{"id":10006223,"date":"2022-08-16T20:58:22","date_gmt":"2022-08-16T12:58:22","guid":{"rendered":"https:\/\/ityet.com\/?p=10006223"},"modified":"2022-08-16T20:58:22","modified_gmt":"2022-08-16T12:58:22","slug":"%e5%89%8d%e7%ab%af%e6%99%ba%e8%83%bd%e5%8c%96%e5%ae%9e%e8%b7%b5-%e5%8f%af%e5%be%ae%e7%bc%96%e7%a8%8b","status":"publish","type":"post","link":"https:\/\/itmax.cn\/?p=10006223","title":{"rendered":"\u524d\u7aef\u667a\u80fd\u5316\u5b9e\u8df5\u2014\u2014\u53ef\u5fae\u7f16\u7a0b"},"content":{"rendered":"<p>\u7b80\u4ecb\uff1a\u00a0\u7814\u7a76\u8005\u8868\u793a\uff0c\u7531\u4e8e\u5e7f\u6cdb\u7684\u79d1\u5b66\u8ba1\u7b97\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u5728\u5e95\u5c42\u7ed3\u6784\u4e0a\u90fd\u9700\u8981\u7ebf\u6027\u4ee3\u6570\u7684\u652f\u6301\uff0c\u56e0\u6b64\u6709\u53ef\u80fd\u4ee5\u53ef\u5fae\u7f16\u7a0b\u7684\u5f62\u5f0f\uff0c\u521b\u9020\u4e00\u79cd\u65b0\u7684\u7f16\u7a0b\u601d\u60f3\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5c31\u4e00\u8d77\u8fdb\u5165\u8fd9\u4e2a\u5168\u65b0\u7684\u9886\u57df\u3002\u00a0\u4ec0\u4e48\u662f\u53ef\u5fae\u7f16\u7a0b\u901a\u8fc7\u52a8\u753b\u3001\u52a8\u6548\u589e\u52a0 UI \u8868\u73b0\u529b\uff0c\u4f5c\u4e3a\u524d\u7aef\u6216\u591a\u6216\u5c11\u90fd\u505a\u8fc7\u3002\u8fd9\u91cc\u4ee5\u5f39\u6027\u963b\u5c3c\u52a8\u753b\u7684\u51fd\u6570\u4e3a\u4f8b\uff1a<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328405\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u51fd\u6570\u5728<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328406\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u65f6\u662f\u6548\u679c\u6700\u597d\u7684\u3002\u6700\u7ec8\uff0c\u5b9e\u73b0\u6210 JavaScript \u4ee3\u7801\uff1a<br \/>function damping(x, max) {<br \/>  let y = Math.abs(x);<br \/>  \/\/ \u4e0b\u9762\u7684\u53c2\u6570\u90fd\u662f\u6765\u6e90\u4e8e\u516c\u5f0f\u7528\u6570\u503c\u62df\u5408\u7684\u7ed3\u679c<br \/>  y = 0.82231 * max \/ (1 + 4338.47 \/ Math.pow(y, 1.14791));<br \/>  return Math.round(x &lt; 0 ? -y : y);<br \/>}<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328407\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u5982\u56fe 1 \u6240\u793a\uff0c2019 \u5e74 Julia Computing \u56e2\u961f\u53d1\u8868\u8bba\u6587\u300aA Differentiable Programming System to Bridge Machine Learning and Scientific Computing\u300b\u8868\u793a\u4ed6\u4eec\u6784\u5efa\u4e86\u4e00\u79cd\u53ef\u5fae\u7f16\u7a0b\u7cfb\u7edf\uff0c\u5b83\u80fd\u5c06\u81ea\u52a8\u5fae\u5206\u5185\u5d4c\u4e8e Julia \u8bed\u8a00\uff0c\u4ece\u800c\u5c06\u5176\u4f5c\u4e3a Julia \u8bed\u8a00\u7684\u7b2c\u4e00\u516c\u6c11\u3002\u5982\u679c\u5c06\u53ef\u5fae\u7f16\u7a0b\u7cfb\u7edf\u89c6\u4e3a\u7f16\u7a0b\u8bed\u8a00\u7b2c\u4e00\u516c\u6c11\uff0c\u90a3\u4e48\u4e0d\u8bba\u662f\u673a\u5668\u5b66\u4e60\u8fd8\u662f\u5176\u5b83\u79d1\u5b66\u8ba1\u7b97\u90fd\u5c06\u65b9\u4fbf\u4e0d\u5c11\u3002Y Combinator Research \u7814\u7a76\u8005 Michael Nielsen \u5bf9\u6b64\u975e\u5e38\u5174\u594b\uff0c\u975e\u5e38\u8d5e\u540c Andrej Karpathy \u7684\u89c2\u70b9\u3002Karpathy \u8bf4\uff1a\u300c\u6211\u4eec\u6b63\u5411\u524d\u8fc8\u51fa\u4e86\u4e00\u6b65\uff0c\u4e0e\u539f\u6765\u5bf9\u7a0b\u5e8f\u6709\u5b8c\u6574\u7684\u5b9a\u4e49\u4e0d\u540c\uff0c\u6211\u4eec\u73b0\u5728\u53ea\u662f\u5199\u4e00\u4e2a\u5927\u81f4\u7684\u89e3\u51b3\u95ee\u9898\u7684\u6846\u67b6\uff0c\u8fd9\u6837\u7684\u6846\u67b6\u4f1a\u901a\u8fc7\u6743\u91cd\u628a\u89e3\u51b3\u8fc7\u7a0b\u53c2\u6570\u5316\u3002\u5982\u679c\u6211\u4eec\u6709\u4e00\u4e2a\u597d\u7684\u8bc4\u4f30\u6807\u51c6\uff0c\u90a3\u4e48\u6700\u4f18\u5316\u7b97\u6cd5\u5c31\u80fd\u5e2e\u6211\u4eec\u627e\u5230\u66f4\u597d\u7684\u89e3\uff08\u53c2\u6570\uff09\u3002\u300d\u00a0\u8fd9\u91cc Karpathy \u8bf4\u7684\u5c31\u662f\u4f20\u7edf\u7f16\u7a0b\u548c\u53ef\u5fae\u7f16\u7a0b\u7684\u533a\u522b\uff0c\u53ef\u5fae\u7f16\u7a0b\u4f1a\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u7b49\u6700\u4f18\u5316\u65b9\u6cd5\u81ea\u52a8\u641c\u7d22\u6700\u4f18\u89e3\u3002\u4f46\u8fd9\u91cc\u6709\u4e2a\u95ee\u9898\uff0c\u7a0b\u5e8f\u9700\u8981\u68af\u5ea6\u624d\u80fd\u5411\u7740\u6700\u4f18\u524d\u8fdb\uff0c\u56e0\u6b64\u7a0b\u5e8f\u7684\u5f88\u591a\u90e8\u5206\u90fd\u8981\u6c42\u662f\u53ef\u5fae\u7684\u3002\u9274\u4e8e\u8fd9\u4e00\u70b9\uff0c\u5f88\u591a\u4eba\u4e5f\u5c31\u5c06\u673a\u5668\u5b66\u4e60\uff08ML\uff09\u79f0\u547c\u4e3a\u53ef\u5fae\u7f16\u7a0b\u4e86\u3002\u00a0\u4f46\u662f\u53ef\u5fae\u7f16\u7a0b\u53ea\u80fd\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u5417\uff1f\u5b83\u80fd\u4e0d\u80fd\u6269\u5c55\u5230\u5176\u5b83\u9886\u57df\uff0c\u751a\u81f3\u6210\u4e3a\u7f16\u7a0b\u8bed\u8a00\u7684\u57fa\u672c\u7279\u6027\uff1f\u7b54\u6848\u662f\u53ef\u4ee5\u7684\uff0c\u8fd9\u5c31\u662f Julia \u56e2\u961f\u53ca MIT \u7b49\u5176\u4ed6\u7814\u7a76\u673a\u6784\u6b63\u5728\u5c1d\u8bd5\u7684\u3002\u8fd1\u5e74\u6765\uff0c\u673a\u5668\u5b66\u4e60\u6a21\u578b\u8d8a\u6765\u8d8a\u7cbe\u5999\uff0c\u5c55\u73b0\u51fa\u4e86\u5f88\u591a\u79d1\u5b66\u8ba1\u7b97\u7684\u7279\u6027\uff0c\u4fa7\u9762\u51f8\u663e\u4e86\u673a\u5668\u5b66\u4e60\u6846\u67b6\u7684\u5f3a\u5927\u80fd\u529b\u3002\u7814\u7a76\u8005\u8868\u793a\uff0c\u7531\u4e8e\u5e7f\u6cdb\u7684\u79d1\u5b66\u8ba1\u7b97\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u5728\u5e95\u5c42\u7ed3\u6784\u4e0a\u90fd\u9700\u8981\u7ebf\u6027\u4ee3\u6570\u7684\u652f\u6301\uff0c\u56e0\u6b64\u6709\u53ef\u80fd\u4ee5\u53ef\u5fae\u7f16\u7a0b\u7684\u5f62\u5f0f\uff0c\u521b\u9020\u4e00\u79cd\u65b0\u7684\u7f16\u7a0b\u601d\u60f3\u3002\u4e0b\u9762\uff0c\u6211\u4eec\u5c31\u4e00\u8d77\u8fdb\u5165\u8fd9\u4e2a\u5168\u65b0\u7684\u9886\u57df\u3002\u00a0\u2590 \u00a0\u53ef\u5fae\u7f16\u7a0b\u548c\u81ea\u52a8\u5fae\u5206\u7684\u5173\u7cfb\u00a0\u5728\u5f00\u59cb\u53ef\u5fae\u7f16\u7a0b\u4e4b\u524d\uff0c\u6211\u60f3\u5148\u7b80\u5355\u56de\u987e\u4e00\u4e0b\u4e4b\u524d\u8ba1\u7b97\u5f39\u6027\u963b\u5c3c\u7684\u4f8b\u5b50\u3002\u4f60\u4f1a\u53d1\u73b0<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328408\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><\/p>\n<p><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328409\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><\/p>\n<p><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328410\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u6570\u503c\u5fae\u5206\u6cd5\uff1a<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328411\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u53ea\u8981 h \u53d6\u5f88\u5c0f\u7684\u6570\u503c\uff0c\u6bd4\u59820.0001\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5f88\u65b9\u4fbf\u6c42\u89e3\u5bfc\u6570\uff0c\u5e76\u4e14\u53ef\u4ee5\u5bf9\u7528\u6237\u9690\u85cf\u6c42\u89e3\u8fc7\u7a0b\uff0c\u7528\u6237\u53ea\u8981\u7ed9\u51fa\u76ee\u6807\u51fd\u6570\u548c\u8981\u6c42\u89e3\u7684\u68af\u5ea6\u7684\u53d8\u91cf\uff0c\u7a0b\u5e8f\u53ef\u4ee5\u81ea\u52a8\u7ed9\u51fa\u76f8\u5e94\u7684\u68af\u5ea6\uff0c\u8fd9\u4e5f\u662f\u67d0\u79cd\u610f\u4e49\u4e0a\u7684\u201c\u81ea\u52a8\u5fae\u5206\u201d\u3002\u800c\u6211\u4eec\u5728 H5 \u5f39\u6027\u963b\u5c3c\u51fd\u6570\u7684\u6c42\u89e3\u8fc7\u7a0b\u4e2d\uff0c\u4f7f\u7528\u7684\u6b63\u5f0f\u8fd9\u79cd\u201c\u81ea\u52a8\u5fae\u5206\u201d\u6280\u672f\u3002\u6570\u503c\u5fae\u5206\u6cd5\u7684\u5f0a\u7aef\u5728\u4e8e\u8ba1\u7b97\u91cf\u5927\uff0c\u7531\u4e8e\u662f\u505a\u62df\u5408\u76f8\u5f53\u4e8e\u6211\u4eec\u8981\u628a\u516c\u5f0f<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328412\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u7b26\u53f7\u5fae\u5206\uff08Symbolic Differentiation\uff09\u5c5e\u7b26\u53f7\u8ba1\u7b97\u7684\u8303\u7574\uff0c\u5176\u8ba1\u7b97\u7ed3\u679c\u662f\u5bfc\u51fd\u6570\u7684\u8868\u8fbe\u5f0f\u3002\u7b26\u53f7\u8ba1\u7b97\u7528\u4e8e\u6c42\u89e3\u6570\u5b66\u4e2d\u7684\u516c\u5f0f\u89e3\uff08\u4e5f\u79f0\u89e3\u6790\u89e3\uff09\u3002\u548c\u524d\u6587\u6570\u503c\u89e3\u4e0d\u540c\u7684\u662f\uff0c\u901a\u8fc7\u7b26\u53f7\u4f4d\u5206\u5f97\u5230\u7684\u662f\u89e3\u7684\u8868\u8fbe\u5f0f\u800c\u975e\u5177\u4f53\u7684\u6570\u503c\u3002\u6839\u636e\u57fa\u672c\u51fd\u6570\u7684\u6c42\u5bfc\u516c\u5f0f\u4ee5\u53ca\u56db\u5219\u8fd0\u7b97\u3001\u590d\u5408\u51fd\u6570\u7684\u6c42\u5bfc\u6cd5\u5219\uff0c\u7b26\u53f7\u5fae\u5206\u7b97\u6cd5\u53ef\u4ee5\u5f97\u5230\u4efb\u610f\u53ef\u5fae\u51fd\u6570\u7684\u5bfc\u6570\u8868\u8fbe\u5f0f\u3002\u00a0<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328413\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u7136\u540e\u5c06\u81ea\u53d8\u91cf\u7684\u503c\u4ee3\u5165\u5bfc\u6570\u516c\u5f0f\uff0c\u5f97\u5230\u4efb\u610f\u70b9\u5904\u7684\u5bfc\u6570\u503c\u3002\u7b26\u53f7\u5fae\u5206\u8ba1\u7b97\u51fa\u7684\u8868\u8fbe\u5f0f\u9700\u8981\u7528\u5b57\u7b26\u4e32\u6216\u5176\u4ed6\u6570\u636e\u7ed3\u6784\u5b58\u50a8\uff0c\u5982\u8868\u8fbe\u5f0f\u6811\u3002\u6570\u5b66\u8f6f\u4ef6\u5982 Mathematica\uff0cMaple\uff0cmatlab \u4e2d\u5b9e\u73b0\u4e86\u8fd9\u79cd\u6280\u672f\uff0cpython \u8bed\u8a00\u7684\u7b26\u53f7\u8ba1\u7b97\u5e93\u4e5f\u63d0\u4f9b\u4e86\u8fd9\u7c7b\u7b97\u6cd5\u3002\u00a0\u5bf9\u4e8e\u6df1\u5c42\u590d\u5408\u51fd\u6570\uff0c\u5982\u673a\u5668\u5b66\u4e60\u4e2d\u795e\u7ecf\u7f51\u7edc\u7684\u6620\u5c04\u51fd\u6570\uff0c\u7b26\u53f7\u5fae\u5206\u7b97\u6cd5\u5f97\u5230\u7684\u5bfc\u6570\u8ba1\u7b97\u516c\u5f0f\u5c06\u4f1a\u975e\u5e38\u5197\u957f\u3002\u8fd9\u79cd\u5197\u957f\u7684\u60c5\u51b5\uff0c\u6211\u4eec\u79f0\u4e3a\u8868\u8fbe\u5f0f\u81a8\u80c0\uff08expression swell\uff09\u3002\u5bf9\u4e8e\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5e94\u7528\uff0c\u4e0d\u9700\u8981\u5f97\u5230\u5bfc\u6570\u7684\u8868\u8fbe\u5f0f\uff0c\u800c\u53ea\u9700\u8ba1\u7b97\u51fd\u6570\u5728\u67d0\u4e00\u70b9\u5904\u7684\u5bfc\u6570\u503c\uff0c\u4ece\u800c\u4ee5\u53c2\u6570\u7684\u5f62\u5f0f\u66f4\u65b0\u795e\u7ecf\u5143\u7684\u6743\u91cd\u3002\u56e0\u6b64\uff0c\u7b26\u53f7\u5fae\u5206\u5728\u8ba1\u7b97\u5197\u4f59\u4e14\u6210\u672c\u9ad8\u6602\u3002\u4f8b\u5982\uff1a\u5bf9\u4e8e\u516c\u5f0f<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328414\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u00a0\u5982\u679c\u91c7\u7528\u7b26\u53f7\u5fae\u5206\u7b97\u6cd5\uff0c\u5f53n=1,2,3,4\u65f6\u7684 ln \u53ca\u5176\u5bfc\u6570\u5982\u56fe 3 \u6240\u793a\u3002<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328415\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u81ea\u52a8\u5fae\u5206\u4e0d\u540c\u4e8e\u6570\u503c\u5fae\u5206\u548c\u7b26\u53f7\u4f4d\u5206\uff0c\u5b83\u662f\u4ecb\u4e8e\u7b26\u53f7\u5fae\u5206\u548c\u6570\u503c\u5fae\u5206\u4e4b\u95f4\u7684\u4e00\u79cd\u65b9\u6cd5\u3002\u6570\u503c\u5fae\u5206\u4e00\u5f00\u59cb\u5c31\u4ee3\u5165\u6570\u503c\u8fd1\u4f3c\u6c42\u89e3\uff0c\u800c\u7b26\u53f7\u5fae\u5206\u76f4\u63a5\u5bf9\u8868\u8fbe\u5f0f\u8fdb\u884c\u63a8\u5bfc\uff0c\u6700\u540e\u624d\u4ee3\u5165\u81ea\u53d8\u91cf\u7684\u503c\u5f97\u5230\u6700\u7ec8\u89e3\u3002\u81ea\u52a8\u5fae\u5206\u5219\u662f\u5c06\u7b26\u53f7\u5fae\u5206\u5e94\u7528\u4e8e\u6700\u57fa\u672c\u7684\u8fd0\u7b97\uff08\u6216\u79f0\u539f\u5b50\u64cd\u4f5c\uff09\uff0c\u5982\u5e38\u6570\uff0c\u5e42\u51fd\u6570\uff0c\u6307\u6570\u51fd\u6570\uff0c\u5bf9\u6570\u51fd\u6570\uff0c\u4e09\u89d2\u51fd\u6570\u7b49\u57fa\u672c\u51fd\u6570\uff0c\u4ee3\u5165\u81ea\u53d8\u91cf\u7684\u503c\u5f97\u5230\u5176\u5bfc\u6570\u503c\uff0c\u4f5c\u4e3a\u4e2d\u95f4\u7ed3\u679c\u8fdb\u884c\u4fdd\u7559\u3002\u7136\u540e\uff0c\u518d\u6839\u636e\u8fd9\u4e9b\u57fa\u672c\u8fd0\u7b97\u5355\u5143\u7684\u6c42\u5bfc\u7ed3\u679c\u8ba1\u7b97\u51fa\u6574\u4e2a\u51fd\u6570\u7684\u5bfc\u6570\u503c\u3002\u00a0\u81ea\u52a8\u5fae\u5206\u7684\u7075\u6d3b\u5f3a\uff0c\u53ef\u5b9e\u73b0\u5b8c\u5168\u5411\u7528\u6237\u9690\u85cf\u6c42\u5bfc\u8fc7\u7a0b\uff0c\u7531\u4e8e\u5b83\u53ea\u5bf9\u57fa\u672c\u51fd\u6570\u6216\u5e38\u6570\u8fd0\u7528\u7b26\u53f7\u5fae\u5206\u6cd5\u5219\uff0c\u56e0\u6b64\u53ef\u4ee5\u7075\u6d3b\u5730\u7ed3\u5408\u7f16\u7a0b\u8bed\u8a00\u7684\u5faa\u73af\u3001\u5206\u652f\u7b49\u7ed3\u6784\uff0c\u6839\u636e\u94fe\u5f0f\u6cd5\u5219\uff0c\u501f\u52a9\u4e8e\u8ba1\u7b97\u56fe\u8ba1\u7b97\u51fa\u4efb\u610f\u590d\u6742\u51fd\u6570\u7684\u5bfc\u6570\u503c\u3002\u7531\u4e8e\u5b58\u5728\u4e0a\u8ff0\u4f18\u70b9\uff0c\u8be5\u65b9\u6cd5\u5728\u73b0\u4ee3\u6df1\u5ea6\u5b66\u4e60\u5e93\u4e2d\u5f97\u5230\u5e7f\u6cdb\u4f7f\u7528\u3002Julia \u7684\u8bba\u6587\u5b9e\u73b0\u7684 zygote \u5de5\u5177\u8fdb\u884c\u7684\u53ef\u5fae\u7f16\u7a0b\uff0c\u7814\u7a76\u4eba\u5458\u5b9a\u4e49\u4e86\u4e00\u4e2a\u635f\u5931\u51fd\u6570\uff0c\u5c06\u70b9\u5149\u6e90\u4f5c\u4e3a\u8f93\u5165\u5728\u56fe\u50cf\u4e0a\u4ea7\u751f\u5149\u7167\uff0c\u5982\u56fe 4 \u6240\u793a\u548c\u53c2\u8003\u56fe\u50cf\u8fdb\u884c\u5bf9\u6bd4\u3002\u901a\u8fc7\u53ef\u5fae\u7f16\u7a0b\u7684\u65b9\u5f0f\u81ea\u52a8\u8ba1\u7b97\u548c\u63d0\u53d6\u68af\u5ea6\uff0c\u5e76\u7528\u4e8e\u66f4\u65b0\u70b9\u5149\u6e90\u7684\u4f4d\u7f6e\uff1ajulia&gt; guess = PointLight(Vec3(1.0), 20000.0, Vec3(1.0, 2.0, -7.0))<br \/>julia&gt; function loss_function(light)<\/p>\n<pre><code>       rendered_color = raytrace(origin, direction, scene, light, eye_pos)\n       rendered_img = process_image(rendered_color, screen_size.w,\n                                    screen_size.h)\n       return mean((rendered_img .- reference_img).^2)\n   end<\/code><\/pre>\n<p>julia&gt; gs = gradient(x -&gt; loss_function(x, image), guess)<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328416\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u53ef\u5fae\u7f16\u7a0b\u5b9e\u73b0\u667a\u80fd\u5e94\u7528\u7a0b\u5e8f\u00a0\u5728 Julia \u4e4b\u540e Swift \u4e5f\u63a8\u51fa\u4e86\u81ea\u5df1\u7684\u53ef\u5fae\u7f16\u7a0b\uff0c\u5bf9\uff0c\u4f60\u6ca1\u542c\u9519\uff0c\u5c31\u662f Apple \u5e94\u7528\u5f00\u53d1\u63a8\u8350\u7f16\u7a0b\u8bed\u8a00 Swift\u3002\u5728 Swift \u7684\u53ef\u5fae\u7f16\u7a0b\u63d0\u6848\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u63d0\u51fa\u4e86\u201c\u667a\u80fd\u5e94\u7528\u7a0b\u5e8f\u201d\u7684\u6982\u5ff5\u3002\u667a\u80fd\u5e94\u7528\u7a0b\u5e8f\u5f88\u667a\u80fd\uff1a\u5b83\u4eec\u4f7f\u7528\u673a\u5668\u5b66\u4e60\u6280\u672f\u6765\u589e\u5f3a\u7528\u6237\u4f53\u9a8c\u3002\u667a\u80fd\u5e94\u7528\u7a0b\u5e8f\u53ef\u4ee5\u501f\u52a9\u53ef\u5fae\u7f16\u7a0b\u7684\u5f3a\u5927\u80fd\u529b\uff0c\u5bf9\u5e94\u7528\u7684\u884c\u4e3a\u505a\u51fa\u9884\u6d4b\u3001\u63d0\u4f9b\u5efa\u8bae\u5e76\u4e86\u89e3\u7528\u6237\u504f\u597d\uff0c\u6839\u636e\u7528\u6237\u504f\u597d\u667a\u80fd\u8c03\u6574\u5e94\u7528\u7684\u884c\u4e3a\u3002\u00a0\u667a\u80fd\u5e94\u7528\u7684\u6838\u5fc3\u662f\u53ef\u5fae\u7f16\u7a0b\uff0c\u81ea\u52a8\u5fae\u5206\u53ef\u7528\u4e8e\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u7cfb\u7edf\u5730\u4f18\u5316\uff08\u5373\u627e\u5230\u201c\u597d\u201d\u503c\uff09\u53c2\u6570\u3002\u901a\u8fc7\u4f20\u7edf\u7f16\u7a0b\u601d\u60f3\u7684\u7b97\u6cd5\u4f18\u5316\uff0c\u8fd9\u4e9b\u53c2\u6570\u901a\u5e38\u5f88\u96be\u5904\u7406\uff0c\u8981\u4e48\u662f\u7c7b\u4f3c\u6570\u503c\u5fae\u5206\u548c\u7b26\u53f7\u5fae\u5206\u4e2d\u90a3\u6837\u53c2\u6570\u592a\u591a\uff0c\u8981\u4e48\u662f\u96be\u4ee5\u548c\u5e94\u7528\u7684\u884c\u4e3a\u505a\u5173\u8054\u3002\u4f8b\u5982\uff0c\u6211\u4eec\u8981\u5f00\u53d1\u4e00\u4e2a\u667a\u80fd\u64ad\u653e\u5668\uff0c\u5b83\u5c1d\u8bd5\u6839\u636e\u64ad\u653e\u5668\u5185\u5bb9\u7c7b\u578b\u548c\u64ad\u653e\u5668\u7684\u7528\u6237\u504f\u597d\u81ea\u52a8\u8c03\u6574\u64ad\u653e\u901f\u5ea6\u3002<br \/>enum PodcastCategory {<\/p>\n<pre><code>case comedy\ncase news\n...<\/code><\/pre>\n<p>}<\/p>\n<p>enum PodcastSection {<\/p>\n<pre><code>case advertisement\ncase introduction\ncase body\ncase conclusion<\/code><\/pre>\n<p>}<\/p>\n<p>struct PodcastState {<\/p>\n<pre><code>let category: PodcastCategory\nlet section: PodcastSection<\/code><\/pre>\n<p>}<\/p>\n<p>struct PodcastSpeedModel {<\/p>\n<pre><code>var minSpeed, maxSpeed: Float\nvar categoryMultipliers: [PodcastCategory: Float]\nvar sectionMultipliers: [PodcastSection: Float]\n\n\/\/\/ Returns a podcast speed multiplier prediction for the given podcast category\n\/\/\/ and section.\nfunc prediction(for state: PodcastState) -&gt; Float {\n    let speed = categoryMultipliers[state.category] * sectionMultipliers[state.section]\n    if speed &lt; minSpeed { return minSpeed }\n    if speed &gt; maxSpeed { return maxSpeed }\n    return speed\n}<\/code><\/pre>\n<p>}\u6b64\u64ad\u653e\u5668\u7684\u64ad\u653e\u901f\u5ea6\u53c2\u6570\u4e3a\uff1aminSpeed\u3001maxSpeed\u3001\u00a0categoryMultipliers\u548csectionMultipliers\u3002\u6839\u636e\u6211\u4eec\u7684\u7ecf\u9a8c\u6765\u5224\u65ad\u7684\u8bdd\uff0c\u4ec0\u4e48\u662f\u597d\u7684\u53c2\u6570\uff1f\u4e0d\u540c\u7684\u7528\u6237\u53ef\u80fd\u4f1a\u6709\u4e0d\u540c\u7684\u7b54\u6848\uff0c\u65e0\u6cd5\u6839\u636e\u7528\u6237\u504f\u597d\u8bbe\u5b9a\u4e0d\u540c\u7684\u53c2\u6570\u503c\u3002\u667a\u80fd\u5e94\u7528\u7a0b\u5e8f\u53ef\u4ee5\u501f\u52a9\u53ef\u5fae\u7f16\u7a0b\u6765\u786e\u5b9a\u4e2a\u6027\u5316\u7684\u53c2\u6570\u503c\uff0c\u5982\u4e0b\uff1a\u8ba9\u7528\u6237\u624b\u52a8\u8bbe\u7f6e\u901f\u5ea6\uff0c\u5e76\u5728\u7528\u6237\u6539\u53d8\u901f\u5ea6\u65f6\u8bb0\u5f55\u89c2\u5bdf\u7ed3\u679c\u7684\u53c2\u6570\u503c\u3002\u5728\u6536\u96c6\u5230\u8db3\u591f\u7684\u89c2\u5bdf\u503c\u540e\uff0c\u641c\u7d22\u53c2\u6570\u503c\uff0c\u4f7f\u6a21\u578b\u9884\u6d4b\u7684\u901f\u5ea6\u63a5\u8fd1\u7528\u6237\u7684\u9996\u9009\u901f\u5ea6\u3002\u5982\u679c\u627e\u5230\u8fd9\u6837\u7684\u503c\uff0c\u64ad\u653e\u5668\u4f1a\u4ea7\u751f\u9884\u6d4b\u5e76\u81ea\u52a8\u8bbe\u7f6e\u901f\u5ea6\u3002\u201c\u68af\u5ea6\u4e0b\u964d\u201d\u662f\u6267\u884c\u8fd9\u79cd\u641c\u7d22\u7684\u7b97\u6cd5\uff0c\u800c\u652f\u6301\u53ef\u5fae\u7f16\u7a0b\u7684\u8bed\u8a00\u53ef\u4ee5\u5f88\u5bb9\u6613\u5730\u5b9e\u73b0\u68af\u5ea6\u4e0b\u964d\u3002\u8fd9\u662f\u4e00\u4e9b\u8bf4\u660e\u68af\u5ea6\u4e0b\u964d\u7684\u4f2a\u4ee3\u7801\uff1a<br \/>\/\/ \u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u68af\u5ea6\u4e0b\u964d\u7684\u76ee\u6807\u51fd\u6570\u6765\u6700\u5c0f\u5316\uff0c\u8fd9\u91cc\u4f7f\u7528\u5e73\u5747\u7edd\u5bf9\u8bef\u5dee\uff1a<br \/>struct Observation {<\/p>\n<pre><code>var podcastState: PodcastState\nvar userSpeed: Float<\/code><\/pre>\n<p>}<\/p>\n<p>func meanError(for model: PodcastSpeedModel, _ observations: [Observation]) -&gt; Float {<\/p>\n<pre><code>var error: Float = 0\nfor observation in observations {\n    error += abs(model.prediction(for: observation.podcastState) - observation.userSpeed)\n}\nreturn error \/ Float(observations.count)<\/code><\/pre>\n<p>}<br \/>\/\/ \u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5b9e\u73b0\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u3002<br \/>var model = PodcastModel()<br \/>let observations = storage.observations()<br \/>for _ in 0..&lt;1000 {<\/p>\n<pre><code>\/\/ The language differentiates `meanError` to get a &quot;gradient&quot;, which is a value indicating\n\/\/ how to change `model` in order to decrease the value of `meanError`.\nlet gradient = gradient(at: model) { meanError(for: $0, observations) }\n\n\/\/ Change `model` in the direction that decreased the value of `meanError`.\nmodel -= 0.01 * gradient<\/code><\/pre>\n<p>}\u81f3\u6b64\uff0c\u6211\u4eec\u5c31\u4f7f\u7528\u53ef\u5fae\u7f16\u7a0b\u7684\u80fd\u529b\u5b9e\u73b0\u4e86\u667a\u80fd\u5e94\u7528\u7684\u5173\u952e\u90e8\u5206\uff0c\u8fd9\u4e2a\u5e94\u7528\u4f1a\u968f\u7740\u7528\u6237\u5b9e\u9645\u4f7f\u7528\u8fc7\u7a0b\u8d8a\u6765\u8d8a\u667a\u80fd\u3001\u8d8a\u6765\u8d8a\u61c2\u7528\u6237\u7684\u504f\u597d\uff0c\u4ece\u800c\u81ea\u52a8\u5e2e\u52a9\u7528\u6237\u8bbe\u7f6e\u64ad\u653e\u901f\u5ea6\u3002\u00a0\u9664\u4e86\u7528\u53ef\u5fae\u7f16\u7a0b\u6765\u5b9e\u73b0\u524d\u6587\u4e2d\u64ad\u653e\u901f\u5ea6\u667a\u80fd\u5316\u63a7\u5236\u5916\uff0c\u52a8\u753b\u53c2\u6570\u7684\u53d8\u5316\u7387\u3001\u4f7f\u7528\u7269\u7406\u65b9\u7a0b\u5728\u6e38\u620f\u5f15\u64ce\u4e2d\u7684\u53ef\u5fae\u51fd\u6570\u5efa\u6a21\u3001\u6e38\u620f\u4e2d\u7684 NPC \u7528\u53ef\u5fae\u7f16\u7a0b\u5b9e\u73b0\u548c\u73a9\u5bb6\u4e4b\u95f4\u667a\u80fd\u7684\u4e92\u52a8\u3001\u6d41\u4f53\u548c\u5176\u4ed6\u7269\u7406\u8fc7\u7a0b\u7684\u6a21\u62df\u6280\u672f\u57fa\u4e8e\u7528\u5bfc\u6570\u5b9a\u4e49\u7684\u65b9\u7a0b\u7684\u8fd1\u4f3c\u89e3\u7b49\u7b49\u3002\u673a\u5668\u4eba\u548c\u673a\u68b0\u5de5\u7a0b\u4e2d\u4f7f\u7528\u7684\u81ea\u52a8\u63a7\u5236\u7b97\u6cd5\u4e5f\u4f9d\u8d56\u4e8e\u5bf9\u5173\u8282\u548c\u5176\u4ed6\u7269\u7406\u7cfb\u7edf\u7684\u884c\u4e3a\u8fdb\u884c\u5efa\u6a21\uff0c\u53ef\u5fae\u7f16\u7a0b\u53ef\u4ee5\u8f7b\u677e\u5f97\u5230\u8fd9\u4e9b\u6a21\u578b\u51fd\u6570\u7684\u5bfc\u6570\u3002\u53ea\u8981\u4f60\u613f\u610f\uff0c\u4f60\u51e0\u4e4e\u53ef\u4ee5\u5728\u6240\u6709\u7f16\u7a0b\u573a\u666f\u91cc\u7528\u53ef\u5fae\u7f16\u7a0b\u7684\u601d\u60f3\u6765\u667a\u80fd\u5316\u89e3\u51b3\u95ee\u9898\u3002\u00a0\u7528\u5de5\u5177\u65b9\u7a0b\u62df\u5408\u5b8c\u6574\u7684\u4ee3\u7801\u53ef\u4ee5\u4ece\uff1a<a href=\"https:\/\/link.segmentfault.com\/?enc=BMtwikcPPLwfkGqOe4%2FYvg%3D%3D.QgFF26CJCZPecXfJxjrgBdK1weJB5gFTXnyTOi3A2%2FFEAqB5%2F9HWz5wzBzjPT7w7\" rel=\"nofollow\">https:\/\/github.com\/JunreyCen\/&#8230;<\/a>\u8fd9\u91cc\u627e\u5230\uff0cJunreyCen \u5728\u8fd9\u91cc\u8be6\u7ec6\u7684\u4ecb\u7ecd\u4e86\u4ed6\u7814\u7a76\u548c\u5b9e\u73b0\u5f39\u6027\u963b\u5c3c\u52a8\u753b\u7684\u8fc7\u7a0b\u3002\u4e3a\u4e86\u89e3\u51b3\u8ba1\u7b97\u52a8\u753b\u53d8\u5316\u901f\u7387\u53c2\u6570\u7684\u95ee\u9898\uff0c\u4ed6\u4f7f\u7528\u4e86 4PL\uff1a<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328417\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u8fdb\u884c\u51fd\u6570\u62df\u5408\u3002\u7528\u5230\u7684\u662f\u4e00\u4e2a\u7f51\u7ad9\u63d0\u4f9b\u7684\u5de5\u5177\uff0c\u8fd9\u4e2a\u7f51\u7ad9\u7684\u7f51\u5740\u662f\uff1a<a href=\"https:\/\/link.segmentfault.com\/?enc=y2aZZ%2FimI%2F3BbaDNfK05dg%3D%3D.DzWEgnBPmZOSaHNnb1srQ%2Fkwa%2BXsovjgb%2FVCKflKVVwlimUxnfX4J361GOA%2Bl0IX\" rel=\"nofollow\">http:\/\/www.qinms.com\/webapp\/c&#8230;<\/a>\u3002\u60a8\u53ef\u4ee5\u5728\u8fd9\u91cc\u901a\u8fc7\u628a JunreyCen \u91c7\u96c6\u7684\uff0ciOS \u52a8\u753b\u6570\u636e\u8f93\u5165\u6765\u83b7\u5f97 4PL \u91cc A\u3001B\u3001C\u3001D \u56db\u4e2a\u53c2\u6570\u7684\u5177\u4f53\u503c\u3002train_x = (0,500,1000,1500,2500,6000,8000,10000,12000)<br \/>train_y = (0,90,160,210,260,347.5,357.5,367.5,377.5)<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328418\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u6709\u4e86 A\u3001B\u3001C\u3001D \u56db\u4e2a\u53c2\u6570\u4ee5\u53ca 4PL \u516c\u5f0f\uff1a<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328419\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u60a8\u5c31\u53ef\u4ee5\u5f97\u5230\u4e4b\u524d JavaScript \u4ee3\u7801\u91cc\u7684\u5f39\u6027\u963b\u5c3c\u7b97\u6cd5\uff0c\u4ece\u800c\u5b9e\u73b0 iOS \u4e00\u6837\u7684\u5f39\u6027\u963b\u5c3c\u6548\u679c\u3002\u5230\u8fd9\u91cc\uff0c\u60a8\u53ef\u80fd\u4f1a\u60f3\uff1a\u80fd\u591f\u505a\u5f39\u6027\u52a8\u753b\u633a\u9177\u7684\u4f46\u8fd8\u6709\u4ec0\u4e48\u7528\u5462\uff1f\u5176\u5b9e\uff0c\u53ea\u8981\u7a0d\u4f5c\u62bd\u8c61\u6211\u4eec\u5c31\u80fd\u628a\u8fd9\u4e2a\u65b9\u6cd5\u63d0\u70bc\u6210\u5904\u7406\u52a8\u753b\u7684\u901a\u7528\u65b9\u6cd5\u3002\u4f8b\u5982\u8bbe\u8ba1\u5e08\u5728 AfterEffect \u91cc\u5236\u4f5c\u4e86\u4e00\u6bb5\u513f\u52a8\u753b\uff0c\u60a8\u53ea\u9700\u8981\u5728\u52a8\u753b\u7684\u5173\u952e\u5e27\u4e0a\u91c7\u96c6\u4e00\u7cfb\u5217\u7684\u6570\u636e\uff0c\u7136\u540e\u7528\u51fd\u6570\u62df\u5408\u7684\u65b9\u6cd5\u627e\u5230\u5bf9\u5e94\u7684\u53c2\u6570\u548c\u51fd\u6570\uff0c\u518d\u5c06\u53c2\u6570\u548c\u51fd\u6570\u878d\u5165\u5230\u7a0b\u5e8f\u7b97\u6cd5\u4e2d\uff0c\u5c31\u80fd\u591f\u901a\u8fc7\u5b83\u4eec\u6765\u63a7\u5236\u52a8\u753b\u6548\u679c\u4e86\u3002\u591a\u9879\u5f0f\u62df\u5408\u8fd9\u79cd\u5168\u65b0\u7684\u52a8\u753b\u7f16\u7a0b\u65b9\u5f0f\u548c\u53ef\u5fae\u7f16\u7a0b\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u5176\u5b9e\uff0c\u7528\u4e00\u4e2a 3rd-party \u7684\u5de5\u5177\u6211\u4eec\u65e2\u4e0d\u77e5\u9053\u5b83\u662f\u5982\u4f55\u5de5\u4f5c\u7684\uff0c\u4e5f\u4e0d\u65b9\u4fbf\u96c6\u6210\u5230\u5de5\u7a0b\u9879\u76ee\u4e2d\u53bb\uff0c\u56e0\u6b64\uff0c\u4f60\u53ef\u4ee5\u7528\u53ef\u5fae\u7f16\u7a0b\u5feb\u901f\u5b9e\u73b0\u4e00\u4e2a\u81ea\u5df1\u7684\u51fd\u6570\u62df\u5408\u7b97\u6cd5\u3002\u7531\u4e8e\u4e4b\u524d\u56f4\u7ed5 TensorFlow \u7684\u81ea\u52a8\u5fae\u5206\u4ecb\u7ecd\u53ef\u5fae\u7f16\u7a0b\uff0c\u8fd9\u91cc\u6211\u5c31\u4ecb\u7ecd\u4e00\u4e0b\u5982\u4f55\u7528\u53ef\u5fae\u7f16\u7a0b\u5b9e\u73b0\u591a\u9879\u5f0f\u62df\u5408\u3002<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328420\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u8bb2\u5b8c\u7406\u8bba\u90e8\u5206\uff0c\u4e0b\u9762\u5c31\u8ba9\u6211\u4eec\u7528\u53ef\u5fae\u7f16\u7a0b\u5728 TensorFlow \u91cc\u5b9e\u64cd\u4e00\u904d\u3002\u73af\u5883\u51c6\u5907\u548c\u4e4b\u524d\u4e00\u6837\uff1a# \u5b89\u88c5 MiniConda \u521b\u5efa\u73af\u5883\uff1a\u5e76\u66f4\u65b0\uff1apip install -U pip<br \/>conda install -c apple tensorflow-deps<br \/>pip uninstall tensorflow-macos<br \/>pip uninstall tensorflow-metal<\/p>\n<h2>\u8fdb\u5165\u5de5\u4f5c\u76ee\u5f55\u542f\u52a8 Jupyter Notebook \u8fdb\u884c\u5b9e\u9a8c<\/h2>\n<p>jupyter notebook\u5728 Notebook \u91cc\u51c6\u5907 TensorFlow \u73af\u5883\uff1aimport tensorflow as tf<\/p>\n<h2>Resets notebook state<\/h2>\n<p>tf.keras.backend.clear_session()<\/p>\n<p>print(&#8220;Version: &#8220;, tf.__version__)<br \/>print(&#8220;Eager mode: &#8220;, tf.executing_eagerly())<br \/>print(<\/p>\n<pre><code>&quot;GPU is&quot;,\n&quot;available&quot; if tf.config.list_physical_devices(&quot;GPU&quot;) else &quot;NOT AVAILABLE&quot;)\u8f93\u51fa\uff1aVersion:  2.8.0<\/code><\/pre>\n<p>Eager mode:  True<br \/>GPU is available\u53ef\u4ee5\u770b\u5230\uff0c\u6211\u4f7f\u7528\u7684 TensorFlow \u662f 2.8.0 \u7248\u672c\uff0c\u7531\u4e8e\u7b14\u8bb0\u672c\u91cc M1 Pro \u6709\u6027\u80fd\u5f3a\u52b2\u7684 GPU\uff0c\u5728\u00a0GPU is available\u00a0\u52a0\u6301\u4e0b\uff0c\u8bad\u7ec3\u901f\u5ea6\u975e\u5e38\u5feb\u3002\u51c6\u5907\u6570\u636e\uff1a<br \/>train_x = [0,500,1000,1500,2500,6000,8000,10000,12000]<br \/>train_y = [0,90,160,210,260,347.5,357.5,367.5,377.5]\u5f00\u59cb\u53ef\u5fae\u7f16\u7a0b\uff1a<\/p>\n<p>optimizer = tf.keras.optimizers.Adam(0.1)<br \/>t_x = tf.constant(train_x,dtype=tf.float32)<br \/>t_y = tf.constant(train_y,dtype=tf.float32)<\/p>\n<p>wa = tf.Variable(0.,dtype = tf.float32,name=&#8217;wa&#8217;)<br \/>wb = tf.Variable(0.,dtype = tf.float32,name=&#8217;wb&#8217;)<br \/>wc = tf.Variable(0.,dtype = tf.float32,name=&#8217;wc&#8217;)<br \/>wd = tf.Variable(0.,dtype = tf.float32,name=&#8217;wd&#8217;)<br \/>variables = [wa,wb,wc,wd]<br \/>for e in range(num):<\/p>\n<pre><code>with tf.GradientTape() as tape:\n    #\u9884\u6d4b\u51fd\u6570\n    y_pred = tf.multiply(wa,t_x)+tf.multiply(w2,tf.pow(t_x,2))+tf.multiply(wb,tf.pow(t_x,2))+tf.multiply(wc,tf.pow(t_x,2))+wd\n    #\u635f\u5931\u51fd\u6570\n    loss=tf.reduce_sum(tf.math.pow(y_pred-t_y,2))\n    #\u8ba1\u7b97\u68af\u5ea6\n    grads=tape.gradient(loss, variables)\n    #\u66f4\u65b0\u53c2\u6570\n    optimizer.apply_gradients(grads_and_vars=zip(grads,variables))\n    if e % 100 == 0:\n        print(&quot;step: %i, loss: %f, a:%f, b:%f, c:%f, d:%f&quot; % (e,loss,wa.numpy(),wb.numpy(),wc.numpy(),wd.numpy()))<\/code><\/pre>\n<p>\u00a0\u5728\u4e0a\u9762\u7684\u4ee3\u7801\u91cc\u6709\u51e0\u4e2a\u5173\u952e\u7684\u90e8\u5206\u9700\u8981\u6ce8\u610f\uff1aoptimizer\u3001wa,wb,wc,wd\u3001loss\u3001grads\u3001apply_gradients\u00a0\u8fd9\u4e94\u4e2a\u90e8\u5206\u3002optimizer\u00a0\u662f\u4f18\u5316\u5668\uff0c\u5e38\u7528\u7684\u6709\u00a0SGD\u00a0\u548c\u00a0Adam\u00a0\uff0c\u524d\u8005\u662f\u68af\u5ea6\u4e0b\u964d\u540e\u8005\u5219\u53ef\u4ee5\u7406\u89e3\u4e3a\u52a0\u5f3a\u7248\uff0c\u5bf9\u4e8e\u672c\u793a\u4f8b\u53ea\u6709 9 \u6761\u6570\u636e\u8fd9\u79cd\u6837\u672c\u6bd4\u8f83\u5c11\u7684\u60c5\u51b5\u6709\u5947\u6548\u3002\u56e0\u4e3a\u00a0Adam\u00a0\u5bf9\u6bcf\u4e2a\u53c2\u6570\u4f7f\u7528\u76f8\u540c\u7684\u5b66\u4e60\u7387\uff0c\u5e76\u968f\u7740\u5b66\u4e60\u7684\u8fdb\u884c\u800c\u72ec\u7acb\u5730\u9002\u5e94\u3002\u6b64\u5916\uff0cAdam \u662f\u57fa\u4e8e\u52a8\u91cf\u7684\u7b97\u6cd5\uff0c\u5229\u7528\u4e86\u68af\u5ea6\u7684\u5386\u53f2\u4fe1\u606f\u3002\u57fa\u4e8e\u8fd9\u4e9b\u7279\u5f81\uff0c\u6211\u9009\u62e9\u4e86\u00a0Adam\u00a0\u800c\u975e\u00a0SGD\u3002\u5176\u6b21\uff0c\u9700\u8981\u5173\u6ce8\u7684\u662f\u7528\u00a0tf.Variable(0.,dtype = tf.float32,name=&#8217;wa&#8217;)\u00a0\u6765\u58f0\u660e\u6211\u4eec\u8981\u8bad\u7ec3\u7684\u53c2\u6570\u00a0wa,wb,wc,wd\uff0c\u8fd9\u90e8\u5206\u5728\u524d\u9762\u4ecb\u7ecd\u81ea\u52a8\u5fae\u5206\u7684\u65f6\u5019\u8bf4\u8fc7\u3002loss\u00a0\u635f\u5931\u51fd\u6570\u5219\u662f\u7528\u62df\u5408\u7ed3\u679c\u5bf9\u6bd4\u5b9e\u9645\u7ed3\u679c\u7684\u65b9\u5dee\u6765\u5b9a\u4e49\u7684\uff0c\u4e5f\u53eb\u5e73\u5747\u65b9\u5dee\u635f\u5931\u3002\u68af\u5ea6\u90e8\u5206\u5219\u5229\u7528 TensorFlow \u81ea\u52a8\u5fae\u5206\u68af\u5ea6\u5e26\u8ba1\u7b97\u65b9\u6cd5\u00a0tape.gradient(loss, variables)\u00a0\u6765\u8fdb\u884c\u8ba1\u7b97\u3002\u6700\u540e\uff0capply_gradients\u00a0\u628a\u6211\u4eec\u8ba1\u7b97\u597d\u7684\u68af\u5ea6\u00a0grads\u00a0\u5e94\u7528\u5230\u53c2\u6570\u4e0a\u53bb\u8fdb\u884c\u4e0b\u4e00\u8f6e\u7684\u62df\u5408\u3002\u6211\u4eec\u91cd\u590d\u8fd9\u4e2a\u8fc7\u7a0b 10000 \u6b21\uff0c\u4e0d\u65ad\u7684\u4f18\u5316\u53c2\u6570\u6765\u903c\u8fd1\u5b9e\u9645\u6570\u636e\uff1a<br \/>step: 0, loss: 4.712249, a:0.100003, b:0.100003, c:0.100003, d:0.100003<br \/>step: 100, loss: 0.164529, a:1.204850, b:-0.219918, c:-0.219918, d:0.294863<br \/>step: 200, loss: 0.082497, a:1.994068, b:-0.615929, c:-0.615929, d:0.209093<br \/>step: 300, loss: 0.073271, a:2.291683, b:-0.766129, c:-0.766129, d:0.176420<br \/>&#8230;<br \/>step: 9700, loss: 0.072893, a:2.371203, b:-0.804242, c:-0.804242, d:0.169179<br \/>step: 9800, loss: 0.072850, a:2.369858, b:-0.805587, c:-0.805587, d:0.167835<br \/>step: 9900, loss: 0.072853, a:2.369503, b:-0.805943, c:-0.805943, d:0.167479<br \/>\u8bad\u7ec3\u597d\u4e4b\u540e\uff0c\u628a\u7ed3\u679c\u6253\u5370\u51fa\u6765\u770b\u770b\u5b9e\u9645\u6548\u679c\uff1a<br \/>plt.scatter(t_x,t_y,c=&#8217;r&#8217;)<br \/>y_predict = tf.multiply(wa,t_x)+tf.multiply(w2,tf.pow(t_x,2))+tf.multiply(wb,tf.pow(t_x,2))+tf.multiply(wc,tf.pow(t_x,2))+wd<br \/>print(y_predict)<br \/>plt.plot(t_x,y_predict,c=&#8217;b&#8217;)<br \/>plt.show()<\/p>\n<h2>\u8f93\u51fa\uff1a<\/h2>\n<p>tf.Tensor(<br \/>[0.16805027 0.2640069  0.3543707  0.4391417  0.59190494 0.95040166<br \/> 1.0322142  1.0245409  0.92738193], shape=(9,), dtype=float32)\u7531\u4e8e\u8bad\u7ec3\u6570\u636e\u548c\u9884\u6d4b\u7684\u6570\u636e\u90fd\u505a\u4e86\u5f52\u4e00\u5316\uff0c\u9700\u8981\u5904\u7406\u4e00\u4e0b\u624d\u80fd\u770b\u5230\u771f\u5b9e\u7ed3\u679c\uff1a<br \/>print(<em>(y_predict.numpy())<\/em>377.5)<\/p>\n<h2>\u8f93\u51fa\uff1a<\/h2>\n<p>63.43898 99.66261 133.77495 165.77599 223.4441 358.77664 389.66086 386.7642 350.08667<\/p>\n<h2>\u771f\u5b9e\u6570\u636e\uff1a<\/h2>\n<p>train_y = [0,90,160,210,260,347.5,357.5,367.5,377.5]\u4ece\u56fe 6 \u4e2d\u53ef\u4ee5\u770b\u5230\uff0c\u6211\u4eec\u5df2\u7ecf\u501f\u52a9\u591a\u9879\u5f0f\u62df\u5408\u548c\u53ef\u5fae\u7f16\u7a0b\u6210\u529f\u201c\u903c\u8fd1\u201d\u4e86\u771f\u5b9e\u6570\u636e\uff0c\u56fe\u4e2d\u7ea2\u70b9\u4ee3\u8868\u771f\u5b9e\u6570\u636e\uff0c\u84dd\u8272\u7ebf\u6761\u662f\u6839\u636e\u9884\u6d4b\u7ed3\u679c\u7ed8\u5236\u3002<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328421\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>scipy\u7528curve_fit\u62df\u54084PL\u00a0\u7531\u4e8e\u6570\u636e\u91cf\u592a\u5c0f\uff0c\u4f7f\u7528\u591a\u9879\u5f0f\u62df\u5408\u7684\u65f6\u5019\uff0c\u5927\u6982\u5728\u7b2c\u4e09\u8f6e\u4e4b\u540e\u00a0loss\u00a0\u7684\u53d8\u5316\u5c31\u4e0d\u5927\u4e86\uff0c\u53ef\u89c1\u591a\u9879\u5f0f\u62df\u5408\u5bf9\u6211\u4eec\u8981\u89e3\u51b3\u7684\u5f39\u6027\u963b\u5c3c\u51fd\u6570\u95ee\u9898\u5e76\u975e\u6700\u4f18\u89e3\u3002\u5728\u7ecf\u8fc7\u4e86\u4e00\u756a\u7814\u7a76\uff0c\u6211\u627e\u5230\u00a0python\u00a0\u7684\u79d1\u5b66\u8ba1\u7b97\u5de5\u5177\u5305\u00a0scipy\u00a0\uff0c\u5728\u00a0optimizer\u00a0\u91cc\u6709\u4e00\u4e2a\u00a0curve_fit\u00a0\u5de5\u5177\u6548\u679c\u5f88\u597d\uff0c\u80fd\u591f\u628a\u6211\u4eec\u7684 4PL \u516c\u5f0f<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328422\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u00a0<br \/>from scipy import stats<br \/>import scipy.optimize as optimization<\/p>\n<p>xdata = t_x<br \/>ydata = t_y<\/p>\n<p>def fourPL(x, A, B, C, D):<\/p>\n<pre><code>return ((A-D)\/(1.0+((x\/C)**(B))) + D)\n<\/code><\/pre>\n<p>guess = [0, -0.3, 0.7, 1]<br \/>params, params_covariance = optimization.curve_fit(fourPL, xdata, ydata, guess)#, maxfev=1)<\/p>\n<p>x_min, x_max = np.amin(xdata), np.amax(xdata)<br \/>xs = np.linspace(x_min, x_max, 1000)<br \/>plt.scatter(xdata, ydata)<br \/>plt.plot(xs, fourPL(xs, *params))<br \/>plt.show()\u5982\u56fe 7 \u6240\u793a\u51fd\u6570\u62df\u5408\u7684\u6548\u679c\u5f88\u597d\uff0c\u53ef\u89c1\uff0c\u7528\u00a0scipy\u00a0\u63d0\u4f9b\u7684\u65b0\u65b9\u6cd5\u00a0optimization.curve_fit()\u00a0\u8fdb\u884c\u53ef\u5fae\u7f16\u7a0b\u548c\u4f7f\u7528 TensorFlow \u533a\u522b\u4e0d\u5927\uff0c\u4e5f\u662f\u9488\u5bf9\u51fd\u6570\u91cc\u7684\u53c2\u6570\u8fdb\u884c\u8bad\u7ec3\uff0c\u8fd4\u56de\u00a0params\u00a0\u4ee3\u8868\u8bad\u7ec3\u540e\u7684\u53c2\u6570\u3002<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328423\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><\/p>\n<p>print(*params)<\/p>\n<h2>\u8f93\u51fa\uff1a# \u4f7f\u7528\u5de5\u5177\u5f97\u5230\u7684\u53c2\u6570\uff1a<\/h2>\n<p>A = 410.517236432893        A = 405.250160538176<br \/>B = 1.1531891657236022      B = -1.17885294211307<br \/>C = 1481.6957597831604      C = 1414.70383142617<br \/>D = -0.16796047781164916    D = -0.516583385175963<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328424\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><br \/>\u5bf9\u6bd4 3rd-party \u5de5\u5177\u4ea7\u51fa\u7684\u53c2\u6570\uff1ay = 0.82231 * max \/ (1 + 4338.47 \/ Math.pow(y, 1.14791));\u00a0\u6700\u7ec8\uff0c\u7a0b\u5e8f\u7b97\u6cd5\u4e0a\u7684\u5dee\u5f02\u5f88\u5c0f\u3002\u6211\u4f7f\u7528\uff1a<a href=\"https:\/\/link.segmentfault.com\/?enc=mA5krChOagcQt%2FOHEbwb6A%3D%3D.33GTEIegP0wuHQBrqDzCvGQfMQymBeXSLPm11YL1wZ9KsWrjeX%2F8%2FM2FxkyzKeCE\" rel=\"nofollow\">https:\/\/github.com\/JunreyCen\/&#8230;<\/a>\u7684\u4ee3\u7801\u8fdb\u884c\u5b9e\u9645\u8fd0\u884c\u6d4b\u8bd5\uff0c\u4e24\u8005\u5b9e\u9645\u8868\u73b0\u4e0a\u5dee\u5f02\u4e0d\u5927\uff0c\u6548\u679c\u90fd\u633a\u597d\u7684\u3002\u60a8\u5728\u4f7f\u7528\u793a\u4f8b\u7684\u65f6\u5019\u8981\u6ce8\u610f\u4e00\u4e0b\uff0c\u5bf9\uff1a&lt;script src=&quot;https:\/\/cdn.jsdelivr.net\/npm\/vue&quot;&gt;&lt;\/script&gt;\u00a0\u505a\u4e2a\u5c0f\u4fee\u6539\uff1a&lt;script src=&quot;http:\/\/static.runoob.com\/assets\/vue\/1.0.11\/vue.min.js&quot;&gt;&lt;\/script&gt;\u5373\u53ef\u3002\u00a0\u795e\u7ecf\u7f51\u7edc\u7684\u62df\u5408\u00a0\u867d\u7136\uff0c\u5230\u8fd9\u91cc\u4f3c\u4e4e\u5df2\u7ecf\u5b8c\u6210\u4e86\u53ef\u5fae\u7f16\u7a0b\u89e3\u51b3\u5f39\u6027\u963b\u5c3c\u51fd\u6570\u62df\u5408\u7684\u95ee\u9898\uff0c\u5e76\u627e\u5230\u4e86\u7a0b\u5e8f\u7684\u7b97\u6cd5\u89e3\u51b3\u65b9\u6848\uff0c\u4f46\u662f\uff0c\u56de\u5230\u667a\u80fd\u5316\u7f16\u7a0b\u601d\u60f3\u91cc\uff0c\u6211\u8111\u6d77\u91cc\u6d6e\u73b0\u4e00\u4e2a\u95ee\u9898\uff1a\u56fe\u8ba1\u7b97\u548c\u795e\u7ecf\u7f51\u7edc\u80fd\u5426\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u5462\uff1f\u5e26\u7740\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u53c8\u5b9a\u4e49\u4e86\u4e00\u4e2a\u56fe\u8ba1\u7b97\u7684\u795e\u7ecf\u7f51\u7edc\uff1a<br \/>model = tf.keras.Sequential()<\/p>\n<h2>\u6dfb\u52a0\u5c42<\/h2>\n<h2>\u6ce8\uff1ainput_dim(\u8f93\u5165\u795e\u7ecf\u5143\u4e2a\u6570)\u53ea\u9700\u8981\u5728\u8f93\u5165\u5c42\u91cd\u89c6\u8bbe\u7f6e\uff0c\u540e\u9762\u7684\u7f51\u7edc\u53ef\u4ee5\u81ea\u52a8\u63a8\u65ad\u51fa\u8be5\u5c42\u7684\u5bf9\u5e94\u8f93\u5165<\/h2>\n<p>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<br \/>model.add(tf.keras.layers.Dense(units=10, input_dim=1, activation=&#8217;selu&#8217;))<\/p>\n<h2>\u795e\u7ecf\u5143\u4e2a\u6570  \u8f93\u5165\u795e\u7ecf\u5143\u4e2a\u6570 \u6fc0\u6d3b\u51fd\u6570<\/h2>\n<p>model.add(tf.keras.layers.Dense(units=1, activation=&#8217;selu&#8217;))<\/p>\n<h2>\u8f93\u51fa\u795e\u7ecf\u5143\u4e2a\u6570<\/h2>\n<h2>2 \u8bbe\u7f6e\u4f18\u5316\u5668\u548c\u635f\u5931\u51fd\u6570<\/h2>\n<p>model.compile(optimizer=&#8217;adam&#8217;, loss=&#8217;mse&#8217;)<\/p>\n<h2>\u4f18\u5316\u5668         \u635f\u5931\u51fd\u6570(\u5747\u65b9\u8bef\u5dee)<\/h2>\n<h2>3 \u8bad\u7ec3<\/h2>\n<p>history = model.fit(t_x, t_y,epochs=2000)<\/p>\n<h2>4 \u9884\u6d4b<\/h2>\n<p>y_pred = model.predict(t_x)\u8fd9\u91cc\u6211\u7528 TensorFlow \u7684\u00a0keras\u00a0API \u5b9a\u4e49\u4e86\u5341\u4e2a\u00a0Dense\u00a0\u5c42\uff0c\u6bcf\u5c42\u6709\u5341\u4e2a\u795e\u7ecf\u5143\u3001\u4e00\u4e2a\u8f93\u5165\u7ef4\u5ea6\u548c\u00a0selu\u00a0\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570\uff0c\u518d\u5b9a\u4e49\u4e86\u4e00\u4e2a\u795e\u7ecf\u5143\u540c\u6837\u6fc0\u6d3b\u51fd\u6570\u7684\u00a0Dense\u00a0\u5c42\u4f5c\u4e3a\u8f93\u51fa\u3002\u8fd9\u4e2a\u5b9a\u4e49\u662f\u901a\u8fc7\u5b9e\u9a8c\u53d1\u73b0\u8fc7\u591a\u6216\u8fc7\u5c11\u7684\u795e\u7ecf\u5143\u90fd\u65e0\u6cd5\u63d0\u5347\u8bad\u7ec3\u6548\u679c\uff0c\u592a\u591a\u7684\u5c42\u4e5f\u65e0\u6cd5\u66f4\u597d\u7684\u4f18\u5316\u51c6\u786e\u7387\u3002\u6a21\u578b\u7684\u4f18\u5316\u5668\u5982\u524d\u9762\u7684\u793a\u4f8b\u4e5f\u662f\u00a0adam\uff0c\u635f\u5931\u51fd\u6570\u4e5f\u662f\u5e73\u5747\u65b9\u5dee\u635f\u5931\u51fd\u6570\u00a0mse\u3002\u8bad\u7ec3\u8fc7\u7a0b\uff1a<br \/>1\/1 [==============================] &#8211; 1s 573ms\/step &#8211; loss: 74593.5156<br \/>Epoch 2\/2000<br \/>1\/1 [==============================] &#8211; 0s 38ms\/step &#8211; loss: 74222.5469<br \/>Epoch 3\/2000<br \/>1\/1 [==============================] &#8211; 0s 31ms\/step &#8211; loss: 74039.7734<br \/>&#8230;<br \/>Epoch 1994\/2000<br \/>1\/1 [==============================] &#8211; 0s 26ms\/step &#8211; loss: 0.3370<br \/>Epoch 1995\/2000<br \/>1\/1 [==============================] &#8211; 0s 25ms\/step &#8211; loss: 0.3370<br \/>Epoch 1996\/2000<br \/>1\/1 [==============================] &#8211; 0s 24ms\/step &#8211; loss: 0.3370<br \/>Epoch 1997\/2000<br \/>1\/1 [==============================] &#8211; 0s 26ms\/step &#8211; loss: 0.3370<br \/>Epoch 1998\/2000<br \/>1\/1 [==============================] &#8211; 0s 24ms\/step &#8211; loss: 0.3370<br \/>Epoch 1999\/2000<br \/>1\/1 [==============================] &#8211; 0s 25ms\/step &#8211; loss: 0.3369<br \/>Epoch 2000\/2000<br \/>1\/1 [==============================] &#8211; 0s 24ms\/step &#8211; loss: 0.3369<br \/>\u53ef\u4ee5\u770b\u5230\uff0c\u6574\u4e2a\u795e\u7ecf\u7f51\u7edc\u7684\u8bad\u7ec3\u8fc7\u7a0b\u6301\u7eed\u7a33\u5b9a\u7684\u63d0\u5347\uff0c\u4e00\u76f4\u5230\u8fd1 2000 \u4e2a\u00a0Epoch\u00a0\u7684\u65f6\u5019\u00a0loss\u00a0\u635f\u5931\u8fd8\u5728\u7ee7\u7eed\u4e0b\u964d\uff0c\u53ef\u89c1\u7ee7\u7eed\u8bad\u7ec3\u8fd8\u80fd\u8fdb\u4e00\u6b65\u63d0\u5347\u62df\u5408\u6548\u679c\uff0c\u66f4\u597d\u7684\u903c\u8fd1\u771f\u5b9e\u6570\u636e\u3002\u6309\u7167\u7ba1\u7406\uff0c\u6211\u4eec\u753b\u4e2a\u56fe\u6765\u89c2\u5bdf\u4e00\u4e0b\u6548\u679c\uff1a<\/p>\n<h2>5 \u753b\u56fe<\/h2>\n<p>plt.scatter(xdata, ydata)<br \/>plt.plot(t_x, y_pred, &#8216;r-&#8216;, lw=5)<br \/>plt.show()\u5982\u56fe 8 \u6240\u793a\uff0c\u8bad\u7ec3\u597d\u7684\u795e\u7ecf\u7f51\u7edc\u9884\u6d4b\u7ed3\u679c\u548c\u771f\u5b9e\u6570\u636e\u5bf9\u6bd4\u51e0\u4e4e\u662f\u4e00\u81f4\u7684\uff0c\u4f46\u662f\uff0c\u5bf9\u6bd4\u4e4b\u524d 4PL \u548c\u591a\u9879\u5f0f\u7684\u51fd\u6570\u62df\u5408\uff0c\u6574\u4f53\u6548\u679c\u5e76\u4e0d\u50cf\u51fd\u6570\u7684\u66f2\u7ebf\u4e00\u6837\u5e73\u6ed1\uff0c\u6574\u4f53\u5448\u73b0\u8fc7\u62df\u5408\u7684\u72b6\u6001\u3002<br \/><img decoding=\"async\" referrerpolicy=\"no-referrer\" src=\"https:\/\/segmentfault.com\/img\/remote\/1460000042328425\" alt=\"\u56fe\u7247\" title=\"\u56fe\u7247\" loading=\"lazy\"><\/p>\n<p>print(t_x.reshape(-1, 1))     print(model.predict(t_x.reshape(-1, 1)))<\/p>\n<h2>\u8f93\u51fa\uff1a\u9884\u6d4b\u8f93\u51fa\uff1a<\/h2>\n<p>[[    0.]<br \/> [  500.]<br \/> [ 1000.]<br \/> [ 1500.]<br \/> [ 2500.]<br \/> [ 6000.]<br \/> [ 8000.]<br \/> [10000.]<br \/> [12000.]]<br \/>print(t_y.reshape(-1,1))<\/p>\n<h2>\u8f93\u51fa\uff1a<\/h2>\n<p>[[  0. ]                    [-1.7345996]<br \/> [ 90. ]                    [90.01992]<br \/> [160. ]                    [159.91837]<br \/> [210. ]                    [210.06012]<br \/> [260. ]                    [260.01797] <br \/> [347.5]                    [347.43182] <br \/> [357.5]                    [357.57867] <br \/> [367.5]                    [367.53287] <br \/> [377.5]]                   [377.4857]\u53ef\u4ee5\u770b\u5230\uff0c\u5bf9\u6bd4\u771f\u5b9e\u6570\u636e\u795e\u7ecf\u7f51\u7edc\u9884\u6d4b\u7684\u7ed3\u679c\u662f\u975e\u5e38\u7cbe\u786e\u7684\uff0c\u8bef\u5dee\u6bd4\u4f7f\u7528\u591a\u9879\u5f0f\u62df\u5408\u7684\u6548\u679c\u597d\u975e\u5e38\u591a\u3002\u00a0\u81f3\u6b64\uff0c\u6211\u4eec\u4f7f\u7528\u4e86 4PL\u3001\u591a\u9879\u5f0f\u4ee5\u53ca\u795e\u7ecf\u7f51\u7edc\u4e09\u79cd\u53ef\u5fae\u7f16\u7a0b\u7684\u65b9\u6cd5\uff0c\u5bf9\u5f39\u6027\u963b\u5c3c\u51fd\u6570\u8fdb\u884c\u62df\u5408\uff0c\u903c\u8fd1\u771f\u5b9e\u6570\u636e\u7684\u6548\u679c\u867d\u7136\u6709\u4e00\u5b9a\u5dee\u5f02\uff0c\u4f46\u603b\u4f53\u90fd\u62df\u5408\u7684\u6bd4\u8f83\u597d\u3002\u540c\u795e\u7ecf\u7f51\u7edc\u7684\u65b9\u6cd5\u4e0d\u540c\uff0c4PL \u548c\u591a\u9879\u5f0f\u62df\u5408\u53ef\u4ee5\u76f4\u63a5\u63d0\u4f9b\u516c\u5f0f\u548c\u53c2\u6570\uff0c\u6211\u4eec\u53ef\u4ee5\u65b9\u4fbf\u7684\u5c06\u5176\u5e94\u7528\u5728\u7a0b\u5e8f\u7684\u7b97\u6cd5\u4e2d\u3002\u800c\u5bf9\u4e8e\u795e\u7ecf\u7f51\u7edc\uff0c\u5219\u9700\u8981\u628a\u795e\u7ecf\u7f51\u7edc\u5728\u6d4f\u89c8\u5668\u91cc\u8dd1\u8d77\u6765\uff0c\u4e0b\u9762\u5c31\u4ecb\u7ecd\u4e00\u4e0b\u8fd9\u4e2a\u8fc7\u7a0b\u3002\u00a0\u6d4f\u89c8\u5668\u6267\u884c\u793a\u4f8b\u00a0\u4e3a\u4e86\u80fd\u591f\u628a\u795e\u7ecf\u7f51\u7edc\u5728\u6d4f\u89c8\u5668\u91cc\u8dd1\u8d77\u6765\uff0c\u5e76\u8ba9 JavaScript \u53ef\u4ee5\u8c03\u7528\uff0c\u9996\u5148\u9700\u8981\u5c06\u795e\u7ecf\u7f51\u7edc\u5b58\u50a8\u6210\u6587\u4ef6\u3002model.save(&#8216;saved_model\/w4model&#8217;)\u5b58\u50a8\u5230\u76ee\u5f55\u540e\u4f1a\u5f97\u5230\u4e24\u4e2a\u6587\u4ef6\uff1akeras_metadata.pb\u00a0\u548c\u00a0saved_model.pb\u00a0\u4ee5\u53ca\u4e24\u4e2a\u76ee\u5f55\uff1aassets\u00a0\u548c \u00a0variables\u00a0\u3002\u8fd9\u91cc\u4f7f\u7528\u7684\u662f TensorFlow \u7684\u00a0tf_saved_model\uff0c\u4e0b\u9762\u8f6c\u6362\u6a21\u578b\u7ed9 TensorFlow.js \u5728\u6d4f\u89c8\u5668\u4f7f\u7528\u7684\u65f6\u5019\u4f1a\u7528\u5230\u8fd9\u4e2a\u53c2\u6570\u3002\u4e3a\u4e86\u80fd\u591f\u8ba9\u6a21\u578b\u5728\u6d4f\u89c8\u5668\u8fd0\u884c\uff0c\u5148\u5b89\u88c5\u00a0pip install tensorflowjs\u00a0\u7528\u00a0tensorflowjs_converter\u00a0\u547d\u4ee4\u884c\u8f6c\u6362\u5de5\u5177\u8fdb\u884c\u6a21\u578b\u7684\u8f6c\u6362\uff1atensorflowjs_converter &#8211;input_format=tf_saved_model \/<br \/>&#8211;output_node_names=&#8221;w4model&#8221; \/<br \/>&#8211;saved_model_tags=serve .\/saved_model\/w4model .\/web_model\u8fd9\u91cc\u00a0&#8211;input_format\u00a0\u53c2\u6570\u00a0tf_saved_model\u00a0\u5bf9\u5e94\u4e4b\u524d\u6a21\u578b\u5b58\u50a8\u4f7f\u7528\u7684\u65b9\u6cd5\uff0c\u8981\u6ce8\u610f\u4e0d\u540c\u65b9\u6cd5\u4fdd\u5b58\u7684\u6587\u4ef6\u683c\u5f0f\u548c\u7ed3\u6784\u7684\u4e0d\u540c\u76f8\u4e92\u4e0d\u517c\u5bb9\u3002&#8211;output_node_names\u00a0\u662f\u6a21\u578b\u7684\u540d\u79f0\uff0c&#8211;saved_model_tags\u00a0\u4e2d\u00a0tag\u00a0\u662f\u7528\u6765\u533a\u522b\u4e0d\u540c\u7684\u00a0MetaGraphDef\uff0c\u8fd9\u662f\u5728\u52a0\u8f7d\u6a21\u578b\u6240\u9700\u8981\u7684\u53c2\u6570\u5176\u9ed8\u8ba4\u503c\u662f\u00a0serve\u3002\u00a0\u901a\u8fc7\u00a0tensorflowjs_converter\u00a0\u8fdb\u884c\u6a21\u578b\u8f6c\u6362\u540e\uff0c\u6211\u4eec\u5728\u00a0web_model\u00a0\u6587\u4ef6\u5939\u91cc\u4f1a\u770b\u5230\u00a0group1-shard1of1.bin\u00a0\u4ee5\u53ca\u00a0model.json\u00a0\u4e24\u4e2a\u6587\u4ef6\u3002\u8fd9\u4e24\u4e2a\u6587\u4ef6\u4e2d\uff0c\u4ee5\u00a0.json\u00a0\u540e\u7f00\u7ed3\u5c3e\u7684\u6587\u4ef6\u662f\u6a21\u578b\u5b9a\u4e49\u6587\u4ef6\uff0c\u4ee5\u00a0.bin\u00a0\u540e\u7f00\u7ed3\u5c3e\u7684\u6587\u4ef6\u662f\u6a21\u578b\u7684\u6743\u91cd\u6587\u4ef6\u3002\u60a8\u53ef\u4ee5\u628a\u6a21\u578b\u5b9a\u4e49\u6587\u4ef6\u770b\u505a 4PL \u548c\u591a\u9879\u5f0f\u7684\u51fd\u6570\uff0c\u628a\u6a21\u578b\u6743\u91cd\u6587\u4ef6\u770b\u505a\u51fd\u6570\u7684\u53c2\u6570\u3002\u00a0\u901a\u8fc7 npm \u521d\u59cb\u5316\u4e00\u4e2a node.js \u9879\u76ee\uff0c\u7136\u540e\u5728\u00a0package.json\u00a0\u914d\u7f6e\u6587\u4ef6\u91cc\u52a0\u5165\uff1a\u00a0&#8220;dependencies&#8221;: {<\/p>\n<pre><code>&quot;@tensorflow\/tfjs&quot;: &quot;^3.18.0&quot;,\n&quot;@tensorflow\/tfjs-converter&quot;: &quot;^3.18.0&quot;<\/code><\/pre>\n<p>},\u5c06\u4f9d\u8d56\u5f15\u5165\u5230\u7a0b\u5e8f\u6587\u4ef6\u4e2d\uff0c\u8fd9\u91cc\u8981\u6ce8\u610f\u00a0loadGraphModel\u00a0\u662f\u6211\u4eec\u4ece\u00a0@tensorflow\/tfjs-converter\u00a0\u00a0\u4f9d\u8d56\u4e2d\u5bfc\u5165\u7684\uff0c\u867d\u7136 \u00a0@tensorflow\/tfjs\u00a0\u63d0\u4f9b\u00a0tf.loadGraphModel()\u00a0\u65b9\u6cd5\u52a0\u8f7d\u6a21\u578b\uff0c\u4f46\u662f\u8fd9\u4e2a\u65b9\u6cd5\u53ea\u9002\u7528\u4e8e TensorFlow.js \u4e2d\u4fdd\u5b58\u7684\u6a21\u578b\uff0c\u6211\u4eec\u901a\u8fc7 Python \u91cc\u00a0model.save()\u00a0\u65b9\u6cd5\u4fdd\u5b58\uff0c\u5e76\u7528 Converter \u8f6c\u6362\u7684\u6a21\u578b\uff0c\u5fc5\u987b\u7528\u00a0tfjs-converter\u00a0\u4f9d\u8d56\u5305\u4e2d\u63d0\u4f9b\u7684\u00a0loadGraphModel\u00a0\u65b9\u6cd5\u8fdb\u884c\u52a0\u8f7d\u3002<br \/>import * as tf from &#8220;@tensorflow\/tfjs&#8221;;<br \/>import { loadGraphModel } from &#8220;@tensorflow\/tfjs-converter&#8221;;<br \/>window.onload = async () =&gt; {<br \/>  const resultElement = document.getElementById(&#8220;result&#8221;);<br \/>  const MODEL_URL = &#8220;model.json&#8221;;<\/p>\n<p>console.time(&#8220;Loading of model&#8221;);<br \/>  const model = await loadGraphModel(MODEL_URL);<br \/>  console.timeEnd(&#8220;Loading of model&#8221;);<\/p>\n<p>const test_data = tf.tensor([<\/p>\n<pre><code>[0.0],\n[500.0],\n[1000.0],\n[1500.0],\n[2500.0],\n[6000.0],\n[8000.0],\n[10000.0],\n[12000.0],<\/code><\/pre>\n<p>]);<br \/>  tf.print(test_data);<br \/>  console.time(&#8220;Loading of model&#8221;);<br \/>  let outputs = model.execute(test_data);<br \/>  console.timeEnd(&#8220;execute\uff1a&#8221;);<br \/>  tf.print(outputs);<br \/>  resultElement.innerText = outputs.toString();<br \/>};\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7531\u4e8e\u6211\u4eec\u7684\u6a21\u578b\u5728\u9884\u6d4b\u65f6\u4f7f\u7528\u7684\u662f\u5f20\u91cf\u4f5c\u4e3a\u8f93\u5165\uff0c\u56e0\u6b64\uff0c\u9700\u8981\u7528\u00a0tf.tensor()\u00a0\u65b9\u6cd5\u6765\u8fd4\u56de\u7ecf\u8fc7\u5305\u88c5\u7684\u5f20\u91cf\u4f5c\u4e3a\u6a21\u578b\u7684\u8f93\u5165\u3002\u8fd0\u884c\u7a0b\u5e8f\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece\u6d4f\u89c8\u5668\u5f00\u53d1\u8005\u5de5\u5177\u7684\u63a7\u5236\u53f0\u770b\u5230\u6253\u5370\u7684\u8c03\u8bd5\u4fe1\u606f\uff1a<br \/>[Violation] &#8216;load&#8217; handler took 340ms<br \/>index.js:12 Loading of model: 67.19482421875 ms<br \/>print.ts:34 Tensor<\/p>\n<pre><code>[[0    ],\n [500  ],\n [1000 ],\n [1500 ],\n [2500 ],\n [6000 ],\n [8000 ],\n [10000],\n [12000]]<\/code><\/pre>\n<p>index.js:28 execute: 257.47607421875 ms<br \/>print.ts:34 Tensor<\/p>\n<pre><code>[[-1.7345995 ],\n [90.0198822 ],\n [159.9183655],\n [210.0600586],\n [260.0179443],\n [347.4320068],\n [357.5788269],\n [367.5332947],\n [377.4856262]]\u6211\u4eec\u4f1a\u770b\u5230\u63a7\u5236\u53f0\u8f93\u51fa\u00a0webgl\u00a0\u4ee3\u8868 TensorFlow.js \u6210\u529f\u542f\u7528\u4e86 WebGL \u7684\u52a0\u901f\u80fd\u529b\uff0c\u5728\u5176\u52a0\u901f\u4e4b\u4e0b\uff0c\u6211\u4eec\u5728\u9884\u6d4b\u7684\u65f6\u5019\u901f\u5ea6\u4f1a\u4ece 257ms \u5927\u5e45\u5ea6\u63d0\u5347\u5230 131ms\uff0c\u591a\u6b21\u9884\u6d4b\u65f6\u95f4\u7531\u4e8e\u6743\u91cd\u548c\u8ba1\u7b97\u56fe\u5df2\u7ecf\u52a0\u8f7d\u5230\u663e\u5b58\u4e2d\u901f\u5ea6\u4f1a\u66f4\u5feb\uff0c\u8fbe\u5230 78ms \u5de6\u53f3\u3002\u5f53\u7136\uff0c\u5bf9\u4e8e\u52a8\u753b\u6765\u8bf4\u8fd9\u79cd\u8017\u65f6\u8fd8\u662f\u6709\u70b9\u591a\uff0c\u60a8\u53ef\u4ee5\u56de\u987e\u672c\u4e66\u7aef\u667a\u80fd\u7684\u90e8\u5206\uff0c\u4f7f\u7528\u76f8\u5173\u7684\u5de5\u5177\u548c\u65b9\u6cd5\u5bf9\u6a21\u578b\u8fdb\u884c\u538b\u7f29\u548c\u4f18\u5316\uff0c\u53ea\u9700\u8981\u5728\u6a21\u578b\u8f93\u51fa\u7684\u65f6\u5019\u9009\u62e9 TensorFlow.js\uff0c\u6216\u8005\u7528 TensorFlow \u63d0\u4f9b\u7684\u5de5\u5177\u628a\u4f18\u5316\u540e\u7684\u6a21\u578b\u8f6c\u6210 TensorFlow.js \u7684\u6a21\u578b\u5373\u53ef\u590d\u7528\u8fd9\u4e2a\u793a\u4f8b\u4e2d\u7684\u4ee3\u7801\u3002\u00a0\u6700\u540e\uff0c\u8ba9\u6211\u4eec\u518d\u6b21\u56de\u5230\u5f39\u6027\u963b\u5c3c\u51fd\u6570\u5728 JavaScript \u91cc\u7684\u5b9a\u4e49\uff1a<\/code><\/pre>\n<p>damping(x, max) {<\/p>\n<pre><code>        let y = Math.abs(x);\n        y = 0.821 * max \/ (1 + 4527.779 \/ Math.pow(y, 1.153));\n        return Math.round(x &lt; 0 ? -y : y);\n      },\u628a\u8fd9\u91cc\u7684\u00a0y\u00a0\u53d8\u6210\u6a21\u578b\u9884\u6d4b\u7684\u7ed3\u679c\uff1ay = model.execute(tf.tensor([[x],]));\u00a0\u5373\u53ef\u7528\u6a21\u578b\u6765\u62df\u5408\u5f39\u6027\u963b\u5c3c\u51fd\u6570\u5e76\u8fd4\u56de\u8ba1\u7b97\u7ed3\u679c\u3002\u60a8\u53ef\u80fd\u4f1a\u95ee\uff1a\u65e2\u7136\u6211\u6709 4PL\u3001\u591a\u9879\u5f0f\u62df\u5408\u7b49\u65b9\u6cd5\uff0c\u4e3a\u4ec0\u4e48\u8981\u7528\u795e\u7ecf\u7f51\u7edc\u5462\uff1f\u662f\u7684\uff0c\u5982\u679c\u60a8\u8981\u89e3\u51b3\u7684\u95ee\u9898\u7b80\u5355\u5230\u8db3\u4ee5\u7528\u51fd\u6570\u62df\u5408\u7684\u65b9\u5f0f\u89e3\u51b3\uff0c\u540c\u65f6\uff0c\u60a8\u4e5f\u77e5\u9053\u5e94\u8be5\u7528 4PL 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href=\"https:\/\/segmentfault.com\/a\/1190000042328403\">https:\/\/segmentfault.com\/a\/1190000042328403<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b80\u4ecb\uff1a\u00a0\u7814\u7a76\u8005\u8868\u793a\uff0c\u7531\u4e8e\u5e7f\u6cdb\u7684\u79d1\u5b66\u8ba1\u7b97\u548c\u673a\u5668\u5b66\u4e60\u9886\u57df\u5728\u5e95\u5c42\u7ed3\u6784\u4e0a\u90fd\u9700\u8981\u7ebf\u6027\u4ee3\u6570\u7684\u652f\u6301\uff0c\u56e0\u6b64\u6709\u53ef\u80fd\u4ee5\u53ef\u5fae\u7f16\u7a0b\u7684\u5f62 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