{"id":5865,"date":"2025-04-19T10:10:48","date_gmt":"2025-04-19T02:10:48","guid":{"rendered":"https:\/\/nullthought.net\/?p=5865"},"modified":"2025-04-19T10:12:25","modified_gmt":"2025-04-19T02:12:25","slug":"%e7%94%a8%e7%89%a9%e7%90%86%e4%bf%a1%e6%81%af%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%ef%bc%88pinns%ef%bc%89%e6%b1%82%e8%a7%a3%e9%9d%9e%e7%a8%b3%e6%80%81%e9%ba%a6%e5%85%8b%e6%96%af%e9%9f%a6%e6%96%b9","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=5865","title":{"rendered":"\u7528\u7269\u7406\u4fe1\u606f\u795e\u7ecf\u7f51\u7edc\uff08PINNs\uff09\u6c42\u89e3\u975e\u7a33\u6001\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b"},"content":{"rendered":"\n<p>\u8bba\u6587<strong><a href=\"https:\/\/arxiv.org\/abs\/2504.12144\" target=\"_blank\" rel=\"noreferrer noopener\">PINNs for Solving Unsteady Maxwell&#8217;s Equations: Convergence Issues and Comparative Assessment with Compact Schemes<\/a><\/strong>\u4e3b\u8981\u7814\u7a76\u4f7f\u7528<strong><a href=\"https:\/\/nullthought.net\/?p=4287\" target=\"_blank\" rel=\"noreferrer noopener\">\u7269\u7406\u4fe1\u606f\u795e\u7ecf\u7f51\u7edc\uff08PINNs\uff09<\/a><\/strong>\u6c42\u89e3\u975e\u7a33\u6001\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7684\u6027\u80fd\uff0c\u5e76\u4e0e\u4f20\u7edf\u6570\u503c\u65b9\u6cd5\uff08\u5982FDTD\u548cPade\u7d27\u81f4\u683c\u5f0f\uff09\u8fdb\u884c\u5bf9\u6bd4\uff0c\u91cd\u70b9\u5206\u6790\u5176\u6536\u655b\u6027\u95ee\u9898\u53ca\u5176\u80cc\u540e\u7684\u8bad\u7ec3\u673a\u5236\u3002<\/p>\n\n\n\n<p>\u8bba\u6587\u4f5c\u8005\u4e3aGal G. Shaviner, Hemanth Chandravamsi, Shimon Pisnoy, Ziv Chen, Steven H. Frankel\uff0c\u6765\u81eaIsrael Institute of Technology\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"802\" height=\"397\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-1.png\" alt=\"\" class=\"wp-image-5866\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-1.png 802w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-1-300x149.png 300w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-1-768x380.png 768w\" sizes=\"auto, (max-width: 802px) 100vw, 802px\" \/><figcaption class=\"wp-element-caption\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2504.12144\" target=\"_blank\" rel=\"noreferrer noopener\">PINNs for Solving Unsteady Maxwell&#8217;s Equations: Convergence Issues and Comparative Assessment with Compact Schemes<\/a><\/strong><\/figcaption><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e00\u3001\u7814\u7a76\u80cc\u666f\u4e0e\u52a8\u673a<\/h5>\n\n\n\n<p>\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u662f\u63cf\u8ff0\u7535\u78c1\u573a\u884c\u4e3a\u7684\u57fa\u7840\u65b9\u7a0b\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u5149\u5b66\u3001\u65e0\u7ebf\u901a\u4fe1\u3001\u7535\u8def\u7b49\u9886\u57df\u3002\u5c3d\u7ba1\u5df2\u6709\u8bb8\u591a\u6570\u503c\u65b9\u6cd5\uff08\u5982\u6709\u9650\u5dee\u5206\u65f6\u57df\u6cd5FDTD\u3001\u6709\u9650\u5143\u6cd5FEM\u7b49\uff09\u7528\u4e8e\u8fd1\u4f3c\u6c42\u89e3\u8fd9\u4e9b\u65b9\u7a0b\uff0c\u4f46\u5b83\u4eec\u901a\u5e38\u53d7\u5236\u4e8e\u201c\u7ef4\u5ea6\u707e\u96be\u201d\u5e26\u6765\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u6fc0\u589e\uff0c\u6b64\u5916\uff0c\u5728\u5904\u7406\u590d\u6742\u51e0\u4f55\u3001\u7a00\u758f\u6216\u566a\u58f0\u6570\u636e\u65f6\u4e5f\u5b58\u5728\u56f0\u96be\u3002<\/p>\n\n\n\n<p>\u4e3a\u6b64\uff0c\u8fd1\u5e74\u6765\u63d0\u51fa\u7684<strong><a href=\"https:\/\/nullthought.net\/?p=4287\" target=\"_blank\" rel=\"noreferrer noopener\">\u7269\u7406\u4fe1\u606f\u795e\u7ecf\u7f51\u7edc\uff08PINNs\uff09<\/a><\/strong>\u4e3a\u6c42\u89e3\u504f\u5fae\u5206\u65b9\u7a0b\u63d0\u4f9b\u4e86\u4e00\u79cd\u65b0\u7684\u601d\u8def\u3002PINNs\u5c06\u7269\u7406\u65b9\u7a0b\u4f5c\u4e3a\u635f\u5931\u51fd\u6570\u9879\u76f4\u63a5\u5d4c\u5165\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\uff0c\u5b9e\u73b0\u4e86\u65e0\u7f51\u683c\uff08mesh-free\uff09\u7684\u6c42\u89e3\u6846\u67b6\u3002\u4f46\u5728\u9762\u5bf9\u975e\u7a33\u6001\u3001\u6ce2\u52a8\u6027\u5f3a\u6216\u5177\u6709\u9ad8\u9891\u7279\u5f81\u7684\u7cfb\u7edf\u65f6\uff0cPINNs\u901a\u5e38\u6536\u655b\u901f\u5ea6\u6162\u3001\u5bb9\u6613\u9677\u5165\u8bad\u7ec3\u75c5\u6001\u95ee\u9898\u3002<\/p>\n\n\n\n<p>\u672c\u8bba\u6587\u56de\u7b54\u4ee5\u4e0b\u4e09\u4e2a\u5173\u952e\u95ee\u9898\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5728\u57fa\u7840PINNs\u67b6\u6784\u57fa\u7840\u4e0a\uff0c\u9700\u8981\u5f15\u5165\u54ea\u4e9b\u589e\u5f3a\u7b56\u7565\u624d\u80fd\u6709\u6548\u6c42\u89e3\u4e8c\u7ef4\u975e\u7a33\u6001\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\uff1f<\/li>\n\n\n\n<li>\u5728\u51c6\u786e\u6027\u4e0e\u8ba1\u7b97\u6548\u7387\u65b9\u9762\uff0cPINNs\u4e0e\u4f20\u7edf\u65b9\u6cd5\u76f8\u6bd4\u5982\u4f55\uff1f<\/li>\n\n\n\n<li>PINNs\u5728\u8bad\u7ec3\u4e2d\u662f\u5426\u5177\u6709\u201c\u81ea\u9002\u5e94\u805a\u7126\u201d\u7684\u80fd\u529b\uff0c\u80fd\u5426\u4f18\u5148\u5b66\u4e60\u9ad8\u6b8b\u5dee\u533a\u57df\u7684\u5185\u5bb9\uff1f<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e8c\u3001\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7b80\u4ecb<\/h5>\n\n\n\n<p>\u4f5c\u8005\u91c7\u7528\u7684\u662f\u65e0\u6e90\u533a\u57df\u4e0b\u7684\u6807\u51c6\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u5f62\u5f0f\uff08\u65e0\u81ea\u7531\u7535\u8377\u548c\u7535\u6d41\uff09\uff0c\u7279\u522b\u5730\uff0c\u7740\u91cd\u4e8e\u4e8c\u7ef4\u60c5\u51b5\u4e0b\u7684\u7535\u573a E<sub>z<\/sub> \u4e0e\u78c1\u573a H<sub>x<\/sub>,H<sub>y<\/sub>\u7684\u8026\u5408\u7cfb\u7edf\u3002\u8be5\u7cfb\u7edf\u5177\u6709\u5f3a\u975e\u7ebf\u6027\u4e0e\u9ad8\u9636\u5bfc\u6570\u7279\u5f81\uff0c\u6570\u503c\u6c42\u89e3\u65f6\u5bf9\u7a7a\u95f4\u4e0e\u65f6\u95f4\u5206\u8fa8\u7387\u5747\u63d0\u51fa\u8f83\u9ad8\u8981\u6c42\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e09\u3001PINNs \u6a21\u578b\u8bbe\u8ba1\u4e0e\u8bad\u7ec3\u7b56\u7565<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u795e\u7ecf\u7f51\u7edc\u67b6\u6784<\/strong><br>\u91c7\u7528\u5168\u8fde\u63a5\u524d\u9988\u795e\u7ecf\u7f51\u7edc\uff0c\u5c06\u8f93\u5165 (x,y,t) \u6620\u5c04\u4e3a\u8f93\u51fa (E<sub>z<\/sub>, H<sub>x<\/sub>, H<sub>y<\/sub>)\u3002\u4e3a\u5e94\u5bf9\u9ad8\u9891\u96be\u4ee5\u5b66\u4e60\u7684\u95ee\u9898\uff0c\u5f15\u5165\u4e86\u4ee5\u4e0b\u5173\u952e\u6280\u672f\uff1a\n<ul class=\"wp-block-list\">\n<li><strong>\u5468\u671f\u6620\u5c04\u4e0eRandom Fourier Features\uff08RFF\uff09<\/strong>\uff1a\u5c06\u8f93\u5165\u5148\u8fdb\u884c\u7a7a\u95f4\u5468\u671f\u53d8\u6362\uff0c\u518d\u901a\u8fc7RFF\u6620\u5c04\u5230\u9ad8\u7ef4\u7a7a\u95f4\uff0c\u6709\u52a9\u4e8e\u7f13\u89e3\u795e\u7ecf\u7f51\u7edc\u7684\u9891\u8c31\u504f\u5dee\uff08\u5373\u66f4\u504f\u597d\u5b66\u4e60\u4f4e\u9891\u89e3\uff09\u3002<\/li>\n\n\n\n<li><strong>Random Weight Factorization\uff08RWF\uff09<\/strong>\uff1a\u521d\u59cb\u5316\u6743\u91cd\u4ee5\u589e\u5f3a\u68af\u5ea6\u4f20\u64ad\uff0c\u4fc3\u8fdb\u8bad\u7ec3\u7a33\u5b9a\u6027\u3002<\/li>\n\n\n\n<li><strong>\u56e0\u679c\u6027\u8bad\u7ec3\uff08Causality Training\uff09<\/strong>\uff1a\u5f15\u5bfc\u7f51\u7edc\u4f18\u5148\u5b66\u4e60\u521d\u671f\u65f6\u95f4\u6b65\u7684\u7269\u7406\u8fc7\u7a0b\uff0c\u907f\u514d\u8fc7\u65e9\u62df\u5408\u9519\u8bef\u7684\u540e\u671f\u89e3\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u635f\u5931\u51fd\u6570\u6784\u6210<\/strong><br>\u603b\u635f\u5931\u7531\u4e09\u90e8\u5206\u7ec4\u6210\uff1a\n<ul class=\"wp-block-list\">\n<li>\u521d\u59cb\u6761\u4ef6\u635f\u5931 L<sub>IC<\/sub>\u200b<\/li>\n\n\n\n<li>\u8fb9\u754c\u6761\u4ef6\u635f\u5931 L<sub>BC<\/sub>\u200b\uff08\u5bf9\u4e8e\u5468\u671f\u8fb9\u754c\u95ee\u9898\u53ef\u7701\u7565\uff09<\/li>\n\n\n\n<li>\u6b8b\u5dee\u635f\u5931 L<sub>res<\/sub>\uff0c\u7528\u4e8e\u7ea6\u675f\u7f51\u7edc\u8f93\u51fa\u6ee1\u8db3\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u56e0\u679c\u6027\u52a0\u6743\u673a\u5236<\/strong><br>\u901a\u8fc7\u65f6\u95f4\u6b65\u957f\u7684\u6743\u91cd w<sub>i<\/sub>\u200b \u63a7\u5236\u8bad\u7ec3\u6ce8\u610f\u529b\u7684\u5206\u5e03\uff0c\u4ece\u800c\u5b9e\u73b0\u5bf9\u65e9\u671f\u52a8\u6001\u7684\u4f18\u5148\u62df\u5408\uff0c\u63d0\u5347\u6574\u4f53\u7a33\u5b9a\u6027\u4e0e\u7269\u7406\u4e00\u81f4\u6027\u3002<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\u56db\u3001\u6570\u503c\u5b9e\u9a8c\u4e0e\u7ed3\u679c\u5206\u6790<\/h5>\n\n\n\n<p>\u4f5c\u8005\u8bbe\u8ba1\u4e86\u4e09\u4e2a\u7ecf\u5178\u7535\u78c1\u573a\u95ee\u9898\uff0c\u5bf9PINNs\u4e0e\u4f20\u7edf\u65b9\u6cd5\u7684\u6027\u80fd\u8fdb\u884c\u5bf9\u6bd4\u5206\u6790\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u4e00\u7ef4\u9ad8\u65af\u8109\u51b2\u4f20\u64ad\u95ee\u9898<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u5728\u81ea\u7531\u7a7a\u95f4\u4e2d\u4f20\u64ad\u7684\u65f6\u95f4\u8870\u51cf\u7535\u573a\u8109\u51b2\uff0c\u8bbe\u5b9a\u6e05\u6670\u7684\u521d\u59cb\u4e0e\u8fb9\u754c\u6761\u4ef6\u3002<\/li>\n\n\n\n<li>\u5bf9\u6bd4\u7ed3\u679c\u663e\u793a\uff0cFDTD\u4e0ePade\u65b9\u6cd5\u5728\u6ce2\u52a8\u533a\u95f4\u6613\u4ea7\u751f\u6570\u503c\u9707\u8361\uff0c\u800cPINNs\u80fd\u591f\u66f4\u7cbe\u786e\u5730\u6355\u6349\u7535\u573a\u7684\u9661\u53d8\u8fb9\u754c\uff0c\u4e14\u65e0\u660e\u663e\u9707\u8361\u3002<\/li>\n\n\n\n<li>\u8bc1\u660ePINNs\u5728\u5904\u7406\u77ed\u65f6\u51b2\u51fb\u95ee\u9898\u65f6\u5177\u6709\u66f4\u9ad8\u7684\u7a33\u5b9a\u6027\u4e0e\u89e3\u6790\u80fd\u529b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u4e8c\u7ef4\u5468\u671f\u76d2\u4e2d\u7684\u9ad8\u65af\u8109\u51b2\u6f14\u5316<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u5b9e\u73b0\u4e86\u7a7a\u95f4\u4e0e\u65f6\u95f4\u53cc\u5468\u671f\u6027\u5efa\u6a21\uff0c\u4f7f\u7528\u5468\u671f\u6620\u5c04\u548cRFF\u5bf9PINNs\u67b6\u6784\u8fdb\u884c\u589e\u5f3a\u3002<\/li>\n\n\n\n<li>\u8fdb\u884c\u4e86\u8be6\u7ec6\u7684\u6d88\u878d\u5b9e\u9a8c\uff0c\u9010\u4e00\u53bb\u9664RFF\u3001\u5468\u671f\u6027\u3001\u56e0\u679c\u6027\u8bad\u7ec3\u7b49\u7ec4\u4ef6\u3002\u7ed3\u679c\u663e\u793a\uff0cRFF\u662f\u6700\u5173\u952e\u7684\u56e0\u7d20\uff0c\u5176\u6b21\u662f\u7a7a\u95f4\u5468\u671f\u6027\uff0c\u800c\u56e0\u679c\u6027\u8bad\u7ec3\u5219\u6709\u52a9\u4e8e\u63d0\u5347\u7a33\u5b9a\u6027\u3002<\/li>\n\n\n\n<li>\u6700\u4f18\u6a21\u578b\u5728\u7a7a\u95f4 L<sup>2<\/sup> \u8bef\u5dee\u4e0a\u8fdc\u4f18\u4e8e\u5176\u4ed6\u914d\u7f6e\uff0c\u4e14\u8bef\u5dee\u5728\u65f6\u95f4\u4e0a\u5206\u5e03\u66f4\u5747\u5300\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u4e8c\u7ef4\u9ad8\u65af\u8109\u51b2\u4e0e\u4ecb\u7535\u4ecb\u8d28\u76f8\u4e92\u4f5c\u7528<\/strong>\n<ul class=\"wp-block-list\">\n<li>\u5728\u4ecb\u7535\u5e38\u6570\u975e\u5747\u5300\uff08\u03b5 = 1 \u548c \u03b5 = 4\uff09\u7684\u60c5\u51b5\u4e0b\u6d4b\u8bd5PINNs\u9c81\u68d2\u6027\u3002<\/li>\n\n\n\n<li>\u51fa\u73b0\u65b0\u73b0\u8c61\uff1a\u82e5\u5f3a\u5236\u52a0\u5165\u7a7a\u95f4\u5468\u671f\u6027\uff0c\u53cd\u800c\u4f1a\u964d\u4f4e\u89e3\u7684\u51c6\u786e\u6027\uff0c\u5c24\u5176\u662f\u5728\u4ecb\u8d28\u8fb9\u754c\u9644\u8fd1\u4ea7\u751f\u8f83\u5927\u8bef\u5dee\u3002<\/li>\n\n\n\n<li>\u53bb\u9664\u7a7a\u95f4\u5468\u671f\u6027\u5e76\u4fdd\u7559RFF\u4e0e\u56e0\u679c\u6027\u8bad\u7ec3\u7684\u914d\u7f6e\uff0c\u53cd\u800c\u8fbe\u5230\u4e86\u6700\u4f18\u7cbe\u5ea6\uff0c\u8868\u660e\u5e94\u5f53\u6839\u636e\u95ee\u9898\u7269\u7406\u7279\u6027\u8c03\u6574PINNs\u67b6\u6784\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\">\u4e94\u3001\u5229\u7528\u795e\u7ecf\u5207\u7ebf\u6838\uff08NTK\uff09\u5206\u6790\u6536\u655b\u6027<\/h5>\n\n\n\n<p>\u4e3a\u4e86\u5206\u6790PINNs\u5728\u65f6\u7a7a\u7ef4\u5ea6\u4e0a\u7684\u6536\u655b\u7279\u6027\uff0c\u4f5c\u8005\u91c7\u7528\u4e86\u7ecf\u9a8c\u795e\u7ecf\u5207\u7ebf\u6838\uff08NTK\uff09\u7406\u8bba\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u8ba1\u7b97NTK\u77e9\u9635\u7684\u7279\u5f81\u503c\u4e4b\u548c\u4f30\u8ba1\u5c40\u90e8\u5b66\u4e60\u901f\u5ea6\uff08\u6536\u655b\u7387\uff09\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"315\" height=\"95\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-2.png\" alt=\"\" class=\"wp-image-5867\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-2.png 315w, https:\/\/nullthought.net\/wp-content\/uploads\/2025\/04\/image-2-300x90.png 300w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/figure>\n\n\n\n<p>\u5206\u6790\u7ed3\u679c\u8868\u660e\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u65f6\u95f4\u7ef4\u5ea6\u4e0a\uff0cNTK\u6536\u655b\u7387\u4e0e L<sup>2<\/sup>(t) \u8bef\u5dee\u9ad8\u5ea6\u76f8\u5173\uff0c\u8bf4\u660e\u8bef\u5dee\u5927\u7684\u65f6\u95f4\u533a\u95f4\u786e\u5b9e\u8bad\u7ec3\u6536\u655b\u6162\u3002<\/li>\n\n\n\n<li>\u7a7a\u95f4\u7ef4\u5ea6\u4e0a\u5374\u6ca1\u6709\u53d1\u73b0\u663e\u8457\u7684\u76f8\u5173\u6027\uff0c\u5373PINNs\u4e0d\u80fd\u81ea\u52a8\u5c06\u8bad\u7ec3\u8d44\u6e90\u96c6\u4e2d\u4e8e\u7a7a\u95f4\u8bef\u5dee\u8f83\u5927\u7684\u533a\u57df\u3002<\/li>\n\n\n\n<li>\u5373\u4f7f\u589e\u52a0\u65f6\u95f4\u91c7\u6837\u70b9\uff0c\u8bef\u5dee\u70ed\u70b9\u533a\u57df\u4ecd\u96c6\u4e2d\u4e8e\u65f6\u95f4\u68af\u5ea6\u5927\u7684\u533a\u57df\uff0c\u8bf4\u660e\u8fd9\u79cd\u5b66\u4e60\u504f\u5dee\u662f\u7f51\u7edc\u8bad\u7ec3\u673a\u5236\u672c\u8eab\u7684\u5c40\u9650\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\">\u516d\u3001\u7ed3\u8bba\u4e0e\u672a\u6765\u65b9\u5411<\/h5>\n\n\n\n<ol class=\"wp-block-list\">\n<li>PINNs\u5728\u975e\u7a33\u6001\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u4e2d\u5c55\u73b0\u51fa\u5f3a\u5927\u7684\u6f5c\u529b\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u975e\u5149\u6ed1\u89e3\u3001\u5f3a\u6ce2\u52a8\u7ed3\u6784\u65b9\u9762\u4f18\u4e8e\u4f20\u7edf\u65b9\u6cd5\u3002<\/li>\n\n\n\n<li>RFF \u662f\u63d0\u9ad8\u9ad8\u9891\u7279\u5f81\u5b66\u4e60\u80fd\u529b\u7684\u5173\u952e\uff0c\u800c\u7a7a\u95f4\/\u65f6\u95f4\u5468\u671f\u6027\u6620\u5c04\u4e0e\u56e0\u679c\u6027\u8bad\u7ec3\u5219\u6839\u636e\u573a\u666f\u8868\u73b0\u51fa\u4e0d\u540c\u7684\u91cd\u8981\u6027\u3002<\/li>\n\n\n\n<li>\u795e\u7ecf\u7f51\u7edc\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\u65e0\u6cd5\u81ea\u53d1\u5173\u6ce8\u201c\u9ad8\u96be\u5ea6\u201d\u533a\u57df\uff08\u9ad8\u8bef\u5dee\u533a\uff09\uff0c\u8bad\u7ec3\u8d44\u6e90\u5206\u914d\u4e0d\u5747\u4ecd\u662f\u9650\u5236\u5176\u7cbe\u5ea6\u4e0e\u7a33\u5b9a\u6027\u7684\u4e3b\u8981\u74f6\u9888\u3002<\/li>\n\n\n\n<li>\u63a8\u8350\u672a\u6765\u7814\u7a76\u5173\u6ce8\u52a8\u6001\u91c7\u6837\u3001\u6b8b\u5dee\u52a0\u6743\u4e0e\u7269\u7406\u81ea\u9002\u5e94\u67b6\u6784\uff0c\u4ee5\u8fdb\u4e00\u6b65\u63d0\u5347PINNs\u5728\u590d\u6742\u7535\u78c1\u95ee\u9898\u4e2d\u7684\u9002\u5e94\u6027\u4e0e\u6536\u655b\u901f\u5ea6\u3002<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u8bba\u6587PINNs for Solving Unsteady Maxwell&#8217;s Equations: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[8,36],"tags":[39,48,71],"class_list":["post-5865","post","type-post","status-publish","format-standard","hentry","category-tech","category-36","tag-ai","tag-48","tag-physics"],"rttpg_featured_image_url":null,"rttpg_author":{"display_name":"NullThought","author_link":"https:\/\/nullthought.net\/?author=1"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/nullthought.net\/?cat=8\" rel=\"category\">Tech<\/a> <a href=\"https:\/\/nullthought.net\/?cat=36\" rel=\"category\">\u79d1\u5b66<\/a>","rttpg_excerpt":"\u8bba\u6587PINNs for Solving Unsteady Maxwell&#8217;s Equations:&hellip;","_links":{"self":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/5865","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5865"}],"version-history":[{"count":2,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/5865\/revisions"}],"predecessor-version":[{"id":5869,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/5865\/revisions\/5869"}],"wp:attachment":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}