{"id":54278,"date":"2024-12-10T21:05:31","date_gmt":"2024-12-10T13:05:31","guid":{"rendered":"https:\/\/swarma.org\/?p=54278"},"modified":"2024-12-10T21:05:31","modified_gmt":"2024-12-10T13:05:31","slug":"%e5%89%8d%e6%b2%bf%e8%bf%9b%e5%b1%95%ef%bc%9a%e7%a5%9e%e7%bb%8f%e6%b5%81%e5%bd%a2%e7%ae%97%e5%ad%90%e5%af%b9%e7%89%a9%e7%90%86%e7%b3%bb%e7%bb%9f%e5%86%85%e5%9c%a8%e7%bb%b4%e5%ba%a6%e7%9a%84%e8%a1%a8","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=54278","title":{"rendered":"\u524d\u6cbf\u8fdb\u5c55\uff1a\u795e\u7ecf\u6d41\u5f62\u7b97\u5b50\u5bf9\u7269\u7406\u7cfb\u7edf\u5185\u5728\u7ef4\u5ea6\u7684\u8868\u5f81\u5b66\u4e60"},"content":{"rendered":"
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\u5185\u5728\u7ef4\u5ea6\uff08Intrinsic Dimension\uff09\u662f\u8868\u5f81\u5b66\u4e60\u4e2d\u7528\u4e8e\u8868\u793a\u4e00\u4e2a\u7cfb\u7edf\u6216\u4e00\u4e2a\u72b6\u6001\u65f6\u6240\u9700\u8981\u7684\u6700\u5c0f\u7ef4\u5ea6\u3002\u5728\u529b\u5b66\u8bed\u5883\u4e0b\u63cf\u8ff0\u8fd0\u52a8\u65f6\uff0c\u8fd9\u4e00\u6982\u5ff5\u4e0e\u7269\u7406\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\uff08degree of freedom\uff09\u7c7b\u4f3c\uff0c\u53ef\u4ee5\u7528\u4e8e\u8868\u5f81\u4e00\u4e2a\u7cfb\u7edf\u65f6\u6240\u9700\u8981\u7684\u6700\u5c0f\u5750\u6807\u7ef4\u5ea6\u3002\u5f53\u5750\u6807\u7cfb\u5904\u4e8e\u8868\u5f81\u8be5\u7269\u7406\u7cfb\u7edf\u7684\u6700\u5c0f\u8868\u793a\u7ef4\u5ea6\u65f6\uff0c\u5176\u6570\u5b66\u6a21\u578b\u5f80\u5f80\u662f\u7b80\u6d01\u4e14\u610f\u4e49\u6e05\u6670\u7684\u3002<\/span><\/span><\/span><\/span><\/strong><\/span><\/strong>\u8fd1\u65e5\uff0c\u6e05\u534e\u5927\u5b66\u5730\u7403\u7cfb\u7edf\u79d1\u5b66\u7cfb\u9ec4\u5c0f\u731b\u6559\u6388\u8bfe\u9898\u7ec4\u53d1\u8868\u4e8e\u4eba\u5de5\u667a\u80fd\u9876\u7ea7\u4f1a\u8bae KDD 2024 \u4e0a\u7684\u4e00\u9879\u7814\u7a76\uff0c\u63a2\u7a76\u4e86\u5982\u4f55\u8ba1\u7b97\u7528\u4e8e\u8868\u5f81\u7269\u7406\u52a8\u529b\u6f14\u5316\u7684\u7b97\u5b50\u5728\u6f5c\u7a7a\u95f4\u4e0b\u7684\u5185\u5728\u7ef4\u5ea6\uff0c\u5e76\u63ed\u793a\u4e86\u5728\u5185\u5728\u7ef4\u5ea6\u4e0b\u795e\u7ecf\u7f51\u7edc\u7ed3\u6784\u80fd\u66f4\u51c6\u786e\u5730\u5efa\u6a21\u7269\u7406\u52a8\u529b\u3002\u6839\u636e\u8fd9\u4e00\u7406\u8bba\uff0c\u8be5\u7814\u7a76\u63d0\u51fa\u4e86\u4e00\u79cd\u540d\u4e3a\u795e\u7ecf\u6d41\u5f62\u7b97\u5b50\uff08Neural Manifold Operators\uff09\u7684\u6a21\u578b\uff0c\u80fd\u591f\u7cbe\u786e\u5efa\u6a21\u53d7\u591a\u79cd\u65b9\u7a0b\u63a7\u5236\u7684\u7269\u7406\u52a8\u529b\u548c\u771f\u5b9e\u4e16\u754c\u7684\u7269\u7406\u52a8\u529b\u3002\u7531\u4e8e\u5bf9\u7269\u7406\u7cfb\u7edf\u8fdb\u884c\u5185\u5728\u7ef4\u5ea6\u8868\u5f81\uff0c\u8be5\u6a21\u578b\u5728\u5b9e\u73b0\u9ad8\u7cbe\u5ea6\u5efa\u6a21\u7684\u540c\u65f6\uff0c\u4e5f\u5b9e\u73b0\u4e86\u8f7b\u91cf\u5316\u548c\u7269\u7406\u4e00\u81f4\u6027\u7b49\u4f18\u70b9\u3002<\/span><\/span><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n

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\u8bba\u6587\u9898\u76ee\uff1aNeural Manifold Operators for Learning the Evolution of Physical Dynamics<\/span><\/section>\n

\u8bba\u6587\u94fe\u63a5\uff1a<\/span>https:\/\/dl.acm.org\/doi\/10.1145\/3637528.3671779<\/span><\/span><\/p>\n

\u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/github.com\/AI4EarthLab\/Neural-Manifold-Operators<\/span><\/p>\n<\/section>\n<\/section>\n<\/blockquote>\n


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\u56fe3 \u5404\u6a21\u578b\u5728SEVIR\u548cNavier-Stokes\u65b9\u7a0b\u573a\u666f\u4e0b\u7684\u8bad\u7ec3\u65f6\u95f4\u53caRMSE\u6027\u80fd\u6392\u540d\u3002<\/span><\/section>\n


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\u56fe4 \u5de6\u56fe\uff1a\u6d45\u6c34\u65b9\u7a0b\u573a\u666f\u4e2d\u6bcf\u4e2a\u65f6\u95f4\u6b65\u7684\u76f8\u5bf9\u8d28\u91cf\u8bef\u5dee\u53ca\u5404\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u7684\u53ef\u89c6\u5316\u3002\u4e2d\u56fe\uff1aRayleigh-B\u00e9nard\u5bf9\u6d41\u573a\u666f\u4e2d\u7684\u6e4d\u6d41\u80fd\u8c31\u3002\u53f3\u56fe\uff1aRayleigh-B\u00e9nard\u5bf9\u6d41\u573a\u666f\u4e2d\u6bcf\u4e2a\u65f6\u95f4\u6b65\u7684\u5e73\u5747\u7edd\u5bf9\u6563\u5ea6\u5bf9\u6d41\u4ee5\u53ca\u5404\u6a21\u578b\u9884\u6d4b\u6b65\u5bf9\u5e94\u7684RMSE\u3002<\/span><\/section>\n


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\u56fe5 \u5728\u6240\u6709\u573a\u666f\u4e2d\u4e0e9\u4e2aBaseline\u6a21\u578b\u8fdb\u884c\u6027\u80fd\u6bd4\u8f83\u3002\u4f7f\u7528RMSE\u4f5c\u4e3a\u6a21\u578b\u8bc4\u4f30\u6307\u6807\uff0cRMSE\u503c\u8d8a\u5c0f\u8868\u793a\u7cbe\u5ea6\u8d8a\u9ad8\u3002\u7531\u4e8eFNO\u4ec5\u9488\u5bf9\u5355\u53d8\u91cf\u9884\u6d4b\u8bbe\u8ba1\uff0c\u56e0\u6b64\u6211\u4eec\u4ec5\u5728\u5355\u53d8\u91cf\u573a\u666f\u4e0b\u8bc4\u4f30\u8fd9\u4e9b\u6a21\u578b\uff0c\u4ee5\u786e\u4fdd\u57fa\u7ebf\u6a21\u578b\u7684\u6700\u4f73\u6027\u80fd\u3002\u4e0b\u5212\u7ebf\u8868\u793a\u57fa\u7ebf\u6a21\u578b\u4e2d\u6700\u51c6\u786e\u7684\u7ed3\u679c\uff0c\u52a0\u7c97\u5b57\u4f53\u8868\u793a\u6240\u6709\u6a21\u578b\u4e2d\u6700\u51c6\u786e\u7684\u7ed3\u679c\u3002\u661f\u53f7\uff08*\uff09\u8868\u793aGPU\u5185\u5b58\u6ea2\u51fa\uff08\u8d85\u8fc740GB\uff09\uff0c\u659c\u6760\uff08\/\uff09\u8868\u793a\u539f\u59cb\u6a21\u578b\u4ec5\u8bbe\u8ba1\u7528\u4e8e\u5355\u53d8\u91cf\u9884\u6d4b\u3002<\/span><\/section>\n


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\u7efc\u4e0a\uff0cNMO \u6a21\u578b\u4ece\u6570\u5b66\u548c\u5b9e\u9a8c\u7684\u89d2\u5ea6\uff0c\u5c1d\u8bd5\u56de\u7b54\u795e\u7ecf\u7b97\u5b50\u5728\u5b66\u4e60\u6f5c\u5728\u7b97\u5b50\u65f6\uff0c\u5982\u4f55\u5229\u7528\u6709\u9650\u7ef4\u53c2\u6570\u7a7a\u95f4\u5bf9\u65e0\u9650\u7ef4\u7b97\u5b50\u8fdb\u884c\u53c2\u6570\u5316\u8868\u793a\u7684\u95ee\u9898\uff0c\u5e76\u4e3a\u795e\u7ecf\u7b97\u5b50\u7ef4\u5ea6\u7684\u9009\u62e9\u63d0\u4f9b\u4e86\u6709\u6548\u4f9d\u636e\u3002<\/span><\/p>\n


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\u76f8\u5173\u6587\u732e<\/span><\/strong><\/span><\/p>\n

[1] Wu H, Weng K, Zhou S, Huang X, Xiong W. Neural Manifold Operators for Learning the Evolution of Physical Dynamics. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining 2024 Aug 25 (pp. 3356-3366).<\/span><\/p>\n

[2] Levina E, Bickel P. Maximum likelihood estimation of intrinsic dimension. Advances in neural information processing systems. 2004;17.<\/span><\/p>\n


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\u96c6\u667a\u5b66\u56ed\u6700\u65b0\u8bfe\u7a0b\uff1a<\/strong><\/p>\n

Koopman\u5206\u6790\u5728\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u662f\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u4e2d\u91cd\u8981\u7684\u7406\u8bba\u57fa\u7840\u548c\u7814\u7a76\u5de5\u5177\uff0c\u5b83\u6709\u52a9\u4e8e\u7406\u89e3\u7cfb\u7edf\u7684\u672c\u8d28\u7279\u6027\uff0c\u901a\u8fc7\u6784\u5efa\u548c\u5206\u6790\u7cfb\u7edf\u7684\u7c97\u7c92\u5316\u7a0b\u5ea6\u4e0d\u540c\u7684\u6570\u5b66\u6a21\u578b\u6765\u89e3\u51b3\u5b9e\u9645\u95ee\u9898\u3002\u5c3d\u7ba1\u4f4e\u7ef4\u975e\u7ebf\u6027\u7cfb\u7edf\u7684\u7406\u8bba\u5df2\u7ecf\u76f8\u5f53\u5b8c\u5907\uff0c\u4f46\u5982\u4f55\u5c06\u5176\u7528\u5230\u9ad8\u7ef4\u975e\u7ebf\u6027\u4f53\u7cfb\u4e2d\uff0c\u83b7\u53d6\u7cfb\u7edf\u7684\u5173\u952e\u52a8\u529b\u5b66\u4fe1\u606f\u662f\u4e00\u4e2a\u957f\u671f\u56f0\u6270\u7814\u7a76\u8005\u7684\u6311\u6218\u3002<\/span><\/section>\n

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\u597d\u7684\u7406\u8bba\u548c\u5de5\u5177\u4f1a\u5927\u5927\u52a0\u5feb\u79d1\u7814\u8fdb\u5c55\uff0cKoopman\u7b97\u7b26\u6709\u671b\u6210\u4e3a\u5206\u6790\u548c\u9884\u6d4b\u52a8\u6001\u7cfb\u7edf\u7684\u6807\u51c6\u7406\u8bba\u3002\u96c6\u667a\u5b66\u56ed\u9080\u8bf7\u5317\u4eac\u90ae\u7535\u5927\u5b66\u5170\u5cb3\u6052\u6559\u6388\u5f00\u8bbe\u300cKoopman\u5206\u6790\u5728\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u4e2d\u7684\u5e94\u7528\u300d\u7cfb\u5217\u8bfe\u7a0b<\/a>\uff0c\u9762\u5411\u81f4\u529b\u4e8e\u5b66\u4e60\u548c\u53d1\u5c55Koopman\u7b97\u7b26\u7406\u8bba\u7684\u793e\u533a\u670b\u53cb\uff0c\u57286\u8282\u8bfe\u7a0b\u65f6\u95f4\u4e2d\uff0c\u901a\u8fc7\u7ec6\u81f4\u7684\u8bb2\u89e3\uff0c\u6df1\u5165\u7684\u4e92\u52a8\uff0c\u5f62\u6210\u82cf\u683c\u62c9\u5e95\u5f0f\u8bfe\u5802\u6c1b\u56f4\uff0c\u5171\u540c\u8fdb\u6b65\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u52a0\u5165\u8bfe\u7a0b\uff01<\/span><\/section>\n

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

<\/strong><\/section>\n
1. <\/strong>\u5085\u7acb\u53f6\u795e\u7ecf\u7b97\u5b50\uff1a\u5085\u7acb\u53f6\u53d8\u6362\u5e94\u7528\u4e8e\u6df1\u5ea6\u5b66\u4e60\uff0c\u987d\u5f3a\u6c42\u89e3\u504f\u5fae\u5206\u65b9\u7a0b<\/a><\/strong><\/span><\/section>\n
2. <\/strong>\u524d\u6cbf\u8fdb\u5c55\uff1aKoopman\u795e\u7ecf\u7b97\u5b50\u6c42\u89e3\u504f\u5fae\u5206\u65b9\u7a0b<\/a><\/strong><\/span><\/section>\n
3. <\/strong>Nat.Rev.Phys.\u89c2\u70b9\uff1a\u8d85\u8d8a\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\uff0c\u795e\u7ecf\u7b97\u5b50\u52a0\u901f\u79d1\u5b66\u4eff\u771f\u4e0e\u8bbe\u8ba1<\/a><\/strong><\/span><\/section>\n
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4. <\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong>5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/section>\n

6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/p>\n


<\/p>\n


<\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfe\u7a0b<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

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