%e4%b8%80%e6%ad%a5%ef%bc%9a%e7%90%86%e8%a7%a3%e9%9d%9e%e7%ba%bf%e6%80%a7%e5%8a%a8%e5%8a%9b%e5%ad%a6-koopman%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=54522","title":{"rendered":"\u7406\u89e3\u590d\u6742\u7cfb\u7edf\u7684\u7b2c\u4e00\u6b65\uff1a\u7406\u89e3\u975e\u7ebf\u6027\u52a8\u529b\u5b66 | Koopman\u5206\u6790\u7cfb\u5217\u8bfe\u7a0b"},"content":{"rendered":"
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\u4f5c\u4e3a\u300cKoopman\u5206\u6790\u5728\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528<\/a>\u300d\u7b2c\u4e00\u8bfe\uff0c\u572812\u670822\u65e5\uff08\u5468\u65e5\uff09 14:00-16:00\u5170\u5cb3\u6052\u6559\u6388\u4f1a\u5e26\u9886\u5927\u5bb6\u9996\u5148\u719f\u6089\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7406\u8bba\u548c\u5176\u4e2d\u5e38\u89c1\u7684\u7814\u7a76\u5de5\u5177\uff0c\u4ecb\u7ecd\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u51e0\u4f55\u63cf\u8ff0\u65b9\u6cd5\u548c\u53c2\u6570\u53d8\u5316\u4e0b\u5404\u7c7b\u52a8\u529b\u5b66\u7684\u4ea7\u751f\u2014\u2014\u5206\u5c94\u73b0\u8c61\uff0c\u5efa\u7acb\u5bf9\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u76f4\u89c2\u611f\u77e5\u3002\u5728\u540e\u7eed\u8bfe\u7a0b\u4e2d\uff0c\u4f1a\u770b\u5230Koopman\u7b97\u7b26\u5982\u4f55\u5e94\u7528\u5230\u8fd9\u4e9b\u9ad8\u7ef4\u7cfb\u7edf\u7684\u5206\u6790\u4e2d\u3002<\/span><\/strong><\/section>\n<\/section>\n
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          \u975e\u7ebf\u6027\u52a8\u529b\u5b66\uff08Nonlinear Dynamics\uff09\uff1b\u590d\u6742\u7cfb\u7edf\uff08Complex Systems\uff09\uff1b\u5206\u5c94\uff08Bifurcation\uff09\uff1b\u978d\u7ed3\u5206\u5c94\uff08Saddle-node Bifurcation\uff09\uff1b\u8de8\u4e34\u754c\u5206\u5c94\uff08Transcritical Bifurcation\uff09\uff1b\u8d85\u4e34\u754c\u5206\u5c94\uff08Supercritical Pitchfork Bifurcation\uff09\uff1bHopf\u5206\u5c94\uff08Hipf Bifurcations\uff09\uff1b\u6df7\u6c8c\uff08Chaos\uff09\uff1b\u4f4e\u7ef4\u52a8\u529b\u5b66\uff08Low-dimensional Dynamics\uff09\uff1b\u56fa\u5b9a\u70b9\uff08Fixed Point\uff09\uff1b\u7a33\u5b9a\u6027\uff08Stability\uff09\uff1b\u5206\u5c94\u70b9\uff08Bifurcation Point\uff09\uff1b\u5468\u671f\u8f68\u9053\uff08Periodic Orbit\uff09\uff1b\u89c4\u5f8b\u6027\u4e0e\u968f\u673a\u6027\uff08Order and Chaos\uff09\uff1b\u5947\u602a\u5438\u5f15\u5b50\uff08Strange Attractor\uff09\uff1b\u52a8\u529b\u5b66\u5b50\u6d41\u5f62\uff08Dynamical Submanifold\uff09\uff1b\u7ef4\u5ea6\u964d\u7ef4\uff08Dimension Reduction\uff09\uff1b\u7a33\u5b9a\u5468\u671f\uff08Stable Periodic Cycle\uff09\uff1b\u4e0d\u7a33\u5b9a\u5468\u671f\uff08Unstable Periodic Cycle\uff09\uff1b\u5468\u671f-\u52a0\u500d\u5206\u5c94\uff08Period-doubling Bifurcation\uff09\uff1b\u6d1b\u4f26\u5179\u65b9\u7a0b\uff08Lorenz Equation\uff09\uff1b\u79d1\u5c14\u83ab\u54e5\u6d1b\u592b\u7406\u8bba\uff08Kolmogorov Theory\uff09\uff1b\u62d3\u6251\u5b66\uff08Topology\uff09\uff1b\u7b26\u53f7\u52a8\u529b\u5b66\uff08Symbolic Dynamics\uff09\uff1b\u9891\u8c31\u5206\u6790\uff08Spectral Analysis\uff09\uff1b\u5085\u91cc\u53f6\u53d8\u6362\uff08Fourier Transform\uff09\uff1b\u62c9\u666e\u62c9\u65af\u53d8\u6362\uff08Laplace Transform\uff09\uff1b\u5c0f\u6ce2\u53d8\u6362\uff08Wavelet Transform\uff09\uff1b\u52a8\u529b\u5b66\u7cfb\u7edf\u7406\u8bba\uff08Dynamical Systems Theory\uff09\uff1b\u53d8\u5206\u65b9\u6cd5\uff08Variational Methods\uff09<\/span><\/section>\n


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          \u5170\u5cb3\u6052<\/strong>\uff0c\u5317\u4eac\u90ae\u7535\u5927\u5b66\u7406\u5b66\u9662\u6559\u6388\uff0c\u535a\u58eb\u5b66\u4f4d\u5728\u4f50\u6cbb\u4e9a\u7406\u5de5\u5b66\u9662\uff08Georgia Institute of Technology\uff09\u83b7\u5f97\u3002\u5148\u540e\u5728\u56fd\u5185\u5916\u591a\u4e2a\u8457\u540d\u5927\u5b66\u5b66\u4e60\u548c\u5de5\u4f5c\u8fc7\uff0c\u6709\u4e30\u5bcc\u7684\u5b66\u79d1\u4ea4\u53c9\u7814\u7a76\u7ecf\u5386\u3002\u4e3b\u8981\u4ece\u4e8b\u975e\u7ebf\u6027\u79d1\u5b66\u3001\u7edf\u8ba1\u7269\u7406\u3001\u751f\u7269\u7269\u7406\u3001\u590d\u6742\u4fe1\u606f\u548c\u667a\u80fd\u7cfb\u7edf\u7b49\u65b9\u9762\u7684\u7814\u7a76\u5de5\u4f5c\uff0c\u6ce8\u91cd\u57fa\u672c\u7406\u8bba\u65b9\u6cd5\u7684\u53d1\u5c55\u548c\u4e0e\u5b9e\u9a8c\u7d27\u5bc6\u7ed3\u5408\u7684\u5e94\u7528\u3002\u73b0\u4e3a\u5317\u4eac\u90ae\u7535\u5927\u5b66\u201c\u6570\u5b66\u4e0e\u4fe1\u606f\u7f51\u7edc\u201d\u6559\u80b2\u90e8\u91cd\u70b9\u5b9e\u9a8c\u5ba4\u526f\u4e3b\u4efb\uff0c\u591a\u6b21\u88ab\u9080\u8bf7\u5728\u56fd\u5185\u5916\u5b66\u672f\u4f1a\u8bae\u4e0a\u62a5\u544a\u81ea\u5df1\u7684\u5de5\u4f5c\uff0c\u540c\u65f6\u62c5\u4efb\u671f\u520a\u201c\u7406\u8bba\u7269\u7406\u901a\u4fe1\u201d\uff08Communications in Theoretical Physics\uff09\u548c\u201c\u73b0\u4ee3\u6570\u5b66\u7269\u7406\u201d\uff08Modern Mathematical Physics\uff09\u7684\u7f16\u59d4\uff0c\u4e5f\u662f\u591a\u4e2a\u56fd\u9645\u8457\u540d\u6742\u5fd7\u7684\u5ba1\u7a3f\u4eba\u3002\u53d1\u8868\u5b66\u672f\u8bba\u6587100\u4f59\u7bc7\uff0c\u5305\u62ec\u56fd\u9645\u9876\u7ea7\u6742\u5fd7PRL\uff0c PNAS\uff0c Nature\u5b50\u520a\u8bba\u6587\u591a\u7bc7\u3002<\/span><\/section>\n


          <\/p>\n


          <\/p>\n

          \n
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          <\/section>\n

          <\/section>\n
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          <\/svg><\/section>\n<\/section>\n<\/section>\n
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          \u7cfb\u5217\u8bfe\u7a0b\u4fe1\u606f<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

          \n

          <\/section>\n

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


          <\/p>\n

          \u8bfe\u7a0b\u9002\u7528\u5bf9\u8c61<\/span><\/strong><\/span><\/h3>\n
            \n
          1. \n

            \u7406\u5de5\u79d1\u7814\u7a76\u751f\u6216\u9ad8\u5e74\u7ea7\u672c\u79d1\u751f<\/strong>\uff1a<\/span><\/p>\n<\/li>\n

              \n
            1. \n

              \u5bf9\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u3001\u6570\u5b66\u5efa\u6a21\u3001\u6570\u5b66\u7269\u7406\u6216\u7edf\u8ba1\u529b\u5b66\u611f\u5174\u8da3\u3002<\/span><\/p>\n<\/li>\n

            2. \n

              \u5177\u5907\u4e00\u5b9a\u7684\u5fae\u5206\u65b9\u7a0b\u3001\u7ebf\u6027\u4ee3\u6570\u53ca\u8ba1\u7b97\u57fa\u7840\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n

            3. \n

              \u5bf9\u7406\u8bba\u4e0e\u5b9e\u8df5\u7ed3\u5408\u611f\u5174\u8da3\u7684\u8de8\u5b66\u79d1\u7814\u7a76\u8005<\/strong>\uff1a<\/span><\/p>\n<\/li>\n

                \n
              1. \n

                \u5e0c\u671b\u901a\u8fc7Koopman\u7b97\u5b50\u63a2\u7d22\u975e\u7ebf\u6027\u7cfb\u7edf\u5728\u81ea\u5df1\u7684\u7814\u7a76\u65b9\u5411\u4e2d\u7684\u5e94\u7528\u3002<\/span><\/p>\n<\/li>\n

              2. \n

                \u4ece\u4e8b\u5404\u7c7b\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u3001\u5bfb\u627e\u6709\u529b\u5206\u6790\u5de5\u5177\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n

              3. \n

                \u5177\u6709\u63a2\u7a76\u7cbe\u795e\u7684\u5b66\u751f<\/strong>\uff1a<\/span><\/p>\n<\/li>\n

                  \n
                1. \n
                  \u4e50\u4e8e\u53c2\u4e0e\u8ba8\u8bba\u3001\u5047\u8bbe\u63a8\u5bfc\u548c\u95ee\u9898\u53cd\u601d\u7684\u5b66\u751f\u3002<\/span><\/section>\n<\/li>\n<\/ol>\n<\/ol>\n


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

                  \u8bfe\u7a0b\u8bc1\u4e66<\/span><\/strong><\/span><\/h3>\n
                  \u8981\u60f3\u89e3\u5f00\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7684\u5965\u79d8\u5e76\u4e0d\u7b80\u5355\uff0c\u4f46\u524d\u8fdb\u7684\u6bcf\u4e00\u6b65\uff0c\u90fd\u503c\u5f97\u6211\u4eec\u6b23\u559c\u3002\u672c\u7cfb\u5217\u8bfe\u7a0b\uff0c\u6211\u4eec\u4f1a\u8fdb\u884c\u4e25\u683c\u7684\u8bfe\u5802\u7ba1\u7406\uff0c\u9f13\u52b1\u5404\u4f4d\u540c\u5b66\u79ef\u6781\u601d\u8003\u3001\u8ba8\u8bba\uff0c\u5e0c\u671b\u80fd\u591f\u901a\u8fc7\u672c\u8bfe\u7a0b\u8ba9\u540c\u5b66\u4eec\u80fd\u5bf9Koopman\u7b97\u7b26\u7406\u8bba\u6709\u6df1\u5165\u7684\u7814\u7a76\uff0c\u5e76\u80fd\u8fdb\u884c\u76f8\u5e94\u7684\u7406\u8bba\u7814\u7a76\u548c\u5e94\u7528\u5b9e\u8df5\u3002\u5bf9\u4e8e\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\u7684\u540c\u5b66\uff0c\u4f1a\u53d1\u653e\u5b9e\u4f53\u8bc1\u4e66\uff0c\u5c06\u9009\u51fa3\u540d\u4f18\u79c0\u7684\u540c\u5b66\u6bcf\u4eba\u8d60\u90011\u4ef6\u96c6\u667a\u5b9a\u5236T\u6064\u3002\u8ba9\u6211\u4eec\u5171\u540c\u5f00\u542f\u4e00\u6b21\u82cf\u683c\u62c9\u5e95\u5f0f\u7684\u8bfe\u7a0b\u5427\u3002<\/span><\/section>\n

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

                  \u8bfe\u7a0b\u8bc1\u4e66\u53d1\u653e\u6807\u51c6\uff1a<\/strong><\/span><\/p>\n

                    \n
                  1. \n

                    \u62a5\u540d\u65f6\u95f4\uff1a2024\u5e7412\u670821\u65e5\u524d\u62a5\u540d\u7684\u6210\u5458\uff1b<\/span><\/p>\n<\/li>\n

                  2. \n

                    \u53c2\u4e0e\u8bfe\u7a0b\u76f4\u64ad\uff1a\u4e0d\u4f4e\u4e8e80%\uff0c\u6839\u636e\u817e\u8baf\u4f1a\u8bae\u7684\u5728\u7ebf\u65f6\u95f4\u8fdb\u884c\u7edf\u8ba1\uff1b<\/span><\/p>\n<\/li>\n

                  3. \n

                    \u52a0\u5206\u9879\uff1a\u8bfe\u7a0b\u76f4\u64ad\u548c\u8bfe\u7a0b\u5fae\u4fe1\u7fa4\u5185\u79ef\u6781\u63d0\u95ee\uff1b<\/span><\/p>\n<\/li>\n

                  4. \n
                    \u52a0\u5206\u9879\uff1a\u5b8c\u6210\u8bfe\u7a0b\u8bbe\u7f6e\u7684\u4efb\u52a1\uff1b<\/span><\/section>\n<\/li>\n<\/ol>\n


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

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

                    \n
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                    \n
                    \n
                    \n

                    <\/section>\n

                    <\/section>\n
                    \n
                    <\/svg><\/section>\n<\/section>\n<\/section>\n
                    \n

                    \u62a5\u540d\u987b\u77e5<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

                    \n

                    <\/section>\n

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

                      
                    <\/p>\n

                      \n
                    1. \n

                      \u8bfe\u7a0b\u5f62\u5f0f\uff1a\u817e\u8baf\u4f1a\u8bae\u76f4\u64ad\uff0c\u96c6\u667a\u5b66\u56ed\u7f51\u7ad9\u5f55\u64ad\u3002\u672c\u7cfb\u5217\u8bfe\u7a0b\u4e0d\u5b89\u6392\u514d\u8d39\u76f4\u64ad\u3002<\/span><\/p>\n<\/li>\n

                    2. \n

                      \u8bfe\u7a0b\u5468\u671f\uff1a2024\u5e7412\u670821\u65e5-2025\u5e741\u670825\u65e5\uff0c\u6bcf\u5468\u516d\u4e0b\u53482\u70b9-4\u70b9\u8fdb\u884c\u3002<\/span><\/p>\n<\/li>\n

                        \n
                      1. \n

                        \u7279\u522b\u8bf4\u660e\uff1a\u7b2c\u4e00\u6b21\u8bfe\u7a0b\u4e34\u65f6\u8c03\u6574\u4e3a12\u670822\u65e5\u4e0b\u53482-4\u70b9\u8fdb\u884c\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n

                      2. \n

                        \u8bfe\u7a0b\u5b9a\u4ef7\uff1a\u539f\u4ef7599\uff0c\u65e9\u9e1f\u4ef7449\uff0c\u65e9\u9e1f\u4f18\u60e0\u622a\u6b62\u52302024\u5e7412\u670821\u65e5\u4e2d\u534812\u70b9\u3002<\/span><\/p>\n<\/li>\n<\/ol>\n

                        <\/section>\n
                        \u626b\u7801\u4ed8\u8d39\u62a5\u540d\u8bfe\u7a0b<\/span><\/section>\n
                        \u8bfe\u7a0b\u94fe\u63a5\uff1ahttps:\/\/campus.swarma.org\/course\/5419?from=wechat<\/span><\/section>\n

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

                        \u4ed8\u8d39\u6d41\u7a0b\uff1a<\/span><\/strong><\/span><\/p>\n

                          \n
                        1. \n

                          \u626b\u7801\u4ed8\u8d39\uff1b<\/span><\/p>\n<\/li>\n

                        2. \n

                          \u8bfe\u7a0b\u9875\u9762\u6dfb\u52a0\u5b66\u5458\u767b\u8bb0\u8868\uff0c\u6dfb\u52a0\u52a9\u6559\u5fae\u4fe1\u5165\u7fa4\uff1b<\/span><\/p>\n<\/li>\n

                        3. \n
                          \u8bfe\u7a0b\u53ef\u5f00\u53d1\u7968\u3002<\/span><\/section>\n<\/li>\n<\/ol>\n


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

                          \u8bfe\u7a0b\u5956\u5b66\u91d1\u673a\u5236<\/span><\/strong><\/span><\/h3>\n
                            \n
                          1. \n

                            \u9014\u5f84\u4e00\uff1a\u53d1\u5e03\u9ad8\u8d28\u91cf\u8bfe\u7a0b\u7b14\u8bb0<\/span><\/p>\n<\/li>\n<\/ol>\n

                            \u5728\u96c6\u667a\u6591\u56fe\u7f51\u7ad9\uff08pattern.swarma.org\uff09\u5b8c\u6210\u672c\u8bfe\u7a0b\u4f53\u7cfb\u4e0b\u67d0\u4e2a\u65b9\u5411\u7684\u603b\u7ed3\u6587\u7ae0\u6216\u5b66\u4e60\u8def\u5f84\u3002\u7ecf\u96c6\u667a\u5b66\u56ed\u52a9\u6559\u56e2\u961f\u8bc4\u5b9a\u8ba4\u53ef\u540e\uff0c\u53ef\u4f5c\u4e3a\u4e00\u6761\u8d21\u732e\u3002\u4e00\u6761\u8d21\u732e\u5956\u52b1200\u5143\u5956\u5b66\u91d1\uff0c\u8d28\u91cf\u4f18\u5f02\u7684\u5185\u5bb9\uff0c\u4f1a\u6709\u6d6e\u52a8\u5956\u52b1\u3002<\/span><\/p>\n

                            \u53ef\u53c2\u8003\uff1a<\/span><\/p>\n