{"id":5389,"date":"2024-12-21T18:35:46","date_gmt":"2024-12-21T10:35:46","guid":{"rendered":"https:\/\/nullthought.net\/?p=5389"},"modified":"2025-02-23T11:08:36","modified_gmt":"2025-02-23T03:08:36","slug":"%e7%a5%9e%e7%bb%8f%e7%ae%97%e5%ad%90%ef%bc%88neural-operators%ef%bc%89%e5%bc%80%e6%ba%90%e5%ba%93","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=5389","title":{"rendered":"\u795e\u7ecf\u7b97\u5b50\uff08Neural Operators\uff09\u5f00\u6e90\u5e93"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u8bba\u6587<strong><a href=\"https:\/\/arxiv.org\/abs\/2412.10354\" target=\"_blank\" rel=\"noreferrer noopener\">A Library for Learning Neural Operators<\/a><\/strong>\u63d0\u51fa\u4e86\u540d\u4e3a <strong><a href=\"https:\/\/github.com\/neuraloperator\/neuraloperator\" target=\"_blank\" rel=\"noreferrer noopener\">NeuralOperator<\/a><\/strong> \u7684\u5f00\u6e90\u5e93\uff0c\u7528\u4e8e\u5b66\u4e60\u548c\u5e94\u7528\u795e\u7ecf\u7b97\u5b50\u6a21\u578b\u3002NeuralOperator \u901a\u8fc7\u6a21\u5757\u5316\u8bbe\u8ba1\u548c\u9ad8\u6548\u5b9e\u73b0\uff0c\u663e\u8457\u964d\u4f4e\u4e86\u795e\u7ecf\u7b97\u5b50\u6a21\u578b\u7684\u5e94\u7528\u95e8\u69db\uff0c\u4e3a\u79d1\u5b66\u8ba1\u7b97\u4e0e\u673a\u5668\u5b66\u4e60\u7684\u7ed3\u5408\u63d0\u4f9b\u4e86\u5f3a\u5927\u7684\u5de5\u5177\u3002\u65e0\u8bba\u662f\u5b66\u672f\u7814\u7a76\u8fd8\u662f\u5de5\u4e1a\u5e94\u7528\uff0c\u8be5\u5e93\u90fd\u5c55\u73b0\u4e86\u5f3a\u5927\u7684\u9002\u5e94\u6027\u548c\u5b9e\u7528\u4ef7\u503c\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8bba\u6587\u4f5c\u8005\u4e3a\uff0c\u6765\u81eaJean Kossaifi, Nikola Kovachki, Zongyi Li, David Pitt, Miguel Liu-Schiaffini, Robert Joseph George, Boris Bonev, Kamyar Azizzadenesheli, Julius Berner, Anima Anandkumar\uff0c\u6765\u81eaNVIDIA\u548cCaltech\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"519\" src=\"https:\/\/nullthought.net\/wp-content\/uploads\/2024\/12\/image-15-1024x519.png\" alt=\"\" class=\"wp-image-5390\" srcset=\"https:\/\/nullthought.net\/wp-content\/uploads\/2024\/12\/image-15-1024x519.png 1024w, https:\/\/nullthought.net\/wp-content\/uploads\/2024\/12\/image-15-300x152.png 300w, https:\/\/nullthought.net\/wp-content\/uploads\/2024\/12\/image-15-768x390.png 768w, https:\/\/nullthought.net\/wp-content\/uploads\/2024\/12\/image-15.png 1175w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\"><strong><a href=\"https:\/\/arxiv.org\/abs\/2412.10354\" target=\"_blank\" rel=\"noreferrer noopener\">A Library for Learning Neural Operators<\/a><\/strong><\/figcaption><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>1. \u80cc\u666f\u4e0e\u95ee\u9898\u5b9a\u4e49<\/strong><\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u79d1\u5b66\u8ba1\u7b97\u4e2d\u7684\u8bb8\u591a\u95ee\u9898\u90fd\u6d89\u53ca\u51fd\u6570\u4e4b\u95f4\u7684\u6620\u5c04\uff0c\u4f8b\u5982\u504f\u5fae\u5206\u65b9\u7a0b\uff08PDEs\uff09\u7684\u6c42\u89e3\u3002\u8fd9\u4e9b\u95ee\u9898\u901a\u5e38\u9700\u8981\u9ad8\u5206\u8fa8\u7387\u7684\u79bb\u6563\u5316\u65b9\u6cd5\u6765\u83b7\u5f97\u7cbe\u786e\u7684\u7ed3\u679c\uff0c\u4f46\u8ba1\u7b97\u4ee3\u4ef7\u9ad8\u6602\u3002\u4ee5\u5929\u6c14\u6a21\u62df\u4e3a\u4f8b\uff0c\u7f51\u683c\u7684\u5206\u8fa8\u7387\u663e\u8457\u5f71\u54cd\u8ba1\u7b97\u590d\u6742\u5ea6\uff0c\u4ece\u800c\u9650\u5236\u4e86\u5728\u5927\u8303\u56f4\u53c2\u6570\u7a7a\u95f4\u4e0a\u7684\u5feb\u901f\u4eff\u771f\u80fd\u529b\u3002<\/p>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>\u4f20\u7edf\u65b9\u6cd5\u7684\u5c40\u9650\u6027<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6570\u503c\u65b9\u6cd5<\/strong>\uff1a\u4f9d\u8d56\u4e8e\u56fa\u5b9a\u7684\u7f51\u683c\u79bb\u6563\u5316\uff0c\u5176\u51c6\u786e\u6027\u548c\u5206\u8fa8\u7387\u76f4\u63a5\u76f8\u5173\uff0c\u96be\u4ee5\u6269\u5c55\u5230\u5927\u89c4\u6a21\u95ee\u9898\u3002<\/li>\n\n\n\n<li><strong>\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc<\/strong>\uff1a\u53ea\u80fd\u5728\u56fa\u5b9a\u7ef4\u5ea6\u7684\u8f93\u5165\u548c\u8f93\u51fa\u4e0a\u8fdb\u884c\u5b66\u4e60\uff0c\u65e0\u6cd5\u6cdb\u5316\u5230\u4e0d\u540c\u5206\u8fa8\u7387\u7684\u6570\u636e\u3002\u56e0\u6b64\uff0c\u751f\u6210\u7684\u6a21\u578b\u5728\u5904\u7406\u8d85\u5206\u8fa8\u7387\u6216\u4f4e\u5206\u8fa8\u7387\u7684\u4efb\u52a1\u65f6\u8868\u73b0\u8f83\u5dee\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>\u795e\u7ecf\u7b97\u5b50\u7684\u63d0\u51fa<\/strong><\/h6>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u89e3\u51b3\u4e0a\u8ff0\u95ee\u9898\uff0c<a href=\"https:\/\/nullthought.net\/?p=4270\" target=\"_blank\" rel=\"noreferrer noopener\">\u795e\u7ecf\u7b97\u5b50\uff08Neural Operators\uff09<\/a>\u88ab\u5f15\u5165\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u540c\u4e8e\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\uff0c\u901a\u8fc7\u76f4\u63a5\u5b66\u4e60\u51fd\u6570\u7a7a\u95f4\u4e4b\u95f4\u7684\u6620\u5c04\uff08\u5373\u65e0\u9650\u7ef4\u7a7a\u95f4\uff09\uff0c\u5b9e\u73b0\u5bf9\u4efb\u610f\u5206\u8fa8\u7387\u8f93\u5165\u7684\u517c\u5bb9\u6027\u3002\u5b83\u4eec\u80fd\u591f\u4fdd\u8bc1\u79bb\u6563\u5316\u6536\u655b\u6027\uff0c\u5373\u968f\u7740\u8f93\u5165\u79bb\u6563\u5316\u7cbe\u5ea6\u7684\u63d0\u9ad8\uff0c\u9884\u6d4b\u7ed3\u679c\u9010\u6e10\u903c\u8fd1\u771f\u5b9e\u89e3\u3002<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>2. \u795e\u7ecf\u7b97\u5b50\u7b80\u4ecb<\/strong><\/h5>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>\u6838\u5fc3\u601d\u60f3<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u795e\u7ecf\u7b97\u5b50\u901a\u8fc7\u6784\u9020\u53ef\u5b66\u4e60\u7684\u79ef\u5206\u53d8\u6362\uff0c\u5b9e\u73b0\u4ece\u8f93\u5165\u51fd\u6570\u5230\u8f93\u51fa\u51fd\u6570\u7684\u6620\u5c04\u3002\u8fd9\u4e00\u8fc7\u7a0b\u4e0d\u53d7\u8f93\u5165\u6570\u636e\u5206\u8fa8\u7387\u7684\u7ea6\u675f\uff0c\u80fd\u591f\u6cdb\u5316\u5230\u4efb\u610f\u79bb\u6563\u5316\u7684\u7f51\u683c\u3002<\/li>\n\n\n\n<li>\u4e0e\u4f20\u7edf\u65b9\u6cd5\u76f8\u6bd4\uff0c\u795e\u7ecf\u7b97\u5b50\u5728\u79bb\u6563\u5316\u7cbe\u5ea6\u53d8\u5316\u65f6\u4ecd\u80fd\u4fdd\u6301\u8f83\u9ad8\u7684\u51c6\u786e\u6027\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>\u4ee3\u8868\u6027\u67b6\u6784<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><a href=\"https:\/\/nullthought.net\/?p=4266\" target=\"_blank\" rel=\"noreferrer noopener\">Fourier \u795e\u7ecf\u7b97\u5b50\uff08FNO\uff09<\/a><\/strong>\uff1a\u901a\u8fc7\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362\uff08FFT\uff09\u5b9e\u73b0\u79ef\u5206\u6838\u7684\u9ad8\u6548\u8ba1\u7b97\u3002<\/li>\n\n\n\n<li><strong>\u56fe\u795e\u7ecf\u7b97\u5b50\uff08GNO\uff09<\/strong>\uff1a\u5141\u8bb8\u5728\u4efb\u610f\u51e0\u4f55\u7ed3\u6784\u4e0a\u8fdb\u884c\u5b66\u4e60\u3002<\/li>\n\n\n\n<li><strong>\u7403\u9762 Fourier \u795e\u7ecf\u7b97\u5b50\uff08SFNO\uff09<\/strong>\uff1a\u57fa\u4e8e\u7403\u9762\u8c10\u6ce2\u53d8\u6362\uff0c\u7528\u4e8e\u7403\u9762\u4e0a\u7684\u6570\u636e\u5904\u7406\u3002<\/li>\n\n\n\n<li><strong>\u51e0\u4f55\u611f\u77e5\u795e\u7ecf\u7b97\u5b50\uff08GINO\uff09<\/strong>\uff1a\u7ed3\u5408 GNO \u548c FNO \u7684\u4f18\u52bf\uff0c\u9002\u5e94\u590d\u6742\u51e0\u4f55\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>3. <a href=\"https:\/\/github.com\/neuraloperator\/neuraloperator\" target=\"_blank\" rel=\"noreferrer noopener\">NeuralOperator \u5e93<\/a>\u7684\u4e3b\u8981\u529f\u80fd<\/strong><\/h5>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>3.1 \u6a21\u5757\u5316\u8bbe\u8ba1<\/strong><\/h6>\n\n\n\n<p class=\"wp-block-paragraph\">NeuralOperator \u63d0\u4f9b\u4e86\u4e00\u6574\u5957\u9ad8\u6548\u3001\u53ef\u9760\u3001\u6613\u7528\u7684\u5de5\u5177\uff0c\u7528\u4e8e\u6784\u5efa\u3001\u8bad\u7ec3\u548c\u90e8\u7f72\u795e\u7ecf\u7b97\u5b50\u6a21\u578b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u8fa8\u7387\u65e0\u5173\u6027<\/strong>\uff1a\u6240\u6709\u6a21\u5757\u652f\u6301\u4efb\u610f\u5206\u8fa8\u7387\u7684\u8f93\u5165\u8f93\u51fa\uff0c\u5305\u62ec\u8d85\u5206\u8fa8\u7387\u4efb\u52a1\u3002<\/li>\n\n\n\n<li><strong>\u9884\u6784\u5efa\u6a21\u5757<\/strong>\uff1a\u5b9e\u73b0\u4e86\u5e7f\u6cdb\u7684\u795e\u7ecf\u7b97\u5b50\u67b6\u6784\u548c\u6784\u5efa\u5757\uff0c\u5982\u79ef\u5206\u53d8\u6362\u3001\u4f4d\u7f6e\u5d4c\u5165\u3001\u70b9\u8fd0\u7b97\u7b49\u3002<\/li>\n\n\n\n<li><strong>\u8bad\u7ec3\u81ea\u52a8\u5316<\/strong>\uff1a\u5185\u7f6e\u7684\u8bad\u7ec3\u5668\u6a21\u5757\uff08Trainer\uff09\u80fd\u591f\u7b80\u5316\u6807\u51c6\u8bad\u7ec3\u6d41\u7a0b\uff0c\u5305\u62ec\u6570\u636e\u9884\u5904\u7406\u3001\u6a21\u578b\u4f18\u5316\u548c\u9a8c\u8bc1\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>3.2 \u795e\u7ecf\u7b97\u5b50\u67b6\u6784<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Fourier \u795e\u7ecf\u7b97\u5b50\uff08FNO\uff09<\/strong>\uff1a\u901a\u8fc7 FFT \u52a0\u901f\u79ef\u5206\u6838\u7684\u8ba1\u7b97\uff0c\u9002\u5408\u89c4\u5219\u7f51\u683c\u3002<\/li>\n\n\n\n<li><strong>Tensorized FNO (TFNO)<\/strong>\uff1a\u5229\u7528\u5f20\u91cf\u5206\u89e3\u51cf\u5c11\u6a21\u578b\u53c2\u6570\u91cf\uff0c\u540c\u65f6\u4f18\u5316\u5185\u5b58\u548c\u8ba1\u7b97\u6548\u7387\u3002<\/li>\n\n\n\n<li><strong>Spherical FNO (SFNO)<\/strong>\uff1a\u7528\u4e8e\u7403\u9762\u6570\u636e\u7684\u9ad8\u6548\u5efa\u6a21\uff0c\u652f\u6301\u7403\u9762\u8c10\u6ce2\u5206\u6790\u3002<\/li>\n\n\n\n<li><strong>\u589e\u91cf\u5b66\u4e60\u4e0e\u591a\u7f51\u683c\u65b9\u6cd5<\/strong>\uff1a\u901a\u8fc7\u591a\u7f51\u683c\u57df\u5206\u89e3\u548c\u589e\u91cf\u8bad\u7ec3\uff0c\u5b9e\u73b0\u5927\u89c4\u6a21\u95ee\u9898\u7684\u9ad8\u6548\u6c42\u89e3\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>3.3 \u6570\u636e\u652f\u6301<\/strong><\/h6>\n\n\n\n<p class=\"wp-block-paragraph\">NeuralOperator \u63d0\u4f9b\u4e86\u5e38\u89c1 PDE \u6570\u636e\u96c6\u7684\u63a5\u53e3\uff0c\u6db5\u76d6\u4ee5\u4e0b\u5185\u5bb9\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Darcy \u6d41\u4f53\u6a21\u578b<\/strong>\uff1a\u89e3\u51b3\u5730\u4e0b\u6c34\u6d41\u52a8\u95ee\u9898\u3002<\/li>\n\n\n\n<li><strong>Navier-Stokes \u65b9\u7a0b<\/strong>\uff1a\u7528\u4e8e\u4e8c\u7ef4\u548c\u4e09\u7ef4\u6d41\u4f53\u52a8\u529b\u5b66\u7684\u6a21\u62df\u3002<\/li>\n\n\n\n<li><strong>\u8f66\u8f86 CFD<\/strong>\uff1a\u901a\u8fc7\u8f66\u8eab\u8868\u9762\u6d41\u573a\u6a21\u62df\u8fdb\u884c\u7a7a\u6c14\u52a8\u529b\u5b66\u4f18\u5316\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>3.4 \u6027\u80fd\u4f18\u5316<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5f20\u91cf\u5316\uff08Tensorization\uff09<\/strong>\uff1a\u901a\u8fc7\u5f20\u91cf\u5206\u89e3\u51cf\u5c11\u53c2\u6570\u91cf\uff0c\u63d0\u9ad8\u8bad\u7ec3\u548c\u63a8\u7406\u6548\u7387\u3002<\/li>\n\n\n\n<li><strong>\u6df7\u5408\u7cbe\u5ea6\u8bad\u7ec3<\/strong>\uff1a\u5229\u7528 PyTorch \u7684\u539f\u751f\u652f\u6301\uff0c\u51cf\u5c11\u5185\u5b58\u5360\u7528\uff0c\u540c\u65f6\u63d0\u5347\u8ba1\u7b97\u901f\u5ea6\u3002<\/li>\n\n\n\n<li><strong>\u5206\u5e03\u5f0f\u8ba1\u7b97<\/strong>\uff1a\u5185\u7f6e\u591a\u7f51\u683c\u57df\u5206\u89e3\u65b9\u6cd5\uff0c\u652f\u6301\u5927\u89c4\u6a21\u5206\u5e03\u5f0f\u8bad\u7ec3\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>3.5 \u7075\u6d3b\u6027\u4e0e\u53ef\u9760\u6027<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6a21\u5757\u5316\u8bbe\u8ba1\u4f7f\u5f97\u7528\u6237\u53ef\u4ee5\u6839\u636e\u9700\u8981\u81ea\u7531\u7ec4\u5408\u548c\u6269\u5c55\u5404\u529f\u80fd\u6a21\u5757\u3002<\/li>\n\n\n\n<li>\u6240\u6709\u6838\u5fc3\u529f\u80fd\u5747\u7ecf\u8fc7\u5355\u5143\u6d4b\u8bd5\u9a8c\u8bc1\uff0c\u5e76\u901a\u8fc7\u6301\u7eed\u96c6\u6210\uff08CI\/CD\uff09\u7ba1\u9053\u786e\u4fdd\u4ee3\u7801\u8d28\u91cf\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>4. \u5b9e\u9a8c\u4e0e\u5e94\u7528<\/strong><\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">\u867d\u7136\u8bba\u6587\u672a\u8be6\u7ec6\u5c55\u5f00\u5b9e\u9a8c\u90e8\u5206\uff0c\u4f46\u63d0\u5230\u4e86\u4e00\u4e9b\u6f5c\u5728\u5e94\u7528\u573a\u666f\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u79d1\u5b66\u8ba1\u7b97<\/strong>\uff1a\u795e\u7ecf\u7b97\u5b50\u80fd\u591f\u9ad8\u6548\u6c42\u89e3\u6d41\u4f53\u52a8\u529b\u5b66\u3001\u4f20\u70ed\u4f20\u8d28\u7b49\u590d\u6742 PDE \u95ee\u9898\u3002<\/li>\n\n\n\n<li><strong>\u5de5\u4e1a\u8bbe\u8ba1<\/strong>\uff1a\u901a\u8fc7\u8f66\u8eab\u7a7a\u6c14\u52a8\u529b\u5b66\u4f18\u5316\uff0c\u7f29\u77ed\u8bbe\u8ba1\u5468\u671f\u3002<\/li>\n\n\n\n<li><strong>\u7269\u7406\u6a21\u62df<\/strong>\uff1a\u5728\u6c14\u5019\u6a21\u62df\u3001\u6750\u6599\u79d1\u5b66\u7b49\u9886\u57df\uff0c\u7528\u4e8e\u5feb\u901f\u9884\u4f30\u548c\u4f18\u5316\u3002<\/li>\n<\/ol>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>5. \u4e0e\u73b0\u6709\u5de5\u5177\u7684\u6bd4\u8f83<\/strong><\/h5>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>\u4f18\u70b9<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u901a\u7528\u6027<\/strong>\uff1a\u652f\u6301\u4e0d\u540c\u7c7b\u578b\u7684\u7f51\u683c\u548c\u51e0\u4f55\u7ed3\u6784\u3002<\/li>\n\n\n\n<li><strong>\u9ad8\u6548\u6027<\/strong>\uff1a\u7ed3\u5408 FFT \u548c\u5f20\u91cf\u5206\u89e3\u7b49\u6280\u672f\uff0c\u5b9e\u73b0\u9ad8\u6548\u8ba1\u7b97\u3002<\/li>\n\n\n\n<li><strong>\u6613\u7528\u6027<\/strong>\uff1a\u63d0\u4f9b\u5f00\u7bb1\u5373\u7528\u7684\u6a21\u5757\u548c\u7b80\u6d01\u7684\u63a5\u53e3\u3002<\/li>\n<\/ul>\n\n\n\n<h6 class=\"wp-block-heading\"><strong>\u4e0d\u8db3\u4e0e\u6311\u6218<\/strong><\/h6>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5e94\u7528\u95e8\u69db<\/strong>\uff1a\u5c3d\u7ba1\u63d0\u4f9b\u4e86\u8be6\u7ec6\u6587\u6863\uff0c\u65b0\u7528\u6237\u53ef\u80fd\u9700\u8981\u4e00\u5b9a\u5b66\u4e60\u65f6\u95f4\u3002<\/li>\n\n\n\n<li><strong>\u6027\u80fd\u5c40\u9650<\/strong>\uff1a\u5bf9\u6781\u9ad8\u5206\u8fa8\u7387\u6216\u7279\u5b9a\u51e0\u4f55\u95ee\u9898\u7684\u6269\u5c55\u6027\u4ecd\u9700\u8fdb\u4e00\u6b65\u7814\u7a76\u3002<\/li>\n<\/ul>\n\n\n\n<h5 class=\"wp-block-heading\"><strong>6. \u672a\u6765\u5c55\u671b<\/strong><\/h5>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u67b6\u6784\u6269\u5c55<\/strong>\uff1a\u968f\u7740\u795e\u7ecf\u7b97\u5b50\u9886\u57df\u7684\u5feb\u901f\u53d1\u5c55\uff0cNeuralOperator \u8ba1\u5212\u52a0\u5165\u66f4\u591a\u5148\u8fdb\u6a21\u578b\uff0c\u4f8b\u5982\u57fa\u4e8e Transformer \u7684\u795e\u7ecf\u7b97\u5b50\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8de8\u9886\u57df\u5e94\u7528<\/strong>\uff1a\u8fdb\u4e00\u6b65\u63a2\u7d22\u5728\u91cf\u5b50\u8ba1\u7b97\u3001\u91d1\u878d\u5efa\u6a21\u3001\u751f\u7269\u533b\u5b66\u7b49\u9886\u57df\u7684\u5e94\u7528\u53ef\u80fd\u6027\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u793e\u533a\u53d1\u5c55<\/strong>\uff1a\u901a\u8fc7\u5f00\u653e\u793e\u533a\u5408\u4f5c\uff0c\u63a8\u52a8\u795e\u7ecf\u7b97\u5b50\u7814\u7a76\u7684\u6807\u51c6\u5316\u548c\u751f\u6001\u7cfb\u7edf\u5efa\u8bbe\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">NeuralOperator Lib on GitHub: <a href=\"https:\/\/github.com\/neuraloperator\/neuraloperator\" target=\"_blank\" rel=\"noreferrer noopener\">https:\/\/github.com\/neuraloperator\/neuraloperator<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8bba\u6587A Library for Learning Neural Operators\u63d0\u51fa\u4e86\u540d\u4e3a NeuralOp [&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":[39,63,84,95,71],"class_list":["post-5389","post","type-post","status-publish","format-standard","hentry","category-tech","category-36","tag-ai","tag-nvidia","tag-transformer","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\u6587A Library for Learning Neural Operators\u63d0\u51fa\u4e86\u540d\u4e3a NeuralOp&hellip;","_links":{"self":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/5389","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=5389"}],"version-history":[{"count":2,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/5389\/revisions"}],"predecessor-version":[{"id":5392,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/5389\/revisions\/5392"}],"wp:attachment":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}