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 \/>\u88681\u603b\u7ed3\u4e86\u4ee5\u4e0a\u4e09\u4e2a\u4f8b\u5b50\u7684\u57fa\u672c\u7279\u5f81\u3002\u53ef\u4ee5\u770b\u51fa\uff0c\u65e0\u8bba\u662f\u4ece\u95ee\u9898\u6027\u8d28\u3001\u5b66\u4e60\u5bf9\u8c61\u3001\u8ba1\u7b97\u8fc7\u7a0b\uff0c\u8fd8\u662f\u76ee\u6807\u51fd\u6570\u7684\u89d2\u5ea6\uff0c\u8fd9\u4e09\u4e2a\u95ee\u9898\u770b\u8d77\u6765\u90fd\u6beb\u65e0\u5173\u8054\u3002\u7136\u800c\uff0c\u5b83\u4eec\u5176\u5b9e\u90fd\u662f\u5fae\u5206\u7f16\u7a0b\u7684\u7279\u4f8b\uff1a\u6211\u4eec\u7a7f\u8fc7\u6574\u4e2a\u8ba1\u7b97\u8fc7\u7a0b\u6c42\u5bfc\uff0c\u5f97\u5230\u76ee\u6807\u51fd\u6570\u76f8\u5bf9\u4e8e\u5b66\u4e60\u5bf9\u8c61\u7684\u68af\u5ea6\uff0c\u4ece\u800c\u89e3\u51b3\u95ee\u9898\u3002<img loading=\"lazy\" class=\"rich_pages\" data-ratio=\"0.4824165915238954\" data-s=\"300,640\"  data-type=\"png\" data-w=\"1109\" height=\"495\" style=\"box-sizing: border-box !important;width: 750px !important;visibility: visible !important;\" width=\"1080\" src=\"\/wp-content\/uploads\/2021\/02\/wxsync-2021-02-af4e5eddd0fe96635e40445ded41c8c0.png\"  \/>\u88681 \u4e09\u4e2a\u5fae\u5206\u7f16\u7a0b\u5b9e\u4f8b\u7684\u57fa\u672c\u7279\u5f81\u548c\u901a\u5e38\u7684\u6df1\u5ea6\u5b66\u4e60\u95ee\u9898\u4e0d\u540c\uff0c\u56fe1(a\uff0cb)\u8fd9\u4e24\u4e2a\u4f8b\u5b50\u4e2d\u90fd\u5305\u542b\u9488\u5bf9\u7279\u5b9a\u7269\u7406\u9886\u57df\u7684\u8ba1\u7b97\u8fc7\u7a0b(\u6c42\u89e3\u859b\u5b9a\u8c14\u65b9\u7a0b\u548c\u725b\u987f\u65b9\u7a0b)\u3002\u53e6\u5916\uff0c\u8bfb\u8005\u4e5f\u8bb8\u6ce8\u610f\u5230\u4e86\uff0c\u5728\u8fd9\u4e24\u4e2a\u4f8b\u5b50\u4e2d\u751a\u81f3\u90fd\u6ca1\u6709\u8c08\u5230\u8bad\u7ec3\u6570\u636e\u3002\u4e8b\u5b9e\u4e0a\uff0c\u6709\u4e0d\u5c11\u79d1\u5b66\u95ee\u9898\u90fd\u662f\u5982\u6b64\u3002\u6211\u4eec\u5e76\u4e0d\u80fd\u591f\u3001\u4e5f\u4e0d\u9700\u8981\u4e8b\u5148\u51c6\u5907\u5927\u91cf\u7684\u8bad\u7ec3\u6570\u636e\u3002\u5bf9\u4e8e\u79d1\u5b66\u95ee\u9898\uff0c\u201c\u4e00\u4e2a\u597d\u7684\u6a21\u578b\u80dc\u8fc7\u4e00\u5343\u4e2a\u6570\u636e\u201d[7]\u3002\u800c\u5fae\u5206\u7f16\u7a0b\u5c06\u6a21\u578b\u8868\u8fbe\u6210\u8ba1\u7b97\u673a\u7a0b\u5e8f\uff0c\u518d\u5229\u7528\u68af\u5ea6\u4fe1\u606f\u5b66\u4e60\u5176\u4e2d\u7684\u672a\u77e5\u6210\u5206\u3002\u8fd9\u80cc\u540e\u7684\u5173\u952e\u65e2\u4e0d\u662f\u5927\u6570\u636e\uff0c\u4e5f\u4e0d\u662f\u795e\u7ecf\u7f51\u7edc\uff0c\u800c\u662f\u81ea\u52a8\u5fae\u5206\u3002<\/p>\n<p>03\u4ec0\u4e48\u662f\u81ea\u52a8\u5fae\u5206\uff1f<\/p>\n<p><br  \/>\u987e\u540d\u601d\u4e49\uff0c\u81ea\u52a8\u5fae\u5206\u5c31\u662f\u81ea\u52a8\u5316\u5730\u8ba1\u7b97\u7a0b\u5e8f\u7684\u8f93\u51fa\u76f8\u5bf9\u4e8e\u8f93\u5165\u7684\u5bfc\u6570\u3002\u8fd9\u9879\u6280\u672f\u7684\u672c\u8d28\u662f\u673a\u68b0\u5730\u5bf9\u8ba1\u7b97\u8fc7\u7a0b\u4f7f\u7528\u94fe\u5f0f\u6cd5\u5219\uff0c\u4ece\u800c\u5f97\u5230\u6570\u503c\u7cbe\u786e\u7684\u5bfc\u6570\u4fe1\u606f\u3002\u6211\u4eec\u53ef\u4ee5\u7528\u8ba1\u7b97\u56fe\u6765\u5f62\u8c61\u5316\u5730\u8868\u8fbe\u7a0b\u5e8f\u8fd0\u884c\u548c\u81ea\u52a8\u5fae\u5206\u7684\u8fc7\u7a0b\u3002\u8ba1\u7b97\u56fe\u662f\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe(directed acyclic graph)\uff0c\u5176\u4e2d\u7684\u8282\u70b9\u548c\u7bad\u5934\u4ee3\u8868\u7a0b\u5e8f\u8fd0\u884c\u65f6\u53d8\u91cf\u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u3002\u56fe2\u5c55\u793a\u4e86\u4e00\u7c7b\u5178\u578b\u7684\u8ba1\u7b97\u56fe\u3002\u5176\u4e2d\u53d8\u91cf x1&nbsp;\u4ee3\u8868\u7a0b\u5e8f\u8f93\u5165\uff0cx2\uff0cx3&nbsp;\u662f\u8ba1\u7b97\u4e2d\u95f4\u7ed3\u679c\uff0c\u03b81\uff0c\u03b82\u662f\u7a0b\u5e8f\u7684\u53c2\u6570\u3002\u6700\u540e\uff0c\u8ba1\u7b97\u56fe\u672b\u7aef\u7684\u8282\u70b9L \u4ee3\u8868\u7a0b\u5e8f\u8f93\u51fa\u7684\u6807\u91cf\u635f\u5931\u51fd\u6570\u3002\u56fe1\u4e2d\u7684\u4e09\u4e2a\u4f8b\u5b50\u6240\u5bf9\u5e94\u7684\u8ba1\u7b97\u56fe\u90fd\u5177\u6709\u8fd9\u6837\u7684\u7ed3\u6784[8]\u3002<\/p>\n<p>\u4e3a\u4e86\u8003\u8651\u81ea\u52a8\u5fae\u5206\uff0c\u6211\u4eec\u5b9a\u4e49\u8ba1\u7b97\u56fe\u4e2d\u67d0\u4e00\u53d8\u91cf&nbsp;x&nbsp;\u7684\u68af\u5ea6\u4e3a\u5176\u4f34\u968f\u53d8\u91cf(adjoint variable)\uff0c\u8bb0\u4e3a<img class=\"rich_pages\" data-ratio=\"1.2702702702702702\" data-s=\"300,640\" data-type=\"png\" data-w=\"37\"  style=\"text-align: center;box-sizing: border-box !important;width: 20px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2021\/02\/wxsync-2021-02-5845d1e2043cdcae27243d325afc2c85.png\"  \/>= \u2202L\/\u2202x\u3002\u81ea\u52a8\u5fae\u5206\u7684\u76ee\u7684\u662f\u628a\u8ba1\u7b97\u56fe\u6700\u672b\u7aef&nbsp;<img class=\"rich_pages\" data-ratio=\"1.0357142857142858\" data-s=\"300,640\" data-type=\"png\" data-w=\"56\"  style=\"text-align: center;box-sizing: border-box !important;width: 23px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2021\/02\/wxsync-2021-02-e895493d3dd99052647c001daa703807.png\"  \/>= 1 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 \/><img class=\"rich_pages\" data-ratio=\"0.4502288329519451\" data-s=\"300,640\" data-type=\"png\" data-w=\"1748\"  style=\"box-sizing: border-box !important;width: 750px !important;visibility: visible !important;\" src=\"\/wp-content\/uploads\/2021\/02\/wxsync-2021-02-ff321ddf298254bcaa8c790056a64e0c.png\"  \/>\u56fe2 \u8ba1\u7b97\u56fe\u8868\u8fbe\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u53d8\u91cf\u4e4b\u95f4\u7684\u4f9d\u8d56\u5173\u7cfb\u3002\u81ea\u52a8\u5fae\u5206\u65b9\u6cd5\u56de\u6eaf\u8ba1\u7b97\u56fe\uff0c\u5f97\u5230\u7a0b\u5e8f\u8f93\u51fa\u76f8\u5bf9\u4e8e\u6240\u6709\u53d8\u91cf\u7684\u68af\u5ea6<br  \/>\u81ea\u52a8\u5fae\u5206\u76f8\u5bf9\u4e8e\u4f7f\u7528\u6570\u503c\u5dee\u5206\u7684\u65b9\u6cd5\u8ba1\u7b97\u68af\u5ea6\u6709\u4e0d\u5c11\u4f18\u70b9\u3002\u9996\u5148\uff0c\u5b83\u53ef\u4ee5\u4fdd\u8bc1\u8ba1\u7b97\u7684\u68af\u5ea6\u662f\u6570\u503c\u7cbe\u786e\u7684\uff0c\u800c\u4e0d\u4f9d\u8d56\u4e8e\u989d\u5916\u7684\u5dee\u5206\u53c2\u6570\u3002\u5176\u6b21 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mode)\u7684\u81ea\u52a8\u5fae\u5206\u3002\u5b9e\u73b0\u53cd\u5411\u6a21\u5f0f\u7684\u81ea\u52a8\u5fae\u5206\u5f80\u5f80\u9700\u8981\u4ed8\u51fa\u989d\u5916\u7684\u5b58\u50a8\u4ee3\u4ef7\uff0c\u4ee5\u8bb0\u5f55\u524d\u5411\u8ba1\u7b97\u65f6\u7684\u4e2d\u95f4\u53d8\u91cf\u4fe1\u606f\u3002\u8fd8\u6709\u4e00\u7c7b\u524d\u5411\u6a21\u5f0f(forward 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 \/>\u5fae\u5206\u7f16\u7a0b\u5e76\u4e0d\u662f\u4e00\u4e2a\u4ece\u5929\u800c\u964d\u7684\u5d2d\u65b0\u65b9\u6cd5\u3002\u79d1\u5b66\u5bb6\u65e9\u572820\u4e16\u7eaa50\u300160\u5e74\u4ee3\u5c31\u5f00\u59cb\u63a2\u7d22\u5bf9\u4e8e\u8ba1\u7b97\u673a\u7a0b\u5e8f\u7684\u81ea\u52a8\u5fae\u5206[2,3]\u3002\u5728\u63a7\u5236\u548c\u53cd\u5411\u8bbe\u8ba1\u7b49\u9886\u57df\uff0c\u4e5f\u65e9\u5df2\u5b58\u5728\u4e0e\u5fae\u5206\u7f16\u7a0b\u5bc6\u5207\u76f8\u5173\u7684\u4f34\u968f\u53d8\u91cf\u65b9\u6cd5\u3002\u800c\u7269\u7406\u5b66\u5bb6\u719f\u77e5\u7684\u5fae\u6270\u8bba\u548c\u7ebf\u6027\u54cd\u5e94\u7406\u8bba\uff0c\u53ef\u4ee5\u8bf4\u5c31\u662f\u7a7f\u8fc7\u7269\u7406\u8fc7\u7a0b\u7684\u5fae\u5206\u8ba1\u7b97\u3002\u5982\u4eca\uff0c\u5728\u57fa\u4e8e\u5f20\u91cf\u8fd0\u7b97\u7684\u81ea\u52a8\u5fae\u5206\u5e94\u7528\u2014\u2014\u6df1\u5ea6\u5b66\u4e60\u2014\u2014\u6210\u4e3a\u4e00\u95e8\u663e\u5b66\u7684\u65f6\u4ee3\uff0c\u5fae\u5206\u7f16\u7a0b\u83b7\u5f97\u4e86\u957f\u8db3\u7684\u8fdb\u6b65\u548c\u66f4\u666e\u904d\u7684\u5173\u6ce8\u3002\u5b83\u4e5f\u7ed9\u7269\u7406\u5b66\u4e2d\u7684\u5efa\u6a21\u3001\u4f18\u5316\u3001\u63a7\u5236\u548c\u53cd\u5411\u8bbe\u8ba1\u95ee\u9898\u63d0\u4f9b\u4e86\u4e00\u4e2a\u7edf\u4e00\u800c\u7075\u6d3b\u7684\u7814\u7a76\u65b9\u6cd5\u3002\u4e0b\u9762\u6211\u4eec\u5206\u522b\u4e3e\u4f8b\u8bf4\u660e\u3002&nbsp;&nbsp;<\/p>\n<p>4.1\u5efa\u6a21\u95ee\u9898<br 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2020\uff0carXiv:2003.04617<\/p>\n<p>\uff08\u53ef\u4e0a\u4e0b\u6ed1\u52a8\u6d4f\u89c8\uff09<\/p>\n<p>\u590d\u6742\u79d1\u5b66\u6700\u65b0\u8bba\u6587<\/p>\n<p>\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science\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<br  \/><img class=\"rich_pages\" data-ratio=\"0.3088962108731466\" data-s=\"300,640\" data-type=\"png\" data-w=\"1214\"  style=\"box-sizing: border-box !important;visibility: visible 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