{"id":2412,"date":"2024-12-26T21:20:14","date_gmt":"2024-12-26T13:20:14","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2412"},"modified":"2025-06-24T14:20:58","modified_gmt":"2025-06-24T06:20:58","slug":"painn","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2412","title":{"rendered":"PAINN"},"content":{"rendered":"\n

1.PAINN\u7684\u5411\u91cf\u4fe1\u606f\u7684\u5f15\u5165<\/h3>\n\n\n\n

PAINN\uff08Polarizable Atom Interaction Neural Networks\uff09\u53ef\u6781\u5316\u539f\u5b50\u76f8\u4e92\u4f5c\u7528\u795e\u7ecf\u7f51\u7edc\uff0c\u901a\u8fc7\u8003\u8651\u539f\u5b50\u95f4\u7684\u53ef\u6781\u5316\u76f8\u4e92\u4f5c\u7528\u6765\u9884\u6d4b\u5206\u5b50\u7684\u6027\u8d28\u3002\u8fd9\u79cd\u6a21\u578b\u7684\u5f00\u53d1\u65e8\u5728\u514b\u670d\u4f20\u7edf\u56fe\u795e\u7ecf\u7f51\u7edc\u5728\u5316\u5b66\u5efa\u6a21\u4e2d\u7684\u4e00\u4e9b\u5c40\u9650\u6027\uff0c\u5c24\u5176\u662f\u5728\u63cf\u8ff0\u7535\u8377\u8f6c\u79fb\u548c\u6781\u5316\u6548\u5e94\u65b9\u9762\u3002PAINN \u7684\u4f1f\u5927\u5728\u4e8e\uff0c\u5b83\u662f\u7b2c\u4e00\u4e2a\u5c06\u7b49\u53d8\u6a21\u578b\u8c03\u53c2\u5230\u8d85\u8d8a\u4e0d\u53d8\u6a21\u578b\u7684\u3002<\/p>\n\n\n\n

PAINN\u5728\u8f93\u5165\u6570\u636e\u7684Embedding\u9636\u6bb5\u4e0d\u4ec5\u4f7f\u7528\u6807\u91cf\u5f62\u5f0f\uff0c\u8fd8\u91c7\u7528\u4e86\u5411\u91cf\u5f62\u5f0f\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u6838\u5fc3\u601d\u60f3\u662f\u901a\u8fc7\u66f4\u4e30\u5bcc\u7684\u8868\u793a\u6765\u6355\u6349\u5206\u5b50\u5185\u90e8\u7684\u590d\u6742\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u662f\u4f20\u7edf\u7684\u57fa\u4e8e\u6807\u91cf\u7684\u65b9\u6cd5\u96be\u4ee5\u5b9e\u73b0\u7684\u3002\u4f8b\u5982\uff0c\u5728\u5316\u5b66\u4e2d\uff0c\u5206\u5b50\u7684\u5c5e\u6027\u901a\u5e38\u88ab\u63cf\u8ff0\u4e3a\u65cb\u8f6c\u4e0d\u53d8\u7684\u6807\u91cf\uff0c\u4f8b\u5982\uff0c\u5206\u5b50\u7684\u603b\u7535\u8377\u3002\u7136\u800c\uff0c\u6709\u4e9b\u5c5e\u6027\u662f\u4ec5\u7528\u6807\u91cf\u8868\u793a\u4e0d\u4e86\u7684\uff0c\u6bd4\u5982\u4e00\u4e2a\u5206\u5b50\u7684\u7535\u8377\u5206\u5e03\u60c5\u51b5\uff0c\u9700\u8981\u4ece\u5355\u6781\uff08\u7535\u8377q<\/em> \uff09\u3001\u5076\u6781\uff08 \u03bc<\/em> \uff09\u3001\u5230\u56db\u6781\u77e9\uff08Q<\/em><\/strong> \uff09\u4ee5\u53ca\u66f4\u9ad8\u9636\u7684\u9879\u8fdb\u884c\u591a\u6781\u5c55\u5f00\u6765\u91cf\u5316\uff0c\u516c\u5f0f\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n\n\n

\\(n(r)=q+\\mu^\\top r+r^\\top Qr+...\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(1)<\/p>\n\n\n

\u8fd9\u4e2a\u4f8b\u5b50\u5c55\u793a\u7684\u662f\u5206\u5b50\u5c5e\u6027\u7684\u590d\u6742\u6027\uff0c\u8868\u660e\u4ec5\u4f7f\u7528\u6807\u91cf\uff08\u5982\u7535\u8377 q <\/em>\uff09\u65e0\u6cd5\u5b8c\u5168\u63cf\u8ff0\u5206\u5b50\u7684\u7269\u7406\u7279\u6027\u3002PAINN\u6a21\u578b\u5728\u5bf9\u8f93\u5165\u6570\u636e\u7684\u5904\u7406\u9636\u6bb5\uff0c\u901a\u8fc7\u5728\u4f20\u7edf\u7684\u6807\u91cfEmbedding\u57fa\u7840\u4e0a\uff0c\u52a0\u5165\u5411\u91cf\u7684Embedding\uff0c\u4f7f\u5f97\u6a21\u578b\u80fd\u591f\u6355\u6349\u5230\u5206\u5b50\u5c5e\u6027\u7684\u8fd9\u79cd\u590d\u6742\u6027\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u57fa\u4e8e\u5411\u91cf\u5f62\u5f0f\u7684\u7279\u5f81\uff0c\u53ef\u4ee5\u901a\u8fc7\u5bf9\u5411\u91cf\u7684\u7b80\u5355\u52a0\u548c\uff0c\u65e2\u80fd\u5b8c\u6210\u89d2\u5ea6\u4fe1\u606f\u7684\u5f15\u5165\uff0c\u540c\u65f6\u80fd\u5c06\u8ba1\u7b97\u89d2\u5ea6\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u4ece\\(O(\\mathrm{nk}^{2})\\)\u964d\u81f3\\(O(\\mathrm{nk})\\)\uff0c\u5982\u88681\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u88681 \u6a21\u578b\u7279\u5f81\u5904\u7406<\/figcaption><\/figure><\/div>\n\n\n

\u88681\u5c55\u793a\u4e86\u4e00\u4e2a\u6a21\u578b\u5982\u4f55\u5904\u7406\u5206\u5b50H\u2082O\u4e2d\u6709\u5173\u539f\u5b50\u95f4\u8ddd\u79bb\u3001\u89d2\u5ea6\u548c\u65b9\u5411\u7684\u4e0d\u540c\u51e0\u4f55\u7279\u5f81\u3002\u5176\u4e2d\u7f16\u53f71\u7684\u539f\u5b50\u662f\u6c27\u539f\u5b50\uff0c\u800c\u7f16\u53f72\u548c3\u7684\u539f\u5b50\u662f\u6c22\u539f\u5b50\u3002<\/p>\n\n\n\n

\u7b2c\u4e00\u5217\u663e\u793a\u4e86\u539f\u5b501\u5230\u539f\u5b502\u548c\u539f\u5b503\u7684\u952e\u957f\uff0c\u4f7f\u7528\u4e86\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u7684\u6807\u51c6\u3002\u5728\u795e\u7ecf\u7f51\u7edc\u4e2d\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u539f\u5b50\\(\\mathrm{i}\\)\uff0c\u5b83\u4f1a\u8ba1\u7b97\u51fa\u4e0e\u5b83\u90bb\u63a5\u7684\u6240\u6709\u539f\u5b50 \\(\\mathrm{j}\\) \u4e4b\u95f4\u7684\u8ddd\u79bb\u7684\u603b\u548c\uff0c\u8fd9\u4e2a\u590d\u6742\u5ea6\u662f\\(O(|N|)\\)\uff0c\u5176\u4e2d \\(\\mathrm{N}\\) \u662f\u90bb\u5c45\u7684\u6570\u91cf\u3002\u795e\u7ecf\u7f51\u7edc\u901a\u8fc7\u8fd9\u4e9b\u8ddd\u79bb\u6765\u89e3\u6790\u90bb\u5c45\u539f\u5b50\u7684\u53d8\u5316\uff0c\u4f46\u8ddd\u79bb\u4fe1\u606f\u4e0d\u8db3\u4ee5\u89e3\u6790\u952e\u89d2\\(\\alpha_{213}\\)\u7684\u53d8\u5316\u3002<\/p>\n\n\n\n

\u7b2c\u4e8c\u5217\u8003\u8651\u4e86\u539f\u5b50\u95f4\u7684\u89d2\u5ea6\uff0c\u7279\u522b\u662f\u539f\u5b502\u30011\u30013\u5f62\u6210\u7684\u952e\u89d2\\(\\alpha_{213}\\)\uff0c\u8fd9\u901a\u8fc7\u8ba1\u7b97\u5411\u91cf\\(r_{12}\\)\u548c\\(r_{13}\\)\u7684\u6784\u6210\u7684\u89d2\u5ea6\u4f59\u5f26\u503c\u6765\u8868\u793a\u3002\u5bf9\u4e8e\u539f\u5b50\\(\\mathrm{i}\\)\uff0c\u8fd9\u9700\u8981\u8003\u8651\u6240\u6709\u90bb\u5c45\\(\\mathrm{j}\\)\u548c\\(\\mathrm{k}\\)\u4e4b\u95f4\u7684\u89d2\u5ea6\uff0c\u56e0\u6b64\u590d\u6742\u5ea6\u589e\u52a0\u5230\\(O(\\left|N\\right|^2)\\)\u3002\u8fd9\u79cd\u8868\u793a\u80fd\u591f\u89e3\u6790\u89d2\u5ea6\u7684\u53d8\u5316\uff0c\u4f46\u4e0d\u89e3\u6790\u8ddd\u79bb\u7684\u53d8\u5316\u3002<\/p>\n\n\n\n

\u7b2c\u4e09\u5217\u5c55\u793a\u4e86\u7528\u5411\u91cf\u5f62\u5f0f\u8868\u5f81\u7684\u65b9\u5411\u7279\u5f81\uff0c\u5b83\u662f\u901a\u8fc7\u90bb\u5c45\u539f\u5b50\\(\\mathrm{j}\\)\u76f8\u5bf9\u4e8e\u539f\u5b50\\(\\mathrm{i}\\)\u7684\u5355\u4f4d\u65b9\u5411\u5411\u91cf\u6765\u8868\u793a\u7684\u3002\u65b9\u5411\u4fe1\u606f\u80fd\u591f\u88ab\u7528\u6765\u89e3\u6790\u952e\u89d2\u7684\u53d8\u5316\uff0c\u8fd9\u4e00\u4f5c\u7528\u4e0e\u76f4\u63a5\u8ba1\u7b97\u539f\u5b50\u95f4\u952e\u89d2\u7684\u6548\u679c\u662f\u4e00\u6837\u7684\uff0c\u4f46\u662f\u5bf9\u6bd4\u76f4\u63a5\u8ba1\u7b97\u952e\u89d2\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u6765\u8bf4\uff0c\u5374\u4ece\\(O(\\left|N\\right|^2)\\)\u4e0b\u964d\u81f3\\(O(|N|)\\)\uff0c\u662f\u4e00\u79cd\u66f4\u9ad8\u6548\u7684\u8003\u8651\u952e\u89d2\\(\\alpha_{213}\\)\u7684\u65b9\u5f0f\u3002<\/p>\n\n\n\n

\u6b64\u5916\uff0c\u4f5c\u8005\u6307\u51fa\uff1a\u7528\u5411\u91cf\u8868\u5f81\u65b9\u5411\u7279\u5f81\u7684\u65b9\u5f0f\u8fd8\u80fd\u9274\u522b\u51fa\u66f4\u591a\u7684\u5206\u5b50\u7ed3\u6784\uff0c\u5982\u56fe1\u6240\u793a\u3002<\/p>\n\n\n

\n
\"\"
\u56fe1 \u5411\u91cf\u8868\u5f81\u65b9\u5411\u7279\u5f81<\/figcaption><\/figure><\/div>\n\n\n

\u5728\u56fe1\u7684\u4e00\u5bf9\u5206\u5b50\u6784\u8c61\u4e2d\uff0c\u5982\u679c\u4f7f\u7528\u76f4\u63a5\u8ba1\u7b97\u89d2\u5ea6\u7684\u65b9\u5f0f\u8fdb\u884c\u65b9\u5411\u7279\u5f81\u8868\u793a\u5219\u65e0\u6cd5\u5206\u522b\u8fd9\u4e24\u4e2a\u5206\u5b50\u7684\u4e0d\u540c\uff0c\u5982\u56fe1(a)\u6240\u793a\u3002\u4f46\u5982\u679c\u4f7f\u7528\u5411\u91cf\u7684\u5f62\u5f0f\u6765\u8868\u5f81\u65b9\u5411\u7279\u5f81\uff0c\u5219\u53ef\u4ee5\u5f88\u597d\u7684\u8fdb\u884c\u9274\u522b\uff0c\u5982\u56fe1(b)\u6240\u793a\u3002<\/p>\n\n\n\n

2.PAINN\u7684\u6a21\u578b\u7ed3\u6784<\/h3>\n\n\n\n

PAINN\u6574\u4f53\u7684\u6a21\u578b\u7ed3\u6784\u5982\u56fe2(a)\u6240\u793a\uff0c\u5176\u52a0\u5165\u7279\u5f81\u8003\u91cf\u7684\u65b9\u5f0f\u975e\u5e38\u7684\u6734\u7d20\u76f4\u63a5\uff0c\u5c31\u662f\u5728\u539f\u5b50\u7c7b\u578b\\(\\mathbb{Z}_{i}\\)\u548c\u76f8\u5bf9\u4f4d\u7f6e\u5411\u91cf\\(r_{ij}\\)\u7684\u8f93\u5165\u57fa\u7840\u4e0a\uff0c\u52a0\u5165\u4e00\u4e2a\u521d\u59cb\u5316\u4e3a0\u7684\u5411\u91cf\u4f5c\u4e3a\u7b2c\u4e09\u79cd\u8f93\u5165\u4fe1\u606f\uff0c\u968f\u7740\u7f51\u7edc\u7684\u66f4\u8fed\u8bad\u7ec3\u81ea\u884c\u5b66\u4e60\u76f8\u5173\u7684\u65b9\u5411\u7279\u5f81\u3002\u63a5\u4e0b\u6765\uff0c\u901a\u8fc7\u591a\u4e2amessage\u548cupdate\u5757\u7684\u53e0\u52a0\u6765\u6784\u5efa\u7279\u5f81\uff0c\u4ee5\u5b66\u4e60\u539f\u5b50\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u548c\u5c5e\u6027\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u5411\u91cf\u8f93\u5165\\(\\nu_{i}^{0}\\)\u548c\u6807\u91cf\u8f93\u5165\\(s_{i}^{0}\\)\u7684\u4e24\u4e2a\u8ba1\u7b97\u8def\u5f84\u4e0a\uff0c\u6bcf\u4e2amessage\u548cupdate\u5757\u90fd\u4f1a\u643a\u5e26\u4e00\u4e2a\u6b8b\u5dee\u8fde\u63a5\uff0c\u5e2e\u52a9\u7f51\u7edc\u66f4\u597d\u7684\u8fdb\u884c\u68af\u5ea6\u7684\u4f20\u64ad\u3002\u53e6\u5916\uff0c\u4f4d\u7f6e\u4fe1\u606f\\({\\boldsymbol{r}}_{ij}\\)\u4e5f\u4f1a\u9001\u8fdb\u6bcf\u4e2amessage\u5757\u4e2d\u4f5c\u4e3a\u8f93\u5165\u3002\u6700\u540e\u4e00\u4e2aupdate\u5757\u7684\u8f93\u51fa\u901a\u8fc7\u6743\u91cd\u77e9\u9635\\(\\text{W}\\)\u548c\u504f\u7f6e\u5411\u91cf\\(\\mathrm{b}\\)\u7684\u7ebf\u6027\u53d8\u6362\uff0c\u7ecf\u8fc7Scaled Exponential Linear Units\uff08SiLU\uff09\u6fc0\u6d3b\u51fd\u6570\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u6807\u91cf\u8f93\u51fa \u3002<\/p>\n\n\n

\n
\"\"
\u56fe2 PAINN\u6a21\u578b\u7ed3\u6784<\/figcaption><\/figure><\/div>\n\n\n

\u6d88\u606f\u4f20\u9012\u6a21\u5757\uff08Message Blocks\uff09\u7684\u8be6\u7ec6\u7ed3\u6784\u5982\u56fe2(b)\u6240\u793a\u3002\u6807\u91cf\u7279\u5f81\u7684\u8ba1\u7b97\u662f\u901a\u8fc7\u4f7f\u7528\u8fde\u7eed\u6ee4\u6ce2\u5377\u79ef\u5f97\u5230\u7684\uff0c\u516c\u5f0f\u89e3\u91ca\u5982\u4e0b\uff1a<\/p>\n\n\n

\\(\\begin{aligned}\\Delta s_{i}^{m}&=(\\phi_s(s)*W_s)_i\\\\&=\\sum_j\\phi_s(s_j)\\circ W_s(\\parallel r_{ij}\\parallel)\\end{aligned}\\) \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(2)<\/p>\n\n\n

\u9996\u5148\uff0c\u5bf9\u4e8e\u6bcf\u4e2a\u539f\u5b50\\(\\boldsymbol{s}_{i}\\)\uff0c\u5e94\u7528\u4e00\u4e2a\u539f\u5b50\u7ea7\u7684\u7279\u5f81\u53d8\u6362\\(\\phi_{s}\\)\uff0c\u5bf9\u5e94\u56fe2(b)\u5219\u662f\u4e2d\u95f4\u7684\u8f93\u5165\u8def\u5f84\uff0c\u8fd9\u4e2a\u53d8\u6362\u7531\u4e24\u4e2a\u795e\u7ecf\u7f51\u7edc\u5c42\u548c\u4e00\u4e2a\u6fc0\u6d3b\u51fd\u6570SiLU\u5b9e\u73b0\uff0c\u7528\u4e8e\u5c06\u8f93\u5165\u7279\u5f81\\(\\boldsymbol{s}_{i}\\)\u6620\u5c04\u5230\u4e00\u4e2a\u65b0\u7684\u7279\u5f81\u7a7a\u95f4\uff0c\u5f97\u5230\u8ba1\u7b97\u7ed3\u679c\\(\\phi\\)\u3002\u63a5\u7740\uff0c\u8fd9\u4e9b\u53d8\u6362\u540e\u7684\u7279\u5f81\\(\\phi\\)\u4e0e\u4e00\u4e2a\u8fde\u7eed\u5377\u79ef\u6838\u751f\u6210\u51fd\u6570\u7684\u7ed3\u679c\\(\\text{W}\\)\u8fdb\u884c\u76f8\u4e58\uff0c\u5373\u8fdb\u884c\u8fde\u7eed\u5377\u79ef\u64cd\u4f5c\u3002\u5176\u4e2d\uff0c\\(\\text{W}\\)\u662f\u8fde\u7eed\u5377\u79ef\u6838\uff0c\u5176\u6743\u91cd\u6570\u503c\u662f\u7ecf\u8fc7\u5f84\u5411\u57fa\u51fd\u6570RBF\u7684\u6620\u5c04\uff0c\u518d\u7ecf\u8fc7\u795e\u7ecf\u7f51\u7edc\u7684\u8c03\u6574\u5e76\u7ed3\u5408\u622a\u65ad\u51fd\u6570\\(f_{\\mathrm{cut}}\\)\u8ba1\u7b97\u5f97\u5230\u7684\u3002\u622a\u65ad\u51fd\u6570\u9650\u5236\u5377\u79ef\u64cd\u4f5c\u65f6\u4ec5\u8003\u8651\u622a\u65ad\u534a\u5f84\u5185\u7684\u539f\u5b50\u4fe1\u606f\uff0c\u4e14\u6743\u91cd\u6839\u636e\u5f84\u5411\u51fd\u6570\u968f\u7740\u8ddd\u79bb\u7684\u589e\u52a0\u800c\u51cf\u5c11\u3002<\/p>\n\n\n\n

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\\(\\Delta\\boldsymbol{\\nu}_i^m=\\sum_j\\boldsymbol{\\nu}_j\\circ\\phi_{\\nu\\nu}(\\boldsymbol{s}_j)\\circ\\boldsymbol{W}_{\\nu\\nu}(\\parallel\\boldsymbol{r}_{ij}\\parallel)+\\sum_j\\phi_{\\nu s}(\\boldsymbol{s}_j)\\circ\\boldsymbol{W}_{\\nu s}^{\\prime}(\\parallel\\boldsymbol{r}_{ij}\\parallel)\\frac{\\boldsymbol{r}_{ij}}{\\parallel\\boldsymbol{r}_{ij}\\parallel}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(3)<\/p>\n\n\n

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