{"id":62256,"date":"2025-07-19T17:37:50","date_gmt":"2025-07-19T09:37:50","guid":{"rendered":"https:\/\/swarma.org\/?p=62256"},"modified":"2025-07-19T17:37:50","modified_gmt":"2025-07-19T09:37:50","slug":"%e4%bb%8e%e4%b8%8d%e7%a1%ae%e5%ae%9a%e5%88%b0%e5%ae%89%e5%85%a8%ef%bc%9a%e5%a6%82%e4%bd%95%e5%ae%89%e5%85%a8%e6%8e%a7%e5%88%b6%e5%a4%8d%e6%9d%82%e7%89%a9%e7%90%86%e7%b3%bb%e7%bb%9f%ef%bd%9cicml2025","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=62256","title":{"rendered":"\u4ece\u4e0d\u786e\u5b9a\u5230\u5b89\u5168\uff1a\u5982\u4f55\u5b89\u5168\u63a7\u5236\u590d\u6742\u7269\u7406\u7cfb\u7edf\uff5cICML2025"},"content":{"rendered":"
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\u8bba\u6587\u9898\u76ee\uff1aFrom Uncertain to Safe: Conformal Adaptation of Diffusion Models for Safe PDE Control<\/span><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2502.02205<\/span><\/p>\n

\u4ee3\u7801\u94fe\u63a5\uff1ahttps:\/\/github.com\/AI4Science-WestlakeU\/safediffcon<\/span><\/p>\n<\/blockquote>\n


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\u5728\u63a7\u5236\u4efb\u52a1\u4e2d\uff0c<\/span><\/span><\/span>\u7531\u4e8e\u5efa\u6a21\u8bef\u5dee\u3001\u73af\u5883\u53d8\u5316\u7b49\u5bfc\u81f4\u7684<\/span><\/span><\/span>\u4e0d\u786e\u5b9a\u6027<\/span><\/span><\/span>\uff0c<\/span><\/span><\/span>\u4ec5\u4ec5\u5f97\u5230\u4e00\u4e2a<\/span><\/span><\/span>\u5bf9\u5b89\u5168\u6307\u6807\u7684<\/span><\/span><\/span>\u5355\u70b9\u9884\u6d4b<\/span><\/span><\/span>\u662f\u4e0d\u591f\u7684<\/span><\/span><\/span>\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\u6a21\u578b\u9884\u6d4b\u6709\u591a\u5927\u4e0d\u786e\u5b9a\u6027<\/span><\/span><\/span>\uff0c<\/span><\/span><\/span>\u9884\u6d4b\u7ed3\u679c\u662f\u5426\u4f1a\u8fdd\u53cd\u7269\u7406\u5b89\u5168\u7ea6\u675f<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>\u8fd9\u5c31\u9700\u8981\u80fd\u591f\u5bf9\u9884\u6d4b\u8f93\u51fa\u8fdb\u884c\u53ef\u9760\u7684\u4e0d\u786e\u5b9a\u6027\u4f30\u8ba1<\/span><\/span><\/span>\uff0c<\/span><\/span><\/span>\u800c\u5171\u5f62\u9884\u6d4b\u6b63\u597d\u63d0\u4f9b\u4e86\u8fd9\u6837\u7684\u80fd\u529b\u3002<\/span><\/span><\/span><\/span><\/section>\n

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\u4e3a\u6b64\uff0c\u6211\u4eec\u5f15\u5165<\/span><\/span><\/span>\u5171\u5f62\u9884\u6d4b <\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span>Conformal Prediction<\/span><\/span><\/span>)<\/span><\/span><\/span> \u6765\u751f\u6210<\/span><\/span><\/span>\u4e00\u5b9a<\/span><\/span><\/span>\u7f6e\u4fe1\u5ea6\u7684\u9884\u6d4b\u533a\u95f4<\/span><\/span><\/span> [<\/span><\/span><\/span>1, 2]<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>\u5171\u5f62\u9884\u6d4b\u662f\u4e00\u79cd\u6a21\u578b\u65e0\u5173\u7684\u4e0d\u786e\u5b9a\u6027\u91cf\u5316\u65b9\u6cd5\uff0c\u53ef\u4ee5\u4e3a\u4efb\u610f\u9884\u6d4b\u6a21\u578b<\/span>\uff08\u5305\u62ec\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\uff09<\/span>\u63d0\u4f9b<\/span><\/span><\/span>\u7f6e\u4fe1\u533a\u95f4<\/span><\/span><\/span>\uff0c\u4ece\u800c\u63a7\u5236\u9884\u6d4b\u7684\u9519\u8bef\u7387\u3002<\/span><\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u662f\uff1a\u5229\u7528\u4e00\u4e2a\u79f0\u4e3a<\/span><\/span><\/span>\u6821\u51c6\u96c6\uff08<\/span><\/span><\/span>C<\/span><\/span><\/span>alibration <\/span><\/span><\/span>S<\/span><\/span><\/span>et\uff09<\/span><\/span><\/span>\u7684\u6570\u636e\u96c6\uff0c<\/span><\/span><\/span>\u6765<\/span><\/span><\/span>\u8bc4\u4f30\u6a21\u578b\u7684\u9884\u6d4b<\/span><\/span><\/span>\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5b83\u57fa\u4e8e\u5176\u4e2d\u7684\u6bcf\u6761\u6570\u636e\u7684\u771f\u5b9e\u503c\u4ee5\u53ca\u6a21\u578b\u9884\u6d4b\u503c\uff0c\u6765\u5f97\u5230\u5bf9\u5e94\u7684\u9884\u6d4b\u8bef\u5dee\uff0c\u4e4b\u540e\u53d6\u8fd9\u4e9b\u8bef\u5dee\u5f97\u5230\u7684\u96c6\u5408<\/span><\/span><\/span>\uff08Score<\/span><\/span><\/span><\/span><\/span>Set\uff09<\/span><\/span><\/span>\u7684\u5206\u4f4d\u6570\u4f5c\u4e3a<\/span><\/span><\/span>\u4e0d\u786e\u5b9a\u6027\u5206\u4f4d\u6570<\/span><\/span><\/span><\/span>Q<\/span><\/span>(1-\u03b1)<\/span><\/span>\uff08<\/span><\/span><\/span>Uncertainty Quantile<\/span><\/span><\/span>\uff09<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>\u6700\u7ec8\uff0c\u5229\u7528<\/span><\/span><\/span><\/span>Q(1-\u03b1)<\/span><\/span>\u4f5c\u4e3a\u533a\u95f4\u5bbd\u5ea6\uff0c\u6211\u4eec\u5f97\u5230\u5982\u56fe1\u6240\u793a\u7684\u3001<\/span><\/span><\/span>\u80fd\u4ee5<\/span><\/span><\/span><\/span>1-\u03b1<\/span><\/span>\u7f6e\u4fe1<\/span><\/span><\/span>\u5ea6<\/span><\/span><\/span>\u5305\u542b\u771f\u5b9e\u6807\u7b7e\u7684<\/span><\/span><\/span>\u7f6e\u4fe1\u533a\u95f4\uff0c\u4e5f\u5c31\u662f<\/span><\/span><\/span>\u201c<\/span><\/span><\/span>\u771f\u5b9e\u503c<\/span><\/span><\/span>\u843d\u5165<\/span><\/span><\/span>\u7f6e\u4fe1<\/span><\/span><\/span>\u533a\u95f4\u7684\u6982\u7387\u2267\u6307\u5b9a\u7f6e\u4fe1\u5ea6<\/span><\/span><\/span>\u201d<\/span><\/span><\/span>\u3002<\/span><\/span><\/span><\/span><\/span><\/section>\n
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<\/span><\/span><\/span><\/span><\/section>\n
\u56fe<\/span><\/span><\/span>2<\/span><\/span><\/span>:<\/span><\/span><\/span>\u7528\u5171\u5f62\u9884\u6d4b\u91cf\u5316\u4e0d\u786e\u5b9a\u5ea6<\/span><\/span><\/span><\/span><\/span>Q<\/span><\/span>(1-\u03b1)<\/span><\/span>\u3002\u5176\u4e2d<\/span><\/span><\/span>1-\u03b1<\/span><\/span>\u662f\u7f6e\u4fe1\u5ea6\uff0c<\/span><\/span><\/span>s<\/span><\/span>0<\/span><\/span><\/sub>\u662f\u5b89\u5168\u754c\u9650\uff0c<\/span><\/span><\/span>s<\/span><\/span>\u03b8<\/span><\/span><\/sub>\u548c<\/span><\/span><\/span>s<\/span><\/span>\u5206\u522b\u662f\u6a21\u578b\u5bf9\u5b89\u5168\u5206\u6570\u7684\u5355\u70b9\u9884\u6d4b\u548c\u8003\u8651\u4e86\u4e0d\u786e\u5b9a\u6027\u7684\u5b89\u5168\u5206\u6570\u7684\u7f6e\u4fe1\u533a\u95f4\u3002<\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u5728<\/span><\/span><\/span>\u6587\u7ae0<\/span><\/span><\/span>\u4e2d\uff0c\u4f5c\u8005\u63d0\u51fa\u5c06\u5171\u5f62\u9884\u6d4b\u673a\u5236\u5f15\u5165\u6269\u6563\u6a21\u578b\u63a7\u5236\u6846\u67b6\uff0c\u5e76\u8fdb\u4e00\u6b65\u8bbe\u8ba1\u4e86<\/span><\/span><\/span>\u5bf9\u4e8e\u6269\u6563\u6a21\u578b\u63a7\u5236\u7684<\/span><\/span><\/span>\u504f\u79fb\u5171\u5f62\u9884\u6d4b <\/span><\/span><\/span><\/span><\/span>(<\/span><\/span><\/span>Shifted Conformal Predictio<\/span><\/span><\/span>n<\/span><\/span><\/span>)<\/span><\/span><\/span>\u3002<\/span><\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u4f20\u7edf\u5171\u5f62\u9884\u6d4b<\/span><\/span><\/span>\u6709\u4e00\u4e2a\u91cd\u8981\u7684<\/span><\/span><\/span>\u5047\u8bbe<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span>\u6d4b\u8bd5\u5206\u5e03\u4e0e\u6821\u51c6\u96c6\u5206\u5e03\u76f8\u540c\u3002\u4f46\u5728\u63a7\u5236\u4efb\u52a1\u4e2d\uff0c\u6a21\u578b\u5e38\u5e38\u5728\u65b0\u7684<\/span><\/span><\/span>\u63a7\u5236\u4efb\u52a1<\/span><\/span><\/span>\u4e0b\u8fdb\u884c\u63a8\u7406\uff0c<\/span><\/span><\/span>\u9700\u8981\u751f\u6210\u4e0e\u5df2\u6709\u6570\u636e\u96c6\u5206\u5e03\u4e0d\u540c\u7684\u63a7\u5236\u5e8f\u5217\uff0c<\/span><\/span><\/span>\u5373<\/span><\/span><\/span>\u5bf9\u5e94\u7684\u6570\u636e<\/span><\/span><\/span>\u5206\u5e03\u53d1\u751f\u4e86\u504f\u79fb\u3002<\/span><\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u4e3a\u4e86\u5e94\u5bf9\u8fd9\u4e00\u95ee\u9898\uff0c<\/span><\/span><\/span>\u504f\u79fb<\/span><\/span><\/span>\u5171\u5f62\u9884\u6d4b<\/span><\/span><\/span>\u901a\u8fc7\u5bf9\u6821\u51c6\u96c6\u4e2d\u7684\u6570\u636e\u8fdb\u884c\u52a0\u6743\uff0c\u6765\u5f97\u5230\u52a0\u6743\u540e\u7684<\/span><\/span><\/span>\u8bef\u5dee\u96c6\u5408\uff08Shifted<\/span><\/span><\/span><\/span><\/span>Score<\/span><\/span><\/span><\/span>Set\uff09\uff0c\u4ee5\u53ca\u5bf9\u5e94\u7684\u4e0d\u786e\u5b9a\u6027\u5206\u4f4d\u6570<\/span><\/span><\/span>\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u6309\u7167\u8fd9\u4e9b\u6570\u636e\u96c6\u5728\u5904\u7406\u63a7\u5236\u4efb\u52a1\u65f6\u51fa\u73b0\u7684\u6982\u7387\u5bf9\u5b83\u4eec\u8fdb\u884c\u52a0\u6743\uff0c\u4e5f\u5c31\u662f\u66f4\u5b89\u5168\u3001\u63a7\u5236\u6548\u679c\u66f4\u4f18\u7684\u6570\u636e\u4f1a\u88ab\u8d4b\u4e88\u66f4\u9ad8\u7684\u6743\u91cd\u3002<\/span><\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u6700\u7ec8\uff0c\u6211\u4eec\u80fd\u57fa\u4e8e\u504f\u79fb\u5171\u5f62\u9884\u6d4b\uff0c\u5f97\u5230\u4e00\u4e2a\u6269\u6563\u6a21\u578b\u63a7\u5236\u7684<\/span><\/span><\/span>\u53ef\u8bc1\u660e<\/span><\/span><\/span>\u7f6e\u4fe1\u533a\u95f4\u3002\u5b83\u80fd\u4fdd\u8bc1\u6269\u6563\u6a21\u578b\u5728\u5e94\u5bf9<\/span><\/span><\/span>\u4f1a\u9020\u6210\u5206\u5e03\u504f\u79fb\u7684<\/span><\/span><\/span>\u63a7\u5236\u4efb\u52a1\u65f6\uff0c\u4ecd\u7136\u6709\u5927\u4e8e\u7b49\u4e8e<\/span><\/span><\/span><\/span>1-\u03b1<\/span><\/span>\u7684\u6982\u7387\u843d\u5728\u7f6e\u4fe1\u533a\u95f4\u4e2d\u3002<\/span><\/span><\/span><\/section>\n

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\u4e09\u3001SafeDiffCon\uff1a\u751f\u6210\u5f0f\u5b89\u5168\u63a7\u5236\u6846\u67b6<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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

\u57fa\u4e8e\u4ee5\u4e0a\u5bf9\u6269\u6563\u6a21\u578b\u63a7\u5236\u7684\u4e0d\u786e\u5b9a\u6027\u91cf\u5316\uff0c\u6211\u4eec\u63d0\u51fa\u4e86<\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span><\/span>afeDiffCon<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>S<\/span><\/span><\/span>afeDiffCon<\/span><\/span><\/span>\u662f\u4e00\u4e2a<\/span><\/span><\/span>\u4e09<\/span><\/span><\/span>\u9636\u6bb5<\/span><\/span><\/span>\u7b97\u6cd5<\/span><\/span><\/span>\uff0c\u4e13\u4e3a\u89e3\u51b3\u5b89\u5168\u63a7\u5236\u4efb\u52a1\u8bbe\u8ba1<\/span><\/span><\/span>\uff0c\u5176\u4e3b\u8981\u7b97\u6cd5\u7531\u56fe<\/span><\/span><\/span>3<\/span><\/span><\/span>\u548c\u56fe<\/span><\/span><\/span>4<\/span><\/span><\/span>\u6240\u793a\u3002<\/span><\/span><\/span><\/span><\/section>\n
<\/span><\/section>\n
<\/span><\/span><\/span><\/span><\/section>\n
\u56fe<\/span><\/span><\/span>3<\/span><\/span><\/span>:<\/span><\/span><\/span><\/span><\/span><\/span>S<\/span><\/span><\/span>afeDiffCon<\/span><\/span><\/span><\/span>\u7684\u4e3b\u8981\u7b97\u6cd5\uff0c\u5305\u62ec\u9884\u8bad\u7ec3\u3001\u540e\u8bad\u7ec3\u548c\u6d4b\u8bd5\u65f6\u5fae\u8c03\u4e09\u4e2a\u9636\u6bb5\u3002<\/span><\/span><\/span><\/span><\/section>\n
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\u56fe<\/span><\/span><\/span>4<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span>S<\/span><\/span><\/span>afeDiffCon<\/span><\/span><\/span>\u7684\u6846\u67b6\u3002<\/span><\/span><\/span>\u9996\u5148\uff0c\u6211\u4eec\u5728\u8bad\u7ec3\u6570\u636e\u4e0a\u9884\u8bad\u7ec3\u4e00\u4e2a\u6269\u6563\u6a21\u578b\u3002\u968f\u540e\uff0c\u7ed3\u5408\u4e0d\u786e\u5b9a\u6027\u5206\u4f4d<\/span><\/span><\/span>\u6570<\/span><\/span><\/span><\/span><\/span>Q<\/span><\/span>\uff0c\u6211\u4eec\u5bf9\u8be5\u6a21\u578b\u8fdb\u884c\u540e\u8bad\u7ec3\uff0c\u4ee5\u5f15\u5bfc\u5176\u751f\u6210\u5206\u5e03\u5411\u66f4\u5b89\u5168\u3001\u63a7\u5236\u6548\u679c\u66f4\u4f18\u7684\u533a\u57df\u504f\u79fb\u3002\u6700\u540e\uff0c\u4e3a\u4e86\u5728\u5177\u4f53\u63a7\u5236\u4efb\u52a1\u4e2d\u8fdb\u4e00\u6b65\u63d0\u5347\u6027\u80fd\u4e0e\u5b89\u5168\u6027\uff0c\u6211\u4eec\u5728\u63a8\u7406\u9636\u6bb5\u8fdb\u884c\u5fae\u8c03\uff0c\u5e76\u518d\u6b21\u5c06\u4e0d\u786e\u5b9a\u6027\u5206\u4f4d<\/span><\/span><\/span>\u6570<\/span><\/span><\/span><\/span>Q<\/span><\/span>\u5f15\u5165\u5176\u4e2d\u3002<\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u5728\u7b2c\u4e00\u9636\u6bb5\uff0c\u6211\u4eec\u5bf9\u6269\u6563\u6a21\u578b\u8fdb\u884c\u9884\u8bad\u7ec3\uff0c\u5176\u65b9\u5f0f\u4e0e\u5e38\u89c4\u5229\u7528\u6269\u6563\u6a21\u578b\u8fdb\u884c\u63a7\u5236\u76f8\u540c <\/span><\/span><\/span>[<\/span><\/span><\/span>3<\/span><\/span><\/span>]<\/span><\/span><\/span>\u3002<\/span><\/span><\/span><\/span><\/section>\n

<\/span><\/section>\n
\u5728<\/span><\/span><\/span>\u7b2c<\/span><\/span><\/span>\u4e8c<\/span><\/span><\/span>\u9636\u6bb5<\/span><\/span><\/span>\uff0c\u6211\u4eec\u5229\u7528<\/span><\/span><\/span>\u4e0b\u5f0f\u7684<\/span><\/span><\/span>\u91cd\u52a0\u6743\u635f\u5931\u51fd\u6570\u8fdb\u884c<\/span><\/span><\/span>\u540e\u8bad\u7ec3<\/span><\/span><\/span>\uff0c\u5f15\u5230\u6a21\u578b\u7684\u751f\u6210\u6570\u636e\u5206\u5e03\u66f4\u7b26\u5408\u5b89\u5168\u3001\u63a7\u5236\u6548\u679c\u597d\u7684\u76ee\u6807\uff0c\u4ee5\u6b64\u51cf\u5c11\u6d4b\u8bd5\u65f6\u5fae\u8c03\u9700\u8981\u7684\u6b65\u6570\uff0c<\/span><\/span><\/span><\/span><\/section>\n

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\u5176\u4e2d<\/span><\/span><\/span><\/section>\n

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<\/p>\n
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\u4ee3\u8868\u4e86\u5bf9\u8003\u8651\u4e86\u4e0d\u786e\u5b9a\u6027\u7684\u5b89\u5168\u9650\u5236\u4ee5\u53ca\u63a7\u5236\u76ee\u6807\u7684\u52a0\u6743\u548c\u3002\u5982\u4ee5\u4e0b\u5b9a\u7406\u6240\u8ff0\uff0c\u901a\u8fc7\u8fd9\u4e2a\u635f\u5931\u51fd\u6570\u8fdb\u884c\u540e\u8bad\u7ec3\uff0c\u6211\u4eec\u80fd\u591f\u5f15\u5bfc\u6269\u6563\u6a21\u578b\u751f\u6210\u7684\u6570\u636e\u5206\u5e03\u96c6\u4e2d\u5230<\/span><\/span><\/span>e<\/span><\/span>-W<\/span><\/span>\u9ad8\u7684\u533a\u57df\u3002<\/span><\/span><\/span><\/section>\n

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\u5728<\/span><\/span><\/span>\u7b2c<\/span><\/span><\/span>\u4e09<\/span><\/span><\/span>\u9636\u6bb5<\/span><\/span><\/span>\uff0c\u6211\u4eec\u901a\u8fc7<\/span><\/span><\/span>\u63a8<\/span><\/span><\/span>\u7406\u65f6\u5fae\u8c03<\/span><\/span><\/span>\uff0c\u6765\u8fdb\u4e00\u6b65\u9488\u5bf9\u7279\u5b9a\u63a7\u5236\u4efb\u52a1\uff0c\u4f18\u5316\u6a21\u578b\u8f93\u51fa\u3002<\/span><\/span><\/span>\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u5728\u8fd9\u4e00\u9636\u6bb5\u8fed\u4ee3\u5730\u8fdb\u884c<\/span><\/span><\/span>\u5f15\u5bfc\u91c7\u6837<\/span><\/span><\/span>\uff08Guidance\uff09<\/span><\/span><\/span>\u4ee5\u53ca<\/span><\/span><\/span>\u5fae\u8c03<\/span><\/span><\/span>\uff08Fine-tuning\uff09<\/span><\/span><\/span>\uff0c\u6765<\/span><\/span><\/span>\u4f18<\/span><\/span><\/span>\u5316\u63a7\u5236\u7b56\u7565<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>\u5176\u4e2d<\/span><\/span><\/span>\uff0c\u91c7\u6837\u65f6\u7684\u5f15\u5bfc\u9879<\/span><\/span><\/span>\u4e3a<\/span><\/span><\/span><\/span><\/section>\n

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\u4e5f\u5c31\u662f\u6a21\u578b\u4f1a\u503e\u5411\u4e8e\u91c7\u6837<\/span><\/span><\/span>W<\/span><\/span>\u66f4\u5c0f\u7684\u63a7\u5236\u5e8f\u5217\u3002\u800c\u5fae\u8c03\u5219\u662f\u901a\u8fc7\u5bf9\u6a21\u578b\u53c2\u6570\u7684\u66f4\u65b0\u6765\u8c03\u6574\u6a21\u578b\u8f93\u51fa\u7684\u5206\u5e03\uff0c\u5177\u4f53\u7684\u5fae\u8c03\u635f\u5931\u51fd\u6570\u5982\u4e0b<\/span><\/span><\/span><\/section>\n

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\u540c\u6837\u610f\u5728\u8ba9\u6a21\u578b\u8f93\u51fa\u5206\u5e03\u5bf9\u5e94\u7684<\/span><\/span><\/span>W<\/span><\/span>\u66f4\u5c0f\u3002<\/span><\/span><\/span><\/section>\n

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\u56db\u3001\u5b9e\u9a8c\u9a8c\u8bc1\uff1a\u591a\u4e2a\u5b89\u5168\u63a7\u5236\u573a\u666f<\/span><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


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\u6211\u4eec\u5728\u4e09\u4e2a\u5177\u6709\u6311\u6218\u6027\u7684<\/span><\/span><\/span>\u5b89\u5168\u63a7\u5236\u573a\u666f<\/span><\/span><\/span>\u4e0a\u6d4b\u8bd5\u4e86<\/span><\/span><\/span>SafeDiffCon<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span><\/span><\/section>\n
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\u7cfb\u7edf<\/span><\/span><\/span><\/section>\n<\/td>\n
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\u5b89\u5168<\/span><\/span><\/span>\u9650\u5236<\/span><\/span><\/span><\/span><\/section>\n<\/td>\n
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\u63a7\u5236\u76ee\u6807<\/span><\/span><\/span><\/section>\n<\/td>\n<\/tr>\n
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1D Burgers \u65b9\u7a0b<\/span><\/span><\/span><\/section>\n<\/td>\n
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\u9650\u5236\u7cfb\u7edf<\/span><\/span><\/span>\u72b6\u6001<\/span><\/span><\/span>\u7684\u6700\u5927\u503c<\/span><\/span><\/span>\u4e0d\u8d85\u8fc7\u9608\u503c<\/span><\/span><\/span><\/span><\/section>\n<\/td>\n
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\u8ba9\u6700\u540e\u65f6\u523b\u7684\u7cfb\u7edf\u72b6\u6001\u8fbe\u5230\u76ee\u6807\u72b6\u6001<\/span><\/span><\/span><\/section>\n<\/td>\n<\/tr>\n
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2D\u4e0d\u53ef\u538b\u7f29\u6d41\u4f53<\/span><\/span><\/span><\/section>\n<\/td>\n
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\u907f\u514d<\/span><\/span><\/span>\u70df\u96fe<\/span><\/span><\/span>\u8fdb\u5165\u5371\u9669<\/span><\/span><\/span>\u533a\u57df<\/span><\/span><\/span><\/span><\/section>\n<\/td>\n
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\u6700\u5927\u5316\u70df\u96fe\u8fdb\u5165\u76ee\u6807\u51fa\u53e3\u7684\u6bd4\u4f8b<\/span><\/span><\/span><\/section>\n<\/td>\n<\/tr>\n
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Tokamak<\/span><\/span><\/span>\u78c1\u7ea6\u675f\u805a\u53d8<\/span><\/span><\/span><\/span><\/section>\n<\/td>\n
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\u7ea6\u675f<\/span><\/span><\/span>\u5b89\u5168\u56e0\u5b50<\/span><\/span><\/span><\/span>q<\/span><\/span>95<\/span><\/span>\u4e0d\u8d85\u8fc7\u9608\u503c<\/span><\/span><\/span><\/section>\n<\/td>\n
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\u8ba9<\/span><\/span><\/span>\u03b2<\/span><\/span>p<\/span><\/span>\u548c<\/span><\/span><\/span>l<\/span><\/span>i<\/span><\/span>\u8fbe\u5230\u76ee\u6807\u503c<\/span><\/span><\/span><\/section>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
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\u56fe<\/span><\/span><\/span>5<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span>1D Burgers \u65b9\u7a0b\u7684\u53ef\u89c6\u5316\u7ed3\u679c<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>\u4e0a\u6392\u5c55\u793a\u7684\u662f<\/span><\/span><\/span>\u6570\u636e\u96c6\u4e2d\u7684<\/span><\/span><\/span>\u539f\u59cb\u8f68\u8ff9\uff0c\u4e0b\u6392\u5c55\u793a\u7684\u662f\u7531<\/span><\/span><\/span>SafeDiffCon<\/span><\/span><\/span>\u63a7\u5236\u5f97\u5230\u7684\u8f68\u8ff9\u3002<\/span><\/span><\/span><\/span><\/span><\/section>\n
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\u56fe<\/span><\/span><\/span>6<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span>SafeDiffCon<\/span><\/span><\/span>\u63a7\u5236\u4e8c\u7ef4\u4e0d\u53ef\u538b\u7f29\u6d41\u4f53\u7684\u53ef\u89c6\u5316\u7ed3\u679c<\/span><\/span><\/span>\u3002<\/span><\/span><\/span>\u901a\u8fc7\u5728<\/span><\/span><\/span>\u8fb9\u6846<\/span><\/span><\/span><\/span>\u5916\u90e8\u65bd\u52a0\u63a7\u5236\uff0c\u70df\u96fe\u88ab\u6210\u529f\u5f15\u5bfc\u81f3\u4e2d\u592e\u9876\u90e8\u51fa\u53e3\uff0c\u540c\u65f6\u907f\u5f00\u4e86\u7ea2\u8272\u7684\u4e0d\u5b89\u5168\u533a\u57df\u3002<\/span><\/span><\/span><\/span><\/section>\n

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\u56fe<\/span><\/span><\/span>7<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span>SafeDiffCon<\/span><\/span><\/span>\u5728\u4ee3\u7406\u6a21\u578b\u4eff\u771f\u5668\u4e2d<\/span><\/span><\/span>\u63a7\u5236<\/span><\/span><\/span>\u6258\u5361\u9a6c\u514b\u7684\u53ef\u89c6\u5316\u7ed3\u679c\u3002<\/span><\/span><\/span>\u5de6\u56fe\u4e3a\u63a7\u5236\u540e\u7684<\/span><\/span><\/span><\/span><\/span>q<\/span><\/span>95<\/span><\/span>\u4ee5\u53ca\u8bbe\u5b9a\u7684\u5b89\u5168\u754c\u9650\uff0c\u53f3\u56fe\u4e3a\u6258\u514b\u9a6c\u514b\u88c5\u7f6e\u7684\u53ef\u89c6\u5316\u3002<\/span><\/span><\/span><\/section>\n

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\u5b9e\u9a8c\u7ed3\u679c<\/span><\/span><\/span>\u8868\u660e<\/span><\/span><\/span>\uff1a<\/span><\/span><\/span><\/span><\/section>\n