{"id":1076229,"date":"2024-03-12T15:25:00","date_gmt":"2024-03-12T22:25:00","guid":{"rendered":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/?post_type=msr-blog-post&p=1076229"},"modified":"2024-09-25T04:15:09","modified_gmt":"2024-09-25T11:15:09","slug":"m-ofdft","status":"publish","type":"msr-blog-post","link":"https:\/\/new-cm-edgedigital.pages.dev\/en-us\/research\/articles\/m-ofdft\/","title":{"rendered":"AI\u52a9\u529bM-OFDFT\u5b9e\u73b0\u517c\u5177\u7cbe\u5ea6\u4e0e\u6548\u7387\u7684\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5"},"content":{"rendered":"\n

\u4f5c\u8005\uff1a\u79d1\u5b66\u667a\u80fd\u4e2d\u5fc3<\/em><\/p>\n\n\n\n

\u7f16\u8005\u6309\uff1a\u4e3a\u4e86\u4f7f\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u7a81\u7834\u5f53\u524d\u5e7f\u6cdb\u5e94\u7528\u7684\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08KSDFT\uff09\u6240\u80fd\u6c42\u89e3\u7684\u5206\u5b50\u4f53\u7cfb\u89c4\u6a21\uff0c\u5fae\u8f6f\u7814\u7a76\u9662\u79d1\u5b66\u667a\u80fd\u4e2d\u5fc3\u7684\u7814\u7a76\u5458\u4eec\u57fa\u4e8e\u4eba\u5de5\u667a\u80fd\u6280\u672f\u548c\u65e0\u8f68\u9053\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08OFDFT\uff09\u5f00\u53d1\u4e86\u4e00\u79cd\u65b0\u7684\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u6846\u67b6 M-OFDFT\u3002\u8fd9\u4e00\u6846\u67b6\u4e0d\u4ec5\u4fdd\u6301\u4e86\u4e0e KSDFT \u76f8\u5f53\u7684\u8ba1\u7b97\u7cbe\u5ea6\uff0c\u800c\u4e14\u5728\u8ba1\u7b97\u6548\u7387\u4e0a\u5b9e\u73b0\u4e86\u663e\u8457\u63d0\u5347\uff0c\u5e76\u5c55\u73b0\u4e86\u4f18\u5f02\u7684\u5916\u63a8\u6027\u80fd\uff0c\u4e3a\u5206\u5b50\u79d1\u5b66\u7814\u7a76\u4e2d\u8bf8\u591a\u8ba1\u7b97\u65b9\u6cd5\u7684\u57fa\u7840\u2014\u2014\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u5f00\u8f9f\u4e86\u65b0\u7684\u601d\u8def\u3002\u76f8\u5173\u7814\u7a76\u6210\u679c\u5df2\u5728\u56fd\u9645\u77e5\u540d\u5b66\u672f\u671f\u520a\u300a\u81ea\u7136-\u8ba1\u7b97\u79d1\u5b66\u300b\uff08Nature Computational Science\uff09\u4e0a\u53d1\u8868\u3002<\/p>\n\n\n\n

\n\n\n\n

\u8fd1\u51e0\u5341\u5e74\u6765\uff0c\u7406\u8bba\u4e0e\u8ba1\u7b97\u5316\u5b66\u9886\u57df\u53d6\u5f97\u7684\u4e00\u5927\u6210\u5c31\u662f\u80fd\u591f\u901a\u8fc7\u8ba1\u7b97\u624b\u6bb5\u5f97\u5230\u5206\u5b50\u4f53\u7cfb\u7684\u7269\u7406\u5316\u5b66\u6027\u8d28\u3002\u8fd9\u4e3a\u836f\u7269\u53d1\u73b0\u548c\u6750\u6599\u8bbe\u8ba1\u7b49\u8bf8\u591a\u5de5\u4e1a\u754c\u95ee\u9898\u5e26\u6765\u4e86\u5168\u65b0\u7684\u7814\u7a76\u624b\u6bb5\uff0c\u6709\u671b\u7f29\u77ed\u5f00\u53d1\u6d41\u7a0b\u5e76\u964d\u4f4e\u5f00\u53d1\u6210\u672c\u3002\u8fd9\u4e9b\u8ba1\u7b97\u65b9\u6cd5\u7684\u57fa\u7840\u6b65\u9aa4\u662f\u4f7f\u7528\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u6c42\u89e3\u7ed9\u5b9a\u5206\u5b50\u4f53\u7cfb\u7684\u7535\u5b50\u72b6\u6001\uff0c\u8fdb\u800c\u5f97\u5230\u8be5\u4f53\u7cfb\u7684\u5404\u79cd\u6027\u8d28\u3002<\/p>\n\n\n\n

\u7136\u800c\uff0c\u5404\u79cd\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u7684\u6c42\u89e3\u7cbe\u5ea6\u548c\u8ba1\u7b97\u6548\u7387\u5f80\u5f80\u65e0\u6cd5\u517c\u5f97\u3002\u5f53\u524d\uff0c\u53d6\u5f97\u76f8\u5bf9\u5408\u7406\u7684\u201c\u7cbe\u5ea6-\u6548\u7387\u201d\u6743\u8861\u800c\u88ab\u5e7f\u6cdb\u5e94\u7528\u7684\u65b9\u6cd5\u662f Kohn-Sham \u5f62\u5f0f\u7684\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08Kohn-Sham density functional theory, KSDFT\uff09\u3002\u4f46 KSDFT \u5177\u6709\u8f83\u9ad8\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u4e0d\u80fd\u5f88\u597d\u5730\u6ee1\u8db3\u65e5\u76ca\u589e\u957f\u7684\u6c42\u89e3\u5927\u89c4\u6a21\u5206\u5b50\u4f53\u7cfb\u7684\u9700\u6c42\u3002\u4e3a\u6b64\uff0c\u5fae\u8f6f\u7814\u7a76\u9662\u79d1\u5b66\u667a\u80fd\u4e2d\u5fc3\u7684\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u548c\u65e0\u8f68\u9053\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08OFDFT\uff09\u7684\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u6846\u67b6 M-OFDFT\uff0c\u5176\u4e0d\u4ec5\u663e\u8457\u8d85\u8d8a\u4e86 KSDFT \u7684\u8ba1\u7b97\u6548\u7387\uff0c\u8fd8\u80fd\u4fdd\u6709\u5176\u6c42\u89e3\u7cbe\u5ea6\u3002\u8fd9\u4e00\u6210\u679c\u5c55\u793a\u4e86\u4eba\u5de5\u667a\u80fd\u5728\u63d0\u5347\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u4e2d\u201c\u7cbe\u5ea6-\u6548\u7387\u201d\u6743\u8861\u65b9\u9762\u7684\u5353\u8d8a\u80fd\u529b\uff0c\u5e76\u5c06\u52a9\u529b\u52a0\u901f\u76f8\u5173\u4e1a\u754c\u95ee\u9898\u7684\u7814\u7a76\u4e0e\u5f00\u53d1\u3002M-OFDFT \u7684\u76f8\u5173\u7814\u7a76\u6210\u679c\u5df2\u5728\u56fd\u9645\u77e5\u540d\u5b66\u672f\u671f\u520a\u300a\u81ea\u7136-\u8ba1\u7b97\u79d1\u5b66\u300b\uff08Nature Computational Science\uff09\u4e0a\u53d1\u8868\u3002<\/p>\n\n\n\n

\"Overcoming<\/figure>\n\n\n\n

Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning<\/strong><\/p>\n\n\n\n

\u300a\u81ea\u7136-\u8ba1\u7b97\u79d1\u5b66\u300b\u6587\u7ae0\u94fe\u63a5\uff1ahttps:\/\/www.nature.com\/articles\/s43588-024-00605-8 (opens in new tab)<\/span><\/a><\/p>\n\n\n\n

SharedIt \u94fe\u63a5\uff1ahttps:\/\/rdcu.be\/dANtS (opens in new tab)<\/span><\/a><\/p>\n\n\n\n

\u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2309.16578 (opens in new tab)<\/span><\/a><\/p>\n\n\n\n

\u4eba\u5de5\u667a\u80fd\u7ed9\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u5e26\u6765\u65b0\u673a\u4f1a<\/h2>\n\n\n\n

\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u662f\u6c42\u89e3\u5206\u5b50\u4f53\u7cfb\u5404\u79cd\u7269\u7406\u5316\u5b66\u6027\u8d28\u7684\u57fa\u7840\u5de5\u5177\u3002\u7531\u4e8e\u591a\u7535\u5b50\u4f53\u7cfb\u672c\u8eab\u5177\u6709\u4e00\u5b9a\u7684\u6c42\u89e3\u96be\u5ea6\uff0c\u6240\u4ee5\u9ad8\u7cbe\u5ea6\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u56e0\u5176\u8f83\u9ad8\u7684\u8ba1\u7b97\u4ee3\u4ef7\u5f88\u96be\u5e94\u7528\u5230\u5de5\u4e1a\u754c\u6240\u5173\u6ce8\u7684\u5206\u5b50\u4f53\u7cfb\u4e2d\uff0c\u800c\u53ef\u8ba1\u7b97\u8f83\u5927\u5206\u5b50\u7684\u65b9\u6cd5\u5219\u4f1a\u56e0\u5f15\u5165\u4e00\u4e9b\u8fd1\u4f3c\u800c\u635f\u5931\u7cbe\u5ea6\u3002\u76ee\u524d KSDFT \u56e0\u5176\u76f8\u5bf9\u5408\u9002\u7684\u7cbe\u5ea6\u4e0e\u6548\u7387\u6743\u8861\u5f97\u5230\u4e86\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n\n\n\n

\u4e0d\u8fc7\uff0c\u8fd1\u671f\u4eba\u5de5\u667a\u80fd\u6280\u672f\u7684\u559c\u4eba\u8fdb\u5c55\u4e5f\u4e3a\u5176\u4ed6\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u6846\u67b6\u5e26\u6765\u4e86\u65b0\u7684\u673a\u4f1a\u3002\u4e3a\u4e86\u4f7f\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u7a81\u7834 KSDFT \u6240\u80fd\u6c42\u89e3\u7684\u5206\u5b50\u4f53\u7cfb\u89c4\u6a21\uff0c\u5fae\u8f6f\u7814\u7a76\u9662\u7684\u7814\u7a76\u5458\u4eec\u5229\u7528\u4eba\u5de5\u667a\u80fd\u6280\u672f\uff0c\u5f00\u53d1\u4e86 M-OFDFT\uff0c\u8be5\u65b9\u6cd5\u6bd4 KSDFT \u6548\u7387\u66f4\u9ad8\uff0c\u540c\u65f6\u53c8\u80fd\u4fdd\u6709\u5176\u7cbe\u5ea6\u3002\u57fa\u4e8e OFDFT \u7684\u5f00\u53d1\uff0c\u8ba9 M-OFDFT \u6210\u4e3a\u4e86\u4e00\u79cd\u6bd4 KSDFT \u7406\u8bba\u590d\u6742\u5ea6\u66f4\u4f4e\u7684\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u6846\u67b6\uff0c\u56e0\u4e3a\u5b83\u53ea\u9700\u4f18\u5316\u7535\u5b50\u5bc6\u5ea6\u51fd\u6570 \u03c1(r) \u8fd9\u4e00\u4e2a\u51fd\u6570\u6765\u6c42\u89e3\u7535\u5b50\u72b6\u6001\u5373\u53ef\uff0cKSDFT \u5219\u9700\u8981\u4f18\u5316\u4e0e\u7535\u5b50\u6570\u76f8\u540c\u7684\u591a\u4e2a\u51fd\u6570\u3002<\/p>\n\n\n\n

\u4e0d\u8fc7\uff0cOFDFT \u9762\u4e34\u7740\u4e00\u4e2a\u5de8\u5927\u7684\u6311\u6218\u2014\u2014\u9700\u8981\u7535\u5b50\u52a8\u80fd\u5173\u4e8e\u5bc6\u5ea6\u51fd\u6570\u7684\u6cdb\u51fd T_S [\u03c1]\uff0c\u4f46\u5b83\u7684\u5f62\u5f0f\u672a\u77e5\uff0c\u5e76\u4e14\u96be\u4ee5\u6784\u9020\u9002\u7528\u4e8e\u5206\u5b50\u4f53\u7cfb\u7684\u9ad8\u7cbe\u5ea6\u8fd1\u4f3c\u3002<\/p>\n\n\n\n

\u9488\u5bf9\u8fd9\u4e00\u96be\u9898\uff0cM-OFDFT \u4f7f\u7528\u4e00\u4e2a\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b T_(S,\u03b8) \u6765\u8fd1\u4f3c\u52a8\u80fd\u6cdb\u51fd\u3002\u501f\u52a9\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u7684\u5f3a\u5927\u62df\u5408\u80fd\u529b\uff0cM-OFDFT \u53ef\u5b9e\u73b0\u6bd4\u57fa\u4e8e\u8fd1\u4f3c\u7269\u7406\u6a21\u578b\u8bbe\u8ba1\u7684\u7ecf\u5178\u52a8\u80fd\u6cdb\u51fd\u66f4\u9ad8\u7684\u51c6\u786e\u5ea6\u3002\u5bf9\u4e8e\u4e00\u4e2a\u5f85\u6c42\u89e3\u7684\u5206\u5b50\u4f53\u7cfb\u7ed3\u6784\uff0cM-OFDFT \u4f1a\u4f7f\u7528\u52a8\u80fd\u6cdb\u51fd\u6a21\u578b T_(S,\u03b8) \u4ee5\u53ca\u5176\u4ed6\u53ef\u76f4\u63a5\u8ba1\u7b97\u7684\u80fd\u91cf\u9879\u6784\u9020\u51fa\u4e00\u4e2a\u7535\u5b50\u5bc6\u5ea6\u7684\u4f18\u5316\u76ee\u6807\uff0c\u7136\u540e\u901a\u8fc7\u4f18\u5316\u8fc7\u7a0b\u6c42\u89e3\u6700\u4f18\uff08\u57fa\u6001\uff09\u7535\u5b50\u5bc6\u5ea6\uff08\u56fe1\uff09\uff0c\u8fdb\u800c\u53ef\u8ba1\u7b97\u80fd\u91cf\u3001\u529b\u3001\u7535\u8377\u5206\u5e03\u7b49\u5206\u5b50\u5c5e\u6027\u3002<\/p>\n\n\n\n

\"Overcoming
\u56fe1\uff1a\u5bf9\u4e8e\u5f85\u6c42\u89e3\u7684\u5206\u5b50\u4f53\u7cfb\u7ed3\u6784 M\uff0cM-OFDFT \u901a\u8fc7\u6700\u5c0f\u5316\u7535\u5b50\u80fd\u91cf E_\u03b8 \u6765\u6c42\u89e3\u7535\u5b50\u5bc6\u5ea6\uff08\u4ee5\u5176\u5411\u91cf\u5316\u7cfb\u6570 p \u8868\u793a\uff09\uff0c\u5176\u4e2d\u96be\u4ee5\u8fd1\u4f3c\u7684\u52a8\u80fd\u90e8\u5206\u7531\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b T_(S,\u03b8) \u6765\u8fd1\u4f3c<\/figcaption><\/figure>\n\n\n\n

M-OFDFT\u5b9e\u73b0\u517c\u5177\u7cbe\u5ea6\u4e0e\u6548\u7387\u7684\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5<\/h2>\n\n\n\n

\u7814\u7a76\u5458\u4eec\u5bf9 M-OFDFT \u8fdb\u884c\u4e86\u4e00\u7cfb\u5217\u7684\u5b9e\u9a8c\u9a8c\u8bc1\u3002\u9996\u5148\u8003\u5bdf\u7684\u662f M-OFDFT \u5728\u5e38\u89c1\u5c0f\u5206\u5b50\u4f53\u7cfb\u4e0a\u7684\u6c42\u89e3\u7cbe\u5ea6\u3002\u7ed3\u679c\u663e\u793a\uff0cM-OFDFT \u5728\u4e59\u9187\u5206\u5b50\u6784\u8c61\u4ee5\u53ca QM9 \u6570\u636e\u96c6\u7684\u5206\u5b50\u4e0a\u53ef\u4ee5\u8fbe\u5230\u4e0eKSDFT\u76f8\u5f53\u7684\u7cbe\u5ea6\uff08\u80fd\u91cf\u8fbe\u5230\u5316\u5b66\u7cbe\u5ea61 kcal\/mol\uff09\u3002\u76f8\u8f83\u4e8e\u7ecf\u5178 OFDFT \u65b9\u6cd5\uff0c\u7cbe\u5ea6\u63d0\u9ad8\u4e86\u4e24\u4e2a\u6570\u91cf\u7ea7\uff08\u56fe2-a\uff09\u3002M-OFDFT \u89e3\u5f97\u7684\u7535\u5b50\u5bc6\u5ea6\u4e5f\u4e0e KSDFT \u7684\u7ed3\u679c\u91cd\u5408\uff08\u56fe2-b\uff09\uff0c\u7279\u522b\u662f\u5f97\u5230\u4e86\u7535\u5b50\u58f3\u5c42\u7ed3\u6784\uff0c\u800c\u7ecf\u5178 OFDFT \u7684\u7ed3\u679c\u5219\u6709\u660e\u663e\u504f\u5dee\u3002\u7531 M-OFDFT \u89e3\u5f97\u7684\u4e59\u9187\u6784\u8c61\u7a7a\u95f4\u4e0a\u7684\u52bf\u80fd\u9762\uff08\u6bcf\u4e2a\u70b9\u90fd\u662f\u901a\u8fc7\u5bc6\u5ea6\u4f18\u5316\u5f97\u5230\u7684\uff0c\u5e76\u4e0d\u662f\u76f4\u63a5\u9884\u6d4b\uff09\u4e5f\u4e0e KSDFT \u7684\u7ed3\u679c\u4e00\u81f4\uff08\u56fe2-c\uff09\u3002<\/p>\n\n\n\n

\"Overcoming
\u56fe2\uff1aM-OFDFT \u548c\u4e00\u4e9b\u7ecf\u5178 OFDFT \u5728\u5206\u5b50\u4f53\u7cfb\u4e0a\u4e0e KSDFT \u7684\u6bd4\u8f83<\/figcaption><\/figure>\n\n\n\n

\u4e4b\u540e\uff0c\u7814\u7a76\u5458\u4eec\u53c8\u9a8c\u8bc1\u4e86 M-OFDFT \u4e0d\u4ec5\u4fdd\u6709 KSDFT \u7ea7\u522b\u7684\u7cbe\u5ea6\uff0c\u5176\u66f4\u4f4e\u7684\u7406\u8bba\u8ba1\u7b97\u590d\u6742\u5ea6\u8fd8\u4f7f\u5176\u5728\u6548\u7387\u4e0a\u4e5f\u8d85\u8d8a\u4e86 KSDFT\u3002\u5728\u5b9e\u9645\u8ba1\u7b97\u4e2d M-OFDFT \u53d6\u5f97\u4e86 O(N^1.46) \u7684\u590d\u6742\u5ea6\uff08\u56fe3\uff09\uff0c\u6bd4 KSDFT \u7684\u5b9e\u9645\u590d\u6742\u5ea6 O(N^2.49) \u4f4e\u4e86\u4e00\u9636\uff0c\u4e14\u5176\u6240\u9700\u7edd\u5bf9\u65f6\u95f4\u4e5f\u660e\u663e\u5c11\u4e8e KSDFT\u3002\u5728\u4e24\u4e2a\u66f4\u5927\u7684\u86cb\u767d\u8d28\u4f53\u7cfb\u4e0a\uff08\u5305\u542b2676\u548c2750\u4e2a\u7535\u5b50\uff09\uff0cM-OFDFT \u5b9e\u73b0\u4e8625.6\u500d\u548c27.4\u500d\u7684\u52a0\u901f\u3002<\/p>\n\n\n\n

\"Overcoming
\u56fe3\uff1aM-OFDFT \u548c KSDFT \u7684\u5b9e\u9645\u8ba1\u7b97\u65f6\u95f4\u53ca\u590d\u6742\u5ea6<\/figcaption><\/figure>\n\n\n\n

M-OFDFT\u5177\u6709\u66f4\u5f3a\u7684\u6cdb\u5316\u80fd\u529b<\/h2>\n\n\n\n

\u6df1\u5ea6\u5b66\u4e60\u6a21\u578b\u5728\u79d1\u5b66\u4efb\u52a1\u4e2d\u7684\u5e94\u7528\u9762\u4e34\u4e00\u5927\u6311\u6218\u662f\uff0c\u5728\u5177\u6709\u4e0e\u8bad\u7ec3\u6570\u636e\u4e0d\u540c\u7279\u70b9\u7684\u6570\u636e\u4e0a\u7684\u6cdb\u5316\u95ee\u9898\u3002\u4f46\u91c7\u7528\u4e86 OFDFT \u6846\u67b6\u540e\uff0c\u52a8\u80fd\u6cdb\u51fd\u6a21\u578b\u9047\u5230\u7684\u6cdb\u5316\u95ee\u9898\u5c31\u4f1a\u51cf\u8f7b\uff0c\u4ece\u800c\u4f7f M-OFDFT \u53ef\u4ee5\u5728\u6bd4\u8bad\u7ec3\u96c6\u5206\u5b50\u89c4\u6a21\u66f4\u5927\u7684\u4f53\u7cfb\u4e0a\u5c55\u73b0\u51fa\u826f\u597d\u7684\u5916\u63a8\u80fd\u529b\u3002<\/p>\n\n\n\n

\u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0cM-OFDFT \u7684\u80fd\u91cf\u9884\u6d4b\u8bef\u5dee\u663e\u8457\u4f4e\u4e8e\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684\u7aef\u5230\u7aef\u80fd\u91cf\u9884\u6d4b\u6a21\u578b\uff08\u56fe4-a\uff09\u3002\u6b64\u5916\uff0c\u7814\u7a76\u5458\u4eec\u8fd8\u5229\u7528\u5728\u591a\u80bd\u7247\u6bb5\u4e0a\u8bad\u7ec3\u7684 M-OFDFT \u6a21\u578b\u6c42\u89e3\u5b8c\u6574\u86cb\u767d\u7ed3\u6784\uff0c\u5e76\u53d6\u5f97\u4e86\u8d85\u8d8a\u7aef\u5230\u7aef\u6a21\u578b\u548c\u7ecf\u5178 OFDFT \u7684\u6cdb\u5316\u6027\u80fd\uff08\u56fe4-c\uff09\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u76f8\u8f83\u7aef\u5230\u7aef\u6a21\u578b\uff0cM-OFDFT \u8fd8\u53ef\u4ee5\u7528\u66f4\u5c11\u7684\u5927\u5206\u5b50\u4f53\u7cfb\u8bad\u7ec3\u6570\u636e\u53d6\u5f97\u66f4\u597d\u7684\u6cdb\u5316\u8868\u73b0\uff08\u56fe4-b\u4e0e\u56fe4-d\uff09\u3002<\/p>\n\n\n\n

\"Overcoming
\u56fe4\uff1aM-OFDFT \u548c\u5176\u4ed6\u6df1\u5ea6\u5b66\u4e60\u65b9\u6cd5\u7684\u6cdb\u5316\u6027\u80fd\u6bd4\u8f83<\/figcaption><\/figure>\n\n\n\n

M-OFDFT\u7684\u5de5\u4f5c\u539f\u7406<\/h2>\n\n\n\n

\u201c\u795e\u9f99\u89c1\u9996\u53c8\u89c1\u5c3e\u201d\uff1a\u9ad8\u6548\u6355\u83b7\u975e\u5c40\u57df\u6548\u5e94\u7684\u52a8\u80fd\u6cdb\u51fd\u6a21\u578b<\/h3>\n\n\n\n

\u52a8\u80fd\u5bc6\u5ea6\u6cdb\u51fd\u5177\u6709\u660e\u663e\u7684\u975e\u5c40\u57df\u6548\u5e94\uff0c\u800c\u7528\u7ecf\u5178\u7684\u57fa\u4e8e\u683c\u70b9\uff08grid\uff09\u7684\u65b9\u5f0f\u8868\u5f81\u7535\u5b50\u5bc6\u5ea6\u5219\u4f1a\u5e26\u6765\u9ad8\u6602\u7684\u975e\u5c40\u57df\u8ba1\u7b97\u4ee3\u4ef7\u3002\u4e3a\u6b64\uff0cM-OFDFT \u5c06\u7535\u5b50\u5bc6\u5ea6\u5728\u4e00\u7ec4\u539f\u5b50\u57fa\u7ec4\u51fd\u6570\u4e0a\u5c55\u5f00\uff0c\u5e76\u4f7f\u7528\u5c55\u5f00\u7cfb\u6570 p \u4f5c\u4e3a\u7535\u5b50\u5bc6\u5ea6\u8868\u5f81\u3002\u7531\u4e8e\u57fa\u51fd\u6570\u53e0\u52a0\u7684\u5f62\u72b6\u4e0e\u7535\u5b50\u5206\u5e03\u63a5\u8fd1\uff0c\u6240\u4ee5\u5176\u6570\u91cf\u53ef\u8fdc\u5c0f\u4e8e\u683c\u70b9\u6570\uff0c\u4f7f\u5f97\u975e\u5c40\u57df\u8ba1\u7b97\u4ee3\u4ef7\u5927\u5927\u964d\u4f4e\uff0c\u5e76\u6709\u52a9\u4e8e\u523b\u753b\u7535\u5b50\u5bc6\u5ea6\u4e2d\u7684\u58f3\u5c42\u7ed3\u6784\u3002<\/p>\n\n\n\n

M-OFDFT \u5c06\u6bcf\u4e2a\u539f\u5b50\u4e0a\u7684\u7535\u5b50\u5bc6\u5ea6\u7cfb\u6570 p \u548c\u7c7b\u578b Z \u4e0e\u5750\u6807 x \u4f5c\u4e3a\u8282\u70b9\u7279\u5f81\uff0c\u5e76\u57fa\u4e8e Graphormer \u6a21\u578b[1]\u9884\u6d4b\u7535\u5b50\u52a8\u80fd T_(S,\u03b8)\uff08\u56fe5\uff09\uff0c\u5176\u81ea\u6ce8\u610f\u529b\u673a\u5236\u663e\u5f0f\u523b\u753b\u4e86\u8377\u8f7d\u5728\u6bcf\u4e24\u4e2a\u539f\u5b50\u4e0a\u7684\u7535\u5b50\u5bc6\u5ea6\u7279\u5f81\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\uff0c\u4ece\u800c\u53ef\u6355\u6349\u975e\u5c40\u57df\u6027\u8d28\u3002\u6b64\u5916\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u52a8\u80fd\u7684\u65cb\u8f6c\u4e0d\u53d8\u6027\uff0cM-OFDFT \u4f7f\u7528\u4e86\u4ee5\u5404\u4e2a\u539f\u5b50\u4e3a\u4e2d\u5fc3\u3001\u57fa\u4e8e\u5176\u76f8\u90bb\u539f\u5b50\u7684\u5c40\u90e8\u5750\u6807\u7cfb\uff0c\u5c06\u7535\u5b50\u5bc6\u5ea6\u7cfb\u6570\u8f6c\u6362\u4e3a\u65cb\u8f6c\u4e0d\u53d8\u7684\u7279\u5f81\u3002<\/p>\n\n\n\n

\"Overcoming
\u56fe5\uff1a\u57fa\u4e8e\u975e\u5c40\u57df\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u52a8\u80fd\u5bc6\u5ea6\u6cdb\u51fd\u6a21\u578b<\/figcaption><\/figure>\n\n\n\n

\u201c\u6a2a\u770b\u6210\u5cad\u4fa7\u6210\u5cf0\uff0c\u8fdc\u8fd1\u9ad8\u4f4e\u5404\u4e0d\u540c\u201d\uff1a\u9ad8\u6548\u5b66\u4e60\u7535\u5b50\u80fd\u91cf\u66f2\u9762\u7684\u8bad\u7ec3\u7b56\u7565<\/h3>\n\n\n\n

\u4e0e\u4f20\u7edf\u673a\u5668\u5b66\u4e60\u4efb\u52a1\u4e0d\u540c\uff0c\u52a8\u80fd\u6cdb\u51fd\u6a21\u578b\u662f\u88ab\u5f53\u4f5c\u5176\u8f93\u5165\u53d8\u91cf\u7684\u4f18\u5316\u76ee\u6807\u4f7f\u7528\u7684\uff0c\u800c\u975e\u7528\u4e8e\u5728\u4e00\u4e9b\u5355\u70b9\u4e0a\u505a\u9884\u6d4b\uff0c\u8fd9\u5bf9\u6a21\u578b\u7684\u5b66\u4e60\u63d0\u51fa\u4e86\u66f4\u9ad8\u7684\u8981\u6c42\uff1a\u6a21\u578b\u5fc5\u987b\u6355\u6349\u5230\u6bcf\u4e2a\u5206\u5b50\u7ed3\u6784\u4e0a\u7535\u5b50\u80fd\u91cf\u66f2\u9762\u7684\u8f6e\u5ed3\u3002<\/p>\n\n\n\n

\u4e3a\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u6df1\u5165\u5206\u6790\u4e86\u7528\u6765\u751f\u6210\u6570\u636e\u7684\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\uff0c\u53d1\u73b0\u5b83\u5176\u5b9e\u53ef\u4ee5\u4e3a\u6bcf\u4e2a\u5206\u5b50\u7ed3\u6784\u751f\u6210\u591a\u4e2a\u6570\u636e\u70b9\uff0c\u800c\u4e14\u8fd8\u80fd\u63d0\u4f9b\u68af\u5ea6\u6807\u6ce8\uff0c\u4ece\u800c\u8ba9\u6a21\u578b\u53ef\u4ee5\u62e5\u6709\u66f4\u4e30\u5bcc\u7684\u66f2\u9762\u8f6e\u5ed3\u7279\u5f81\u3002\u7136\u800c\u68af\u5ea6\u7684\u5de8\u5927\u8303\u56f4\u4e5f\u4f7f\u795e\u7ecf\u7f51\u7edc\u96be\u4ee5\u4f18\u5316\u3002\u5bf9\u6b64\uff0c\u7814\u7a76\u5458\u4eec\u8fd8\u63d0\u51fa\u4e86\u4e00\u7cfb\u5217\u589e\u5f3a\u6a21\u5757\uff0c\u8ba9\u6a21\u578b\u80fd\u591f\u66f4\u5bb9\u6613\u5730\u8868\u8fbe\u5de8\u5927\u7684\u68af\u5ea6\u3002<\/p>\n\n\n\n

\u5f00\u542f\u672a\u6765\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u7684\u65b0\u7bc7\u7ae0<\/h2>\n\n\n\n

M-OFDFT \u6210\u529f\u7a81\u7834\u4e86\u65e0\u8f68\u9053\u5bc6\u5ea6\u6cdb\u51fd\u6846\u67b6\u5728\u5206\u5b50\u4f53\u7cfb\u4e2d\u7684\u74f6\u9888\uff0c\u5c06\u5176\u6c42\u89e3\u7cbe\u5ea6\u63d0\u5347\u5230\u4e86\u5e38\u7528\u7684 KSDFT \u7684\u6c34\u5e73\uff0c\u540c\u65f6\u4fdd\u6709\u4e86\u5176\u66f4\u4f4e\u7684\u8ba1\u7b97\u4ee3\u4ef7\uff0c\u63a8\u8fdb\u4e86\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u5728\u201c\u7cbe\u5ea6-\u6548\u7387\u201d\u65b9\u9762\u7684\u6743\u8861\uff0c\u4e3a\u5206\u5b50\u79d1\u5b66\u7814\u7a76\u63d0\u4f9b\u4e86\u4e00\u79cd\u66f4\u6709\u6f5c\u529b\u7684\u7814\u7a76\u5de5\u5177\u3002<\/p>\n\n\n\n

\u5c3d\u7ba1 M-OFDFT \u5df2\u7ecf\u5728\u67d0\u4e9b\u5206\u5b50\u4f53\u7cfb\u4e0a\u5c55\u73b0\u4e86\u51fa\u8272\u7684\u6cdb\u5316\u6027\u80fd\uff0c\u4f46\u5728\u66f4\u5927\u7684\u5206\u5b50\u4f53\u7cfb\u4e0a\u5b9e\u73b0\u957f\u65f6\u95f4\u4e14\u7a33\u5b9a\u7684\u9ad8\u7cbe\u5ea6\u6a21\u62df\u4ecd\u662f\u4e00\u4e2a\u5de8\u5927\u7684\u6311\u6218\u3002\u5fae\u8f6f\u7814\u7a76\u9662\u671f\u5f85 M-OFDFT \u53ef\u4ee5\u6cbf\u7740\u8fd9\u4e00\u65b9\u5411\u6fc0\u53d1\u66f4\u591a\u7814\u7a76\u4e0e\u521b\u65b0\uff0c\u5e76\u5728\u672a\u6765\u548c\u5176\u4ed6\u65b9\u6cd5\u4e00\u8d77\u4e3a\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u5e26\u6765\u66f4\u591a\u7a81\u7834\u6027\u7684\u6210\u679c\u548c\u5f71\u54cd\u3002<\/p>\n\n\n\n

\u76f8\u5173\u6587\u7ae0<\/p>\n\n\n\n

[1] Do Transformers really perform badly for graph representation? Advances in Neural Information Processing Systems 34 (NeurIPS 2021)<\/p>\n\n\n\n

https:\/\/proceedings.neurips.cc\/paper\/2021\/hash\/f1c1592588411002af340cbaedd6fc33-Abstract.html (opens in new tab)<\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u4f5c\u8005\uff1a\u79d1\u5b66\u667a\u80fd\u4e2d\u5fc3 \u7f16\u8005\u6309\uff1a\u4e3a\u4e86\u4f7f\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u7a81\u7834\u5f53\u524d\u5e7f\u6cdb\u5e94\u7528\u7684\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08KSDFT\uff09\u6240\u80fd\u6c42\u89e3\u7684\u5206\u5b50\u4f53\u7cfb\u89c4\u6a21\uff0c\u5fae\u8f6f\u7814\u7a76\u9662\u79d1\u5b66\u667a\u80fd\u4e2d\u5fc3\u7684\u7814\u7a76\u5458\u4eec\u57fa\u4e8e\u4eba\u5de5\u667a\u80fd\u6280\u672f\u548c\u65e0\u8f68\u9053\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08OFDFT\uff09\u5f00\u53d1\u4e86\u4e00\u79cd\u65b0\u7684\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u6846\u67b6 M-OFDFT\u3002\u8fd9\u4e00\u6846\u67b6\u4e0d\u4ec5\u4fdd\u6301\u4e86\u4e0e KSDFT \u76f8\u5f53\u7684\u8ba1\u7b97\u7cbe\u5ea6\uff0c\u800c\u4e14\u5728\u8ba1\u7b97\u6548\u7387\u4e0a\u5b9e\u73b0\u4e86\u663e\u8457\u63d0\u5347\uff0c\u5e76\u5c55\u73b0\u4e86\u4f18\u5f02\u7684\u5916\u63a8\u6027\u80fd\uff0c\u4e3a\u5206\u5b50\u79d1\u5b66\u7814\u7a76\u4e2d\u8bf8\u591a\u8ba1\u7b97\u65b9\u6cd5\u7684\u57fa\u7840\u2014\u2014\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u5f00\u8f9f\u4e86\u65b0\u7684\u601d\u8def\u3002\u76f8\u5173\u7814\u7a76\u6210\u679c\u5df2\u5728\u56fd\u9645\u77e5\u540d\u5b66\u672f\u671f\u520a\u300a\u81ea\u7136-\u8ba1\u7b97\u79d1\u5b66\u300b\uff08Nature Computational Science\uff09\u4e0a\u53d1\u8868\u3002 \u8fd1\u51e0\u5341\u5e74\u6765\uff0c\u7406\u8bba\u4e0e\u8ba1\u7b97\u5316\u5b66\u9886\u57df\u53d6\u5f97\u7684\u4e00\u5927\u6210\u5c31\u662f\u80fd\u591f\u901a\u8fc7\u8ba1\u7b97\u624b\u6bb5\u5f97\u5230\u5206\u5b50\u4f53\u7cfb\u7684\u7269\u7406\u5316\u5b66\u6027\u8d28\u3002\u8fd9\u4e3a\u836f\u7269\u53d1\u73b0\u548c\u6750\u6599\u8bbe\u8ba1\u7b49\u8bf8\u591a\u5de5\u4e1a\u754c\u95ee\u9898\u5e26\u6765\u4e86\u5168\u65b0\u7684\u7814\u7a76\u624b\u6bb5\uff0c\u6709\u671b\u7f29\u77ed\u5f00\u53d1\u6d41\u7a0b\u5e76\u964d\u4f4e\u5f00\u53d1\u6210\u672c\u3002\u8fd9\u4e9b\u8ba1\u7b97\u65b9\u6cd5\u7684\u57fa\u7840\u6b65\u9aa4\u662f\u4f7f\u7528\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u6c42\u89e3\u7ed9\u5b9a\u5206\u5b50\u4f53\u7cfb\u7684\u7535\u5b50\u72b6\u6001\uff0c\u8fdb\u800c\u5f97\u5230\u8be5\u4f53\u7cfb\u7684\u5404\u79cd\u6027\u8d28\u3002 \u7136\u800c\uff0c\u5404\u79cd\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u7684\u6c42\u89e3\u7cbe\u5ea6\u548c\u8ba1\u7b97\u6548\u7387\u5f80\u5f80\u65e0\u6cd5\u517c\u5f97\u3002\u5f53\u524d\uff0c\u53d6\u5f97\u76f8\u5bf9\u5408\u7406\u7684\u201c\u7cbe\u5ea6-\u6548\u7387\u201d\u6743\u8861\u800c\u88ab\u5e7f\u6cdb\u5e94\u7528\u7684\u65b9\u6cd5\u662f Kohn-Sham \u5f62\u5f0f\u7684\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08Kohn-Sham density functional theory, KSDFT\uff09\u3002\u4f46 KSDFT \u5177\u6709\u8f83\u9ad8\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u4e0d\u80fd\u5f88\u597d\u5730\u6ee1\u8db3\u65e5\u76ca\u589e\u957f\u7684\u6c42\u89e3\u5927\u89c4\u6a21\u5206\u5b50\u4f53\u7cfb\u7684\u9700\u6c42\u3002\u4e3a\u6b64\uff0c\u5fae\u8f6f\u7814\u7a76\u9662\u79d1\u5b66\u667a\u80fd\u4e2d\u5fc3\u7684\u7814\u7a76\u5458\u4eec\u63d0\u51fa\u4e86\u4e00\u79cd\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u548c\u65e0\u8f68\u9053\u5bc6\u5ea6\u6cdb\u51fd\u7406\u8bba\uff08OFDFT\uff09\u7684\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u6846\u67b6 M-OFDFT\uff0c\u5176\u4e0d\u4ec5\u663e\u8457\u8d85\u8d8a\u4e86 KSDFT \u7684\u8ba1\u7b97\u6548\u7387\uff0c\u8fd8\u80fd\u4fdd\u6709\u5176\u6c42\u89e3\u7cbe\u5ea6\u3002\u8fd9\u4e00\u6210\u679c\u5c55\u793a\u4e86\u4eba\u5de5\u667a\u80fd\u5728\u63d0\u5347\u7535\u5b50\u7ed3\u6784\u8ba1\u7b97\u4e2d\u201c\u7cbe\u5ea6-\u6548\u7387\u201d\u6743\u8861\u65b9\u9762\u7684\u5353\u8d8a\u80fd\u529b\uff0c\u5e76\u5c06\u52a9\u529b\u52a0\u901f\u76f8\u5173\u4e1a\u754c\u95ee\u9898\u7684\u7814\u7a76\u4e0e\u5f00\u53d1\u3002M-OFDFT \u7684\u76f8\u5173\u7814\u7a76\u6210\u679c\u5df2\u5728\u56fd\u9645\u77e5\u540d\u5b66\u672f\u671f\u520a\u300a\u81ea\u7136-\u8ba1\u7b97\u79d1\u5b66\u300b\uff08Nature Computational Science\uff09\u4e0a\u53d1\u8868\u3002 Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning \u300a\u81ea\u7136-\u8ba1\u7b97\u79d1\u5b66\u300b\u6587\u7ae0\u94fe\u63a5\uff1ahttps:\/\/www.nature.com\/articles\/s43588-024-00605-8 (opens in new tab) SharedIt \u94fe\u63a5\uff1ahttps:\/\/rdcu.be\/dANtS (opens in new tab) \u8bba\u6587\u94fe\u63a5\uff1ahttps:\/\/arxiv.org\/abs\/2309.16578 (opens in new tab) \u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u662f\u6c42\u89e3\u5206\u5b50\u4f53\u7cfb\u5404\u79cd\u7269\u7406\u5316\u5b66\u6027\u8d28\u7684\u57fa\u7840\u5de5\u5177\u3002\u7531\u4e8e\u591a\u7535\u5b50\u4f53\u7cfb\u672c\u8eab\u5177\u6709\u4e00\u5b9a\u7684\u6c42\u89e3\u96be\u5ea6\uff0c\u6240\u4ee5\u9ad8\u7cbe\u5ea6\u7535\u5b50\u7ed3\u6784\u65b9\u6cd5\u56e0\u5176\u8f83\u9ad8\u7684\u8ba1\u7b97\u4ee3\u4ef7\u5f88\u96be\u5e94\u7528\u5230\u5de5\u4e1a\u754c\u6240\u5173\u6ce8\u7684\u5206\u5b50\u4f53\u7cfb\u4e2d\uff0c\u800c\u53ef\u8ba1\u7b97\u8f83\u5927\u5206\u5b50\u7684\u65b9\u6cd5\u5219\u4f1a\u56e0\u5f15\u5165\u4e00\u4e9b\u8fd1\u4f3c\u800c\u635f\u5931\u7cbe\u5ea6\u3002\u76ee\u524d KSDFT 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