{"id":34380,"date":"2022-05-15T16:43:00","date_gmt":"2022-05-15T08:43:00","guid":{"rendered":"https:\/\/swarma.org\/?p=34380"},"modified":"2022-05-15T16:43:00","modified_gmt":"2022-05-15T08:43:00","slug":"%e5%bd%93%e7%89%a9%e7%90%86%e5%ad%a6%e9%81%87%e5%88%b0%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%ef%bc%9a%e5%9f%ba%e4%ba%8e%e7%89%a9%e7%90%86%e7%9f%a5%e8%af%86%e7%9a%84%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=34380","title":{"rendered":"\u5f53\u7269\u7406\u5b66\u9047\u5230\u673a\u5668\u5b66\u4e60\uff1a\u57fa\u4e8e\u7269\u7406\u77e5\u8bc6\u7684\u673a\u5668\u5b66\u4e60\u7efc\u8ff0"},"content":{"rendered":"
\n
\n
\n
\n
\n

<\/p>\n<\/section>\n

\n
\n
\n
\n
\n
\n

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

\u6458\u8981<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

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

\u7269\u7406\u4fe1\u606f\u673a\u5668\u5b66\u4e60\uff08Physics-informed machine learning\uff0cPIML\uff09\uff0c\u6307\u7684\u662f\u5c06\u7269\u7406\u5b66\u7684\u5148\u9a8c\u77e5\u8bc6\uff08\u5386\u53f2\u4e0a\u81ea\u7136\u73b0\u8c61\u548c\u4eba\u7c7b\u884c\u4e3a\u7684\u9ad8\u5ea6\u62bd\u8c61\uff09\uff0c\u4e0e\u6570\u636e\u9a71\u52a8\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u76f8\u7ed3\u5408\uff0c\u8fd9\u5df2\u7ecf\u6210\u4e3a\u7f13\u89e3\u8bad\u7ec3\u6570\u636e\u77ed\u7f3a\u3001\u63d0\u9ad8\u6a21\u578b\u6cdb\u5316\u80fd\u529b\u548c\u786e\u4fdd\u7ed3\u679c\u7684\u7269\u7406\u5408\u7406\u6027\u7684\u6709\u6548\u9014\u5f84\u3002\u5728\u672c\u6587\u4e2d\uff0c\u6211\u4eec\u8c03\u67e5\u4e86\u6700\u8fd1\u5728PIML\u65b9\u9762\u7684\u5927\u91cf\u5de5\u4f5c\uff0c\u5e76\u4ece\u4e09\u4e2a\u65b9\u9762\u8fdb\u884c\u4e86\u603b\u7ed3\uff1a\uff081\uff09PIML\u53d1\u5c55\u7684\u52a8\u673a\uff0c\uff082\uff09PIML\u4e2d\u7684\u7269\u7406\u77e5\u8bc6\uff0c\uff083\uff09PIML\u4e2d\u7684\u7269\u7406\u77e5\u8bc6\u6574\u5408\u65b9\u6cd5\u3002\u6211\u4eec\u8fd8\u8ba8\u8bba\u4e86\u5f53\u524dPIML\u7684\u6311\u6218\u548c\u76f8\u5e94\u7684\u7814\u7a76\u673a\u4f1a\u3002<\/span><\/strong><\/strong><\/p>\n


<\/p>\n

\u7814\u7a76\u9886\u57df\uff1a\u673a\u5668\u5b66\u4e60\uff0c\u7269\u7406\u5b66<\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n
\u200d\u200d<\/span><\/strong><\/section>\n<\/section>\n
\n

\u6f58\u4f73\u680b<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/strong><\/p>\n

\u6881\u91d1<\/span> <\/span>| \u5ba1\u6821<\/strong><\/span>
<\/strong><\/span><\/p>\n

\u9093\u4e00\u96ea<\/span> | \u7f16\u8f91<\/strong><\/span><\/strong><\/span><\/p>\n


<\/p>\n


<\/p>\n<\/section>\n

<\/p>\n

\n
\n
\n

\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/p>\n

When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learning<\/span><\/p>\n

\u8bba\u6587\u94fe\u63a5\uff1a<\/span><\/section>\n
https:\/\/arxiv.org\/abs\/2203.16797<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

 <\/span><\/p>\n


<\/section>\n

<\/h1>\n

\n
\n
\n
\n
\n

<\/section>\n

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

1. \u7b80\u4ecb\uff1a\u7269\u7406\u77e5\u8bc6\u5d4c\u5165\u673a\u5668\u5b66\u4e60<\/span><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u673a\u5668\u5b66\u4e60\/\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u5df2\u7ecf\u5728\u4e00\u4e9b\u9886\u57df\u53d6\u5f97\u4e86\u5de8\u5927\u7684\u6210\u529f\uff0c\u5982\u8ba1\u7b97\u673a\u89c6\u89c9[1-5]\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406[6-14]\uff0c\u5927\u91cf\u7684\u8bad\u7ec3\u6570\u636e\u548c\u9ad8\u8868\u73b0\u529b\u7684\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u7ed9\u51fa\u4e86\u8d85\u8d8a\u4e4b\u524d\u65b9\u6cd5\u7684\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6848\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u4eba\u5458\u4e5f\u5f00\u59cb\u63a2\u7d22\u5e94\u7528\u673a\u5668\u5b66\u4e60\u6a21\u578b\u6765\u63a8\u8fdb\u79d1\u5b66\u53d1\u73b0\u548c\u8fdb\u4e00\u6b65\u6539\u5584\u4f20\u7edf\u5206\u6790\u5efa\u6a21\u7684\u53ef\u80fd\u6027[15-21]\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u867d\u7136\u7ed9\u5b9a\u4e00\u7ec4\u8f93\u5165\u548c\u8f93\u51fa\u5bf9\uff0c\u6df1\u5ea6\u795e\u7ecf\u7f51\u7edc\u80fd\u591f\u5728\u5145\u5206\u7684\u5927\u91cf\u6570\u636e\u4e0a\u901a\u8fc7\u9002\u5f53\u7684\u4f18\u5316\u6765\u5f97\u5230\u8f93\u5165\u548c\u8f93\u51fa\u4e4b\u95f4\u7684\u590d\u6742\u5173\u7cfb\uff0c\u4f46\u5148\u9a8c\u77e5\u8bc6\u4ecd\u7136\u5728\u5bfb\u627e\u6700\u4f18\u89e3\u65b9\u9762\u8d77\u7740\u91cd\u8981\u4f5c\u7528\u3002\u4f5c\u4e3a\u5bf9\u6570\u636e\u5206\u5e03\u548c\u4efb\u52a1\u5c5e\u6027\u7684\u9ad8\u5c42\u6b21\u63d0\u53d6\uff0c\u5148\u9a8c\u77e5\u8bc6\u5982\u679c\u7eb3\u5165\u5f97\u5f53\uff0c\u53ef\u4ee5\u63d0\u4f9b\u5728\u6709\u9650\u7684\u8bad\u7ec3\u6570\u636e\u4e2d\u4e0d\u5b58\u5728\u6216\u96be\u4ee5\u63d0\u53d6\u7684\u4e30\u5bcc\u4fe1\u606f\uff0c\u5e76\u6709\u52a9\u4e8e\u63d0\u9ad8\u6570\u636e\u6548\u7387\u3001\u6cdb\u5316\u80fd\u529b\u548c\u4ea7\u751f\u6a21\u578b\u7684\u5408\u7406\u6027\u3002<\/strong><\/span><\/section>\n
 <\/span><\/section>\n
\u5728\u6f2b\u957f\u7684\u5386\u53f2\u4e2d\uff0c\u7269\u7406\u77e5\u8bc6\u5728\u7406\u8bba\u548c\u5b9e\u9a8c\u4e0a\u90fd\u5f97\u5230\u4e86\u660e\u786e\u7684\u6536\u96c6\u548c\u9a8c\u8bc1\uff0c\u5728\u8bb8\u591a\u91cd\u8981\u7684\u79d1\u5b66\u548c\u5de5\u7a0b\u5e94\u7528\u4e2d\u5305\u542b\u4e86\u5bf9\u81ea\u7136\u73b0\u8c61\u548c\u4eba\u7c7b\u884c\u4e3a\u7684\u62bd\u8c61\u548c\u603b\u7ed3\u3002\u56e0\u6b64\u672c\u6587\u91cd\u70b9\u8ba8\u8bba\u4e86\u5c06\u5148\u9a8c\u7269\u7406\u77e5\u8bc6\u6574\u5408\u5230\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4e2d\u7684\u8bfe\u9898\uff0c\u5373\u7269\u7406\u4fe1\u606f\u673a\u5668\u5b66\u4e60<\/strong><\/span>\uff08PIML\uff09<\/span>\u3002\u4e0e\u5176\u4ed6\u7c7b\u578b\u7684\u5148\u9a8c\u77e5\u8bc6\uff0c\u5982\u77e5\u8bc6\u56fe\u8c31\u3001\u903b\u8f91\u89c4\u5219\u548c\u4eba\u7c7b\u53cd\u9988[22]\u7684\u6574\u5408\u76f8\u6bd4\uff0c\u7531\u4e8e\u7269\u7406\u77e5\u8bc6\u7684\u7279\u6b8a\u5c5e\u6027\u548c\u5f62\u5f0f\uff0c\u7269\u7406\u77e5\u8bc6\u7684\u6574\u5408\u9700\u8981\u7279\u6b8a\u8bbe\u8ba1\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u672c\u6587\u8c03\u67e5\u4e86\u6700\u8fd1\u5728PIML\u65b9\u9762\u7684\u5927\u91cf\u5de5\u4f5c\uff0c\u5e76\u4ece\u4e09\u4e2a\u65b9\u9762\u5bf9\u5176\u8fdb\u884c\u603b\u7ed3\u3002(1) PIML\u7684\u52a8\u673a\uff0c\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5f52\u7c7b\u4e3a\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u6765\u670d\u52a1\u4e8e\u7269\u7406\u9886\u57df\u7684\u4efb\u52a1\uff0c\u548c\u5c06\u7269\u7406\u5b66\u539f\u7406\u878d\u5165\u5230\u73b0\u6709\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4e2d\u7528\u4e8e\u73b0\u5b9e\u4e16\u754c\u7684\u4efb\u52a1\u3002(2) PIML\u4e2d\u7684\u7269\u7406\u77e5\u8bc6\uff0c\u6bcf\u4e00\u7c7b\u90fd\u662f\u6db5\u76d6\u5e7f\u6cdb\u95ee\u9898\u7684\u4e00\u822c\u539f\u5219\u3002(3) PIML\u4e2d\u7269\u7406\u5b66\u77e5\u8bc6\u6574\u5408\u7684\u65b9\u6cd5\u3002\u6839\u636e\u77e5\u8bc6\u6574\u5408\u7684\u4f4d\u7f6e\uff0c\u6211\u4eec\u5c06\u8fd9\u4e9b\u65b9\u6cd5\u5206\u4e3a\u6570\u636e\u589e\u5f3a\u3001\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u8bbe\u8ba1\u548c\u7269\u7406\u4fe1\u606f\u4f18\u5316\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u672c\u6587\u7684\u7ed3\u6784\u5982\u4e0b\u3002\u7b2c2\u8282\u4f7f\u7528 PIML\u5206\u6790\u4e86\u4e24\u5927\u52a8\u673a\uff1a\u4e00\u7c7b\u4e3b\u8981\u670d\u52a1\u4e8e\u7269\u7406\u9886\u57df\u7684\u4efb\u52a1\uff0c\u53e6\u4e00\u7c7b\u670d\u52a1\u4e8e\u73b0\u5b9e\u4e16\u754c\u7684\u95ee\u9898\u3002\u7b2c3\u8282\u4ecb\u7ecd\u4e86PIML\u4e2d\u5e7f\u6cdb\u4f7f\u7528\u7684\u51e0\u4e2a\u901a\u7528\u7269\u7406\u539f\u7406\u3002\u7b2c4\u8282\u7814\u7a76\u7269\u7406\u77e5\u8bc6\u6574\u5408\u7684\u65b9\u6cd5\u3002\u7b2c5\u8282\u8ba8\u8bba\u4e86PIML\u7684\u6311\u6218\u548c\u6f5c\u5728\u7684\u672a\u6765\u7814\u7a76\u65b9\u5411\u3002\u7b2c6\u8282\u662f\u6574\u7bc7\u8bba\u6587\u7684\u603b\u7ed3\u3002<\/span><\/section>\n

\n
 <\/span><\/section>\n<\/h1>\n
 <\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

2. PIML\u7684\u52a8\u673a\uff1a<\/span><\/strong><\/strong><\/p>\n

\u7269\u7406\u7528\u4e8e\u673a\u5668\u5b66\u4e60\uff0c\u673a\u5668\u5b66\u4e60\u7528\u4e8e\u7269\u7406<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u7269\u7406\u79d1\u5b66\u95ee\u9898\u6d89\u53ca\u5404\u79cd\u6570\u636e\u5bc6\u96c6\u578b\u4efb\u52a1\uff0c\u5305\u62ec\u65f6\u7a7a\u6570\u636e\u5efa\u6a21\u3001\u56e0\u679c\u63a8\u7406\u3001\u8ba1\u7b97\u673a\u89c6\u89c9\u3001\u6982\u7387\u63a8\u7406\u7b49\u3002\u7531\u4e8e\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u5728\u8fd9\u4e9b\u4efb\u52a1\u4e2d\u53d6\u5f97\u4e86\u5de8\u5927\u7684\u6210\u529f\uff0c\u8fd1\u5e74\u6765\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u6a21\u578b\u6765\u4fc3\u8fdb\u7269\u7406\u5b66\u7684\u79d1\u5b66\u53d1\u73b0\u8d8a\u6765\u8d8a\u53d7\u5230\u5173\u6ce8\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u53e6\u4e00\u65b9\u9762\uff0c\u4e0e\u73b0\u6709\u7684\u57fa\u4e8e\u6570\u503c\u6216\u7eaf\u7269\u7406\u7684\u65b9\u6cd5\u76f8\u6bd4\uff0c\u57fa\u4e8e\u7269\u7406\u7684\u673a\u5668\u5b66\u4e60\u65b9\u6cd5\u5728\u7075\u6d3b\u6027\u3001\u901a\u7528\u6027\u548c\u8ba1\u7b97\u6210\u672c\u65b9\u9762\u5177\u6709\u4f18\u52bf\u3002\u540c\u65f6\uff0c\u5b83\u4eec\u4ecd\u7136\u5177\u6709\u7269\u7406\u4e0a\u7684\u5408\u7406\u6027\u3002\u672c\u8282\u4ecb\u7ecd\u4e86\u5c06\u673a\u5668\u5b66\u4e60\u7528\u4e8e\u82e5\u5e72\u7269\u7406\u76f8\u5173\u4efb\u52a1\u7684\u6700\u65b0\u8fdb\u5c55\uff0c\u5305\u62ec\u66ff\u4ee3\u6a21\u578b\u6a21\u62df\u3001\u6570\u636e\u9a71\u52a8\u7684PDE\u6c42\u89e3\u5668\u3001\u7269\u7406\u6a21\u578b\u7684\u53c2\u6570\u5316\u3001\u964d\u7ef4\u6a21\u578b\u548c\u77e5\u8bc6\u53d1\u73b0\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

3. PIML\u4e2d\u7684\u7269\u7406\u77e5\u8bc6<\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u672c\u8282\u4ecb\u7ecd\u4e86\u96c6\u6210\u5728PIML\u4e2d\u7684\u51e0\u7c7b\u901a\u7528\u7269\u7406\u77e5\u8bc6\u3002\u867d\u7136\u6709\u66f4\u591a\u7684\u9886\u57df\/\u4efb\u52a1\u7279\u5b9a\u7684\u77e5\u8bc6\u53ef\u4ee5\u7528\u4e8e\u76f8\u5e94\u7684\u89e3\u51b3\u65b9\u6848\uff0c\u4f46\u6211\u4eec\u5728\u672c\u8282\u4e2d\u4ecb\u7ecd\u7684\u6bcf\u4e2a\u7c7b\u522b\u90fd\u6db5\u76d6\u4e86\u5e7f\u6cdb\u7684\u95ee\u9898\uff0c\u5e76\u7ed9\u51fa\u4e86\u4e00\u7cfb\u5217\u666e\u904d\u9002\u7528\u7684\u89e3\u51b3\u9014\u5f84\uff0c\u800c\u4e0d\u662f\u4ec5\u4ec5\u89e3\u51b3\u4e00\u4e24\u4e2a\u7279\u5b9a\u4efb\u52a1\u7684\u65b9\u6848\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u9996\u5148\u662f\u7ecf\u5178\u529b\u5b66\u548c\u80fd\u91cf\u5b88\u6052\u5b9a\u5f8b<\/strong>\u3002\u725b\u987f\u529b\u5b66\u3001\u62c9\u683c\u6717\u65e5\u529b\u5b66\u548c\u54c8\u5bc6\u987f\u529b\u5b66\u662f\u63cf\u8ff0\u7ecf\u5178\u529b\u5b66\u7cfb\u7edf\u7684\u4e09\u79cd\u5178\u578b\u65b9\u6cd5\u3002\u725b\u987f\u529b\u5b66\u88ab\u5e7f\u6cdb\u7528\u4e8e\u63cf\u8ff0\u4f4d\u7f6e\u3001\u901f\u5ea6\u3001\u52a0\u901f\u5ea6\u548c\u529b\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u800c\u62c9\u683c\u6717\u65e5\u548c\u54c8\u5bc6\u987f\u529b\u5b66\u5219\u63d0\u4f9b\u4e86\u6709\u6548\u7684\u5de5\u5177\uff0c\u9075\u5b88\u52a8\u529b\u5b66\u7cfb\u7edf\u5efa\u6a21\u4e2d\u7684\u80fd\u91cf\u5b88\u6052\u5b9a\u5f8b\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u5176\u6b21\u662f\u5bf9\u79f0\u6027\u548c\u4e0d\u53d8\u91cf<\/strong>\u3002\u5b9a\u4e49\u5728\u4e00\u4e2a\u7269\u4f53\u6216\u7cfb\u7edf\u4e0a\u7684\u5bf9\u79f0\u6027\u662f\u4e00\u4e9b\u4fdd\u6301\u67d0\u4e9b\u5c5e\u6027\u4e0d\u53d8\u7684\u53d8\u6362\u3002\u5178\u578b\u7684\u5bf9\u79f0\u6027\u5305\u62ec\u89c6\u89c9\u5bf9\u8c61\u5206\u7c7b\u95ee\u9898\u4e2d\u7684\u79fb\u52a8\u3001\u5206\u5b50\u5c5e\u6027\u9884\u6d4b\u95ee\u9898\u4e2d\u7684\u65cb\u8f6c\u4ee5\u53ca\u7c92\u5b50\u7cfb\u7edf\u4e2d\u7684\u6392\u5217\u7ec4\u5408\u3002<\/span><\/section>\n
 <\/span><\/section>\n
PIML\u4e2d\u7684\u901a\u7528\u7269\u7406\u77e5\u8bc6\u8fd8\u5305\u62ec\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u6570\u503c\u65b9\u6cd5\u548cKoopman\u7406\u8bba<\/strong>\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

4. PIML\u7684\u65b9\u6cd5<\/span><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u673a\u5668\u5b66\u4e60\u95ee\u9898\u7684\u5178\u578b\u89e3\u51b3\u65b9\u6848\u6d89\u53ca\u4e09\u4e2a\u5173\u952e\u90e8\u5206\uff1a\u6570\u636e\u3001\u6a21\u578b<\/strong>\u548c\u4f18\u5316<\/strong>\uff0c\u6bcf\u4e2a\u90e8\u5206\u90fd\u53ef\u4ee5\u4e0e\u7269\u7406\u77e5\u8bc6\u76f8\u7ed3\u5408\u3002\u63a5\u4e0b\u6765\u7684\u90e8\u5206\u5206\u522b\u4ecb\u7ecd\u5c06\u7269\u7406\u77e5\u8bc6\u7ed3\u5408\u5230\u6bcf\u4e2a\u90e8\u5206\u7684\u73b0\u6709\u6280\u672f\u3002\u4f46\u662f\uff0c\u6211\u4eec\u5e94\u8be5\u6ce8\u610f\u5230\uff0c\u8fd9\u4e9b\u6280\u672f\u5e76\u4e0d\u662f\u76f8\u4e92\u6392\u65a5\u7684\uff1a\u7269\u7406\u77e5\u8bc6\u53ef\u4ee5\u96c6\u6210\u5230\u673a\u5668\u5b66\u4e60\u89e3\u51b3\u65b9\u6848\u7684\u591a\u4e2a\u90e8\u5206\u4e2d\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6211\u4eec\u6839\u636e\u7269\u7406\u77e5\u8bc6\u7684\u5f62\u5f0f\u548c\u6574\u5408\u65b9\u6cd5\u5bf9\u73b0\u6709\u7684\u5de5\u4f5c\u8fdb\u884c\u5206\u7c7b\u3002\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u5bf9\u4e8e\u5177\u6709\u5206\u6790\u5f62\u5f0f\u7684\u77e5\u8bc6\uff0c\u73b0\u6709\u7684\u5de5\u4f5c\u53ef\u4ee5\u5c06\u77e5\u8bc6\u6574\u5408\u5230\u6240\u6709\u4e09\u4e2a\u65b9\u9762\uff0c\u5305\u62ec\u6570\u636e\u3001\u6a21\u578b\u548c\u4f18\u5316\u3002\u7136\u800c\uff0c\u5173\u4e8e\u6574\u5408\u5176\u4ed6\u901a\u7528\u7c7b\u578b\u7269\u7406\u77e5\u8bc6\u7684\u7814\u7a76\u5de5\u4f5c\uff0c\u5305\u62ec\u80fd\u91cf\u5b88\u6052\u5b9a\u5f8b\u3001\u5bf9\u79f0\u6027\u3001\u504f\u5fae\u5206\u65b9\u7a0b\u7684\u6570\u503c\u65b9\u6cd5\u548cKoopman\u7406\u8bba\uff0c\u4e3b\u8981\u4fa7\u91cd\u4e8e\u5c06\u76f8\u5e94\u7684\u77e5\u8bc6\u7eb3\u5165\u8ba1\u7b97\u56fe\u3002\u4e3b\u8981\u539f\u56e0\u662f\u8fd9\u79cd\u901a\u7528\u7684\u7269\u7406\u77e5\u8bc6\u6709\u53ef\u80fd\u8f6c\u5316\u4e3a\u53ef\u91cd\u590d\u4f7f\u7528\u7684\u7f51\u7edc\u67b6\u6784\u4e2d\u7684\u5f52\u7eb3\u504f\u5dee\uff0c\u8fd9\u5728\u9884\u6d4b\u6027\u80fd\u548c\u6570\u636e\u6548\u7387\u65b9\u9762\u6bd4\u6570\u636e\u589e\u5f3a\u548c\u57fa\u4e8e\u7269\u7406\u77e5\u8bc6\u7684\u635f\u5931\u51fd\u6570\u6709\u4f18\u52bf\u3002\u8fd9\u662f\u7531\u4e8e (1) \u901a\u7528\u7684\u7269\u7406\u77e5\u8bc6\u9002\u7528\u4e8e\u5404\u79cd\u95ee\u9898\uff0c\u4ece\u800c\u5bfc\u81f4\u901a\u7528\u7684\u7f51\u7edc\u67b6\u6784\uff0c(2) \u4e0e\u4e3a\u7279\u5b9a\u9886\u57df\u95ee\u9898<\/span>\uff08\u5982\u5929\u6c14\u548c\u6e4d\u6d41\uff09<\/span>\u8bbe\u8ba1\u7684\u590d\u6742\u6570\u503c\u6a21\u62df\u5668\u76f8\u6bd4\uff0c\u5f52\u7eb3\u504f\u5dee\u5177\u6709\u66f4\u7b80\u5355\u7684\u5f62\u5f0f\uff0c\u53ef\u4ee5\u8f6c\u5316\u4e3a\u6709\u9650\u6570\u91cf\u7684\u4e0d\u540c\u53ef\u5fae\u7b97\u5b50\u7684\u7ec4\u5408\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

5. \u6311\u6218\u548c\u672a\u6765\u7684\u65b9\u5411<\/span><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u6311\u6218\u4e00\uff1a\u624b\u5de5\u9009\u62e9\u5bfc\u5165\u7684\u7269\u7406\u77e5\u8bc6<\/span><\/strong><\/section>\n
 <\/span><\/section>\n
\u73b0\u6709\u5de5\u4f5c\u9700\u8981\u5bf9\u4efb\u52a1\u7279\u5b9a\u9886\u57df\u7684\u4e13\u4e1a\u77e5\u8bc6\u6709\u6240\u4e86\u89e3\uff0c\u4ee5\u9009\u62e9\u6700\u5408\u9002\u7684\u7269\u7406\u5b66\u77e5\u8bc6\u3002\u867d\u7136\u8fd9\u80fd\u591f\u5229\u7528\u9886\u57df\u77e5\u8bc6\u7f13\u89e3\u7eaf\u6570\u636e\u9a71\u52a8\u65b9\u6cd5\u7684\u7f3a\u9677\uff0c\u4f46\u5b83\u7f3a\u4e4f\u6839\u636e\u4efb\u52a1\u786e\u5b9a\u6b63\u786e\u7269\u7406\u77e5\u8bc6\u7684\u7075\u6d3b\u6027\u3002\u56e0\u6b64\uff0c\u4e00\u4e2a\u7814\u7a76\u65b9\u5411\u662f\u81ea\u52a8\u8bc6\u522b\u8981\u7eb3\u5165\u7684\u9002\u5f53\u7684\u7269\u7406\u77e5\u8bc6\u3002\u8fd9\u9700\u8981\u5728\u7279\u5b9a\u9886\u57df\u7684\u77e5\u8bc6\u548c\u7eaf\u6570\u636e\u9a71\u52a8\u7684\u65b9\u5f0f\u4e4b\u95f4\u627e\u5230\u4e00\u4e2a\u4e2d\u95f4\u70b9\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6311\u6218\u4e8c\uff1a\u7f3a\u4e4fPIML\u65b9\u6cd5\u7684\u57fa\u51c6\u548c\u8bc4\u4f30<\/span><\/strong><\/section>\n
 <\/span><\/section>\n
\u7efc\u5408\u6027\u7684\u57fa\u51c6\u5df2\u7ecf\u663e\u793a\u51fa\u5bf9\u76f8\u5e94\u7814\u7a76\u9886\u57df\u53d1\u5c55\u7684\u5de8\u5927\u63a8\u52a8\u4f5c\u7528\u3002\u4f8b\u5982\uff0c\u8ba1\u7b97\u673a\u89c6\u89c9\u9886\u57df\u7684ImageNet Large Scale Visual Recognition Challenge<\/span>\uff08ILSVRC\uff09<\/span>[23]\u548cCommon Objects in Context<\/span>\uff08COCO\uff09<\/span>[24]\uff0c\u81ea\u7136\u8bed\u8a00\u5904\u7406\u9886\u57df\u7684Workshop on Statistical Machine Translation<\/span>\uff08WMT\uff09<\/span>[25]\u548c Stanford Question Answering Dataset<\/span>\uff08SQuAD\uff09<\/span>[26]\u3002\u7136\u800c\uff0c\u7531\u4e8e\u95ee\u9898\u8bbe\u7f6e\u7684\u590d\u6742\u6027\uff0cPIML\u4ecd\u7136\u7f3a\u4e4f\u8bc4\u4f30\u5404\u79cd\u77e5\u8bc6\u6574\u5408\u65b9\u6cd5\u7684\u5168\u9762\u57fa\u51c6\uff0c\u8fd9\u7ed9PIML\u7684\u53d1\u5c55\u5e26\u6765\u4e86\u969c\u788d\u3002\u9996\u5148\uff0cPIML\u4e2d\u7684\u5927\u591a\u6570\u95ee\u9898\u6765\u81ea\u4e8e\u7269\u7406\u6216\u5de5\u7a0b\u5e94\u7528\uff0c\u5728\u8fd9\u4e9b\u5e94\u7528\u4e2d\uff0c\u83b7\u53d6\u6570\u636e\u548c\u5f62\u5f0f\u5316\u4efb\u52a1\u5bf9\u4e8e\u6ca1\u6709\u9886\u57df\u77e5\u8bc6\u548c\u7ecf\u9a8c\u7684\u518d\u641c\u7d22\u8005\u6765\u8bf4\u53ef\u80fd\u662f\u4e00\u79cd\u6311\u6218\u3002\u5176\u6b21\uff0c\u73b0\u6709\u7684\u5de5\u4f5c\uff0c\u6709\u4e9b\u4e25\u91cd\u4f9d\u8d56\u7279\u5b9a\u9886\u57df\u6570\u636e\u96c6\uff0c\u8fd9\u5927\u5927\u589e\u52a0\u4e86\u516c\u5e73\u6bd4\u8f83\u4e0d\u540cPIML\u65b9\u6cd5\u7684\u96be\u5ea6\u3002\u6784\u5efaPIML\u7684\u7efc\u5408\u57fa\u51c6\u662f\u63a8\u52a8\u5176\u53d1\u5c55\u7684\u8feb\u5207\u9700\u8981\u3002<\/span><\/section>\n
 <\/span><\/section>\n
\u6311\u6218\u4e09\uff1a\u73b0\u6709\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u7684\u6b21\u4f18\u6027\u548cPIML\u7684\u4f18\u5316\u65b9\u6cd5<\/span><\/strong><\/section>\n
 <\/span><\/section>\n
\u795e\u7ecf\u7f51\u7edc\u67b6\u6784\u548c\u4f18\u5316\u65b9\u6cd5\u7684\u7406\u8bba\u548c\u7ecf\u9a8c\u7ed3\u8bba\u5927\u591a\u662f\u5728\u795e\u7ecf\u7f51\u7edc\u65b9\u6cd5\u9996\u5148\u83b7\u5f97\u4f18\u52bf\u7684\u9886\u57df\u53d1\u5c55\u8d77\u6765\u7684\uff0c\u5982\u8ba1\u7b97\u673a\u89c6\u89c9\u548c\u81ea\u7136\u8bed\u8a00\u5904\u7406\u3002\u7136\u800c\uff0c\u5b83\u4eec\u5728PIML\u4e2d\u53ef\u80fd\u4e0d\u518d\u6709\u6548\u3002\u539f\u56e0\u662fPIML\u65b9\u6cd5\u901a\u5e38\u6d89\u53ca\u5728\u524d\u5411\u8fc7\u7a0b\u548c\u76ee\u6807\u51fd\u6570\u4e2d\u660e\u786e\u4f7f\u7528\u68af\u5ea6\uff0c\u5bfc\u81f4\u5728\u53cd\u5411\u8fc7\u7a0b\u4e2d\u5b58\u5728\u9ad8\u9636\u5bfc\u6570\uff0c\u8fd9\u4f7f\u5f97\u4f18\u5316\u7a7a\u95f4\u7684\u5f62\u72b6\u4e0e\u5178\u578b\u7684\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u660e\u663e\u4e0d\u540c\u3002\u4f8b\u5982\uff0c\u5e38\u89c4\u7684\u53c2\u6570\u521d\u59cb\u5316\u65b9\u6cd5\uff0c\u5982Kaiming\u548cXavier\u662f\u4e0d\u591f\u7684\uff0c\u56e0\u4e3a\u4e0d\u5bfb\u5e38\u7684\u4f18\u5316\u76ee\u6807\u662f\u7279\u6b8a\u7684\u975e\u7ebf\u6027\u7684\u3002PIML\u7684\u65b0\u578b\u795e\u7ecf\u7f51\u7edc\u8bbe\u8ba1\u548c\u4f20\u7edf\u7684\u6df1\u5ea6\u5b66\u4e60\u4efb\u52a1\u5728\u7f51\u7edc\u7ed3\u6784\u548c\u76ee\u6807\u4e0a\u5b58\u5728\u5de8\u5927\u5dee\u5f02\uff0c\u8fd9\u610f\u5473\u7740PIML\u7684\u65b0\u578b\u795e\u7ecf\u7f51\u7edc\u8bbe\u8ba1\u5728\u7ed3\u6784\u548c\u4f18\u5316\u65b9\u9762\u90fd\u5f88\u91cd\u8981\u3002<\/span><\/section>\n

<\/section>\n
 <\/span><\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

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

6. \u603b\u7ed3<\/span><\/strong><\/strong><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

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


<\/p>\n

\u672c\u6587\u5bf9\u73b0\u6709\u7684PIML\u5de5\u4f5c\u8fdb\u884c\u4e86\u5f7b\u5e95\u548c\u5168\u9762\u7684\u8c03\u67e5\u3002\u6587\u7ae0\u4ece\u4e09\u4e2a\u65b9\u9762\u8fdb\u884c\u603b\u7ed3\uff1a\uff081\uff09PIML\u7684\u52a8\u673a\uff1b\uff082\uff09PIML\u4e2d\u7684\u7269\u7406\u77e5\u8bc6\uff1b\uff083\uff09PIML\u4e2d\u7684\u77e5\u8bc6\u6574\u5408\u65b9\u6cd5\u3002\u6700\u540e\u8ba8\u8bba\u4e86PIML\u7684\u73b0\u6709\u6311\u6218\uff0c\u5e76\u76f8\u5e94\u5730\u6307\u51fa\u4e86\u672a\u6765\u6f5c\u5728\u7684\u7814\u7a76\u65b9\u5411\u3002\u6211\u4eec\u5e0c\u671b\u672c\u6587\u80fd\u6210\u4e3aPIML\u7528\u6237\u9009\u62e9\u5408\u9002\u7684\u7269\u7406\u77e5\u8bc6\u548c\u9002\u5f53\u7684\u6574\u5408\u65b9\u6cd5\u7684\u6307\u5357\uff0c\u4e5f\u80fd\u6210\u4e3aPIML\u7814\u7a76\u8005\u786e\u5b9a\u73b0\u6709\u5dee\u8ddd\u548c\u6709\u524d\u666f\u7684\u7814\u7a76\u65b9\u5411\u7684\u6307\u5357\u3002<\/span><\/section>\n
 <\/span><\/section>\n
 <\/span><\/section>\n
\n
\n
\n

\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n
\n
\n

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

[1]  Yann LeCun, Le\u0301on Bottou, Yoshua Bengio, and Patrick Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86(11):2278\u20132324, 1998.<\/span><\/section>\n
[2] Alex Krizhevsky,Ilya Sutskever, and Geoffrey E.Hinton. Imagenet classification with deep convolutional neural networks. In Advances in neural information processing systems, pages 1097\u20131105, 2012.<\/span><\/section>\n
[3]  Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770\u2013778, 2016.<\/span><\/section>\n
[4]  Joseph Redmon, Santosh Divvala, Ross Girshick, and Ali Farhadi. You only look once: Unified, real-time object detection. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 779\u2013788, 2016.<\/span><\/section>\n
[5]  Kaiming He, Georgia Gkioxari, Piotr Dolla\u0301r, and Ross Girshick. Mask r-cnn. In Proceedings of the IEEE international conference on computer vision, pages 2961\u20132969, 2017.<\/span><\/section>\n
[6]  Tomas Mikolov, Kai Chen, Greg Corrado, and Jeffrey Dean. Efficient estimation of word representations in vector space. International Conference on Learning Representations, 2013.<\/span><\/section>\n
[7]  Richard Socher, Alex Perelygin, Jean Wu, Jason Chuang, Christopher D Manning, Andrew Y Ng, and Christopher Potts. Recursive deep models for semantic compositionality over a sentiment treebank. In Proceedings of the 2013 conference on empirical methods in natural language processing, pages 1631\u20131642, 2013.<\/span><\/section>\n
[8]  Ilya Sutskever, Oriol Vinyals, and Quoc V Le. Sequence to sequence learning with neural networks. Advances in Neural Information Processing Systems, 2014.<\/span><\/section>\n
[9]  Yoon Kim. Convolutional neural networks for sentence classification. In Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP), pages 1746\u20131751, Doha, Qatar, October 2014. Association for Computational Linguistics.<\/span><\/section>\n
[10]  Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473, 2014.<\/span><\/section>\n
[11]  Ankit Kumar, Ozan Irsoy, Peter Ondruska, Mohit Iyyer, James Bradbury, Ishaan Gulrajani, Victor Zhong, Romain Paulus, and Richard Socher. Ask me anything: Dynamic memory networks for natural language processing. In International conference on machine learning, pages 1378\u20131387. PMLR, 2016.<\/span><\/section>\n
[12]  Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, \u0141 ukasz Kaiser, and Illia Polosukhin. Attention is all you need. In I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett, editors, Advances in Neural Information Processing Systems, volume 30, pages 5998\u20136008. Curran Associates, Inc., 2017.<\/span><\/section>\n
[13]  Matthew E Peters, Mark Neumann, Mohit Iyyer, Matt Gardner, Christopher Clark, Kenton Lee, and Luke Zettlemoyer. Deep contextualized word representations. arXiv preprint arXiv:1802.05365, 2018.<\/span><\/section>\n
[14]  Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. BERT: Pre-training of deep bidirectional transformers for language understanding. In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pages 4171\u20134186, Minneapolis, Minnesota, June 2019. Association for Computational Linguistics.<\/span><\/section>\n
[15]  William W Hsieh. Machine learning methods in the environmental sciences: Neural networks and kernels. Cambridge university press, 2009.<\/span><\/section>\n
[16]Z\u030celjkoIvezic \u0301,AndrewJConnolly,JacobTVanderPlas,andAlexanderGray. Statistics,datamining,and machine learning in astronomy: a practical Python guide for the analysis of survey data, volume 1. Princeton University Press, 2014.<\/span><\/section>\n
[17]  Anuj Karpatne, Gowtham Atluri, James H Faghmous, Michael Steinbach, Arindam Banerjee, Auroop Ganguly, Shashi Shekhar, Nagiza Samatova, and Vipin Kumar. Theory-guided data science: A new paradigm for scien- tific discovery from data. IEEE Transactions on knowledge and data engineering, 29(10):2318\u20132331, 2017.<\/span><\/section>\n
[18]  Anuj Karpatne, Imme Ebert-Uphoff, Sai Ravela, Hassan Ali Babaie, and Vipin Kumar. Machine learning for the geosciences: Challenges and opportunities. IEEE Transactions on Knowledge and Data Engineering, 31(8):1544\u20131554, 2018.<\/span><\/section>\n
[19]  J Nathan Kutz. Deep learning in fluid dynamics. Journal of Fluid Mechanics, 814:1\u20134, 2017.<\/span><\/section>\n
[20]  Markus Reichstein, Gustau Camps-Valls, Bjorn Stevens, Martin Jung, Joachim Denzler, Nuno Carvalhais, et al. Deep learning and process understanding for data-driven earth system science. Nature, 566(7743):195\u2013204, 2019.<\/span><\/section>\n
[21] Zhen Wang,Hai bin Di,Muhammad Amir Shafiq,Yazeed Alaudah,and Ghassan AlRegib. Successful leveraging of image processing and machine learning in seismic structural interpretation: A review. The Leading Edge, 37(6):451\u2013461, 2018. <\/span><\/section>\n
[22]  Laura von Rueden, Sebastian Mayer, Katharina Beckh, Bogdan Georgiev, Sven Giesselbach, Raoul Heese, Birgit Kirsch, Julius Pfrommer, Annika Pick, Rajkumar Ramamurthy, et al. Informed machine learning\u2013a taxonomy and survey of integrating knowledge into learning systems. arXiv preprint arXiv:1903.12394, 2019. <\/span><\/section>\n
[23]Olga Russakovsky, Jia Deng, Hao Su, Jonathan Krause, Sanjeev Satheesh, Sean Ma, Zhiheng Huang, Andrej Karpathy, Aditya Khosla, Michael Bernstein, Alexander C. Berg, and Li Fei-Fei. ImageNet Large Scale Visual Recognition Challenge. International Journal of Computer Vision (IJCV), 115(3):211\u2013252, 2015.     <\/span><\/section>\n
[24]Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dolla\u0301r, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In European conference on computer vision, pages 740\u2013755. Springer, 2014.<\/span><\/section>\n
[25]Ond\u02c7rej Bojar, Christian Buck, Christian Federmann, Barry Haddow, Philipp Koehn, Johannes Leveling, Christof Monz, Pavel Pecina, Matt Post, Herve Saint-Amand, et al. Findings of the 2014 workshop on sta- tistical machine translation. In Proceedings of the ninth workshop on statistical machine translation, pages 12\u201358, 2014.<\/span><\/section>\n
[26]Pranav Rajpurkar, Jian Zhang, Konstantin Lopyrev, and Percy Liang. Squad: 100, 000+ questions for machine comprehension of text. In EMNLP, 2016.    <\/span><\/section>\n


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

\n
\n

\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


<\/section>\n

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

\u590d\u6742\u79d1\u5b66\u6700\u65b0\u8bba\u6587<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n


<\/p>\n<\/section>\n

\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>
<\/p>\n

<\/p>\n

\n


<\/p>\n


<\/p>\n<\/section>\n

\n

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