{"id":4401,"date":"2024-08-23T18:46:03","date_gmt":"2024-08-23T10:46:03","guid":{"rendered":"https:\/\/nullthought.net\/?p=4401"},"modified":"2025-12-01T11:41:16","modified_gmt":"2025-12-01T03:41:16","slug":"%e7%89%a9%e7%90%86%e5%bc%95%e5%af%bc%e6%9c%ba%e5%99%a8%e5%ad%a6%e4%b9%a0%ef%bc%8cphysics-informed-machine-learning%ef%bc%88piml%ef%bc%89","status":"publish","type":"post","link":"https:\/\/nullthought.net\/?p=4401","title":{"rendered":"\u7269\u7406\u5f15\u5bfc\u673a\u5668\u5b66\u4e60\uff0cPhysics-Informed Machine Learning\uff08PIML\uff09"},"content":{"rendered":"\n<p>\u534e\u76db\u987f\u5927\u5b66\u7684<a href=\"https:\/\/www.youtube.com\/@Eigensteve\" target=\"_blank\" rel=\"noreferrer noopener\">Steve Brunton<\/a>\u6559\u6388<a href=\"https:\/\/www.youtube.com\/playlist?list=PLMrJAkhIeNNQ0BaKuBKY43k4xMo6NSbBa\" target=\"_blank\" rel=\"noreferrer noopener\">\u5173\u4e8e\u201c\u7269\u7406\u5f15\u5bfc\u7684\u673a\u5668\u5b66\u4e60\u201d\uff08Physics-Informed Machine Learning\uff0cPIML\uff09\u7684\u8bb2\u5ea7<\/a>\u975e\u5e38\u503c\u5f97\u89c2\u770b\u5b66\u4e60\u3002\u8bb2\u5ea7\u63a2\u8ba8\u5982\u4f55\u5c06\u7269\u7406\u5b9a\u5f8b\u3001\u539f\u7406\u548c\u77e5\u8bc6\u878d\u5165\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u4ee5\u63d0\u9ad8\u8fd9\u4e9b\u6a21\u578b\u7684\u51c6\u786e\u6027\u3001\u6548\u7387\u548c\u6cdb\u5316\u80fd\u529b\uff0c\u7279\u522b\u662f\u5728\u5de5\u7a0b\u3001\u6d41\u4f53\u52a8\u529b\u5b66\u548c\u81ea\u7136\u79d1\u5b66\u7b49\u590d\u6742\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528\u3002<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Physics Informed Machine Learning: High Level Overview of AI and ML in Science and Engineering\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JoFW2uSd3Uo?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">Physics Informed Machine Learning: High Level Overview of AI and ML in Science and Engineering<\/figcaption><\/figure>\n\n\n\n<p>\u4e00\u3001<strong>\u7269\u7406\u5f15\u5bfc\u7684\u673a\u5668\u5b66\u4e60<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PIML\u88ab\u5f3a\u8c03\u4e3a\u5728\u7269\u7406\u5b66\u4e0e\u673a\u5668\u5b66\u4e60\u4ea4\u53c9\u9886\u57df\u4e2d\u7684\u4e00\u4e2a\u5173\u952e\u7814\u7a76\u65b9\u5411\u3002<\/li>\n\n\n\n<li>\u5176\u76ee\u6807\u662f\u5229\u7528\u73b0\u6709\u7684\u7269\u7406\u77e5\u8bc6\u6765\u6539\u8fdb\u673a\u5668\u5b66\u4e60\u6a21\u578b\uff0c\u540c\u65f6\u5229\u7528\u673a\u5668\u5b66\u4e60\u6765\u53d1\u73b0\u65b0\u7684\u7269\u7406\u89c4\u5f8b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u4e8c\u3001<strong>\u7269\u7406\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u91cd\u8981\u6027<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5c3d\u7ba1\u673a\u5668\u5b66\u4e60\u53d6\u5f97\u4e86\u663e\u8457\u8fdb\u5c55\uff0c\u5c06\u7269\u7406\u77e5\u8bc6\u878d\u5165\u8fd9\u4e9b\u6a21\u578b\u53ef\u4ee5\u663e\u8457\u63d0\u5347\u5176\u6027\u80fd\uff0c\u5c24\u5176\u662f\u5728\u5de5\u7a0b\u548c\u81ea\u7136\u79d1\u5b66\u9886\u57df\u3002<\/li>\n\n\n\n<li>\u8ba8\u8bba\u4e86\u4e24\u4e2a\u4e3b\u8981\u4e3b\u9898\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5c06\u5df2\u77e5\u7684\u7269\u7406\u5b9a\u5f8b\uff08\u5982\u5b88\u6052\u5b9a\u5f8b\u3001\u5bf9\u79f0\u6027\uff09\u5d4c\u5165\u673a\u5668\u5b66\u4e60\u6a21\u578b\u4e2d\u3002<\/li>\n\n\n\n<li>\u5229\u7528\u673a\u5668\u5b66\u4e60\u4ece\u6570\u636e\u4e2d\u53d1\u73b0\u65b0\u7684\u7269\u7406\u89c4\u5f8b\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u4e09\u3001<strong>\u673a\u5668\u5b66\u4e60\u7684\u4e94\u4e2a\u9636\u6bb5<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u95ee\u9898\u5b9a\u4e49<\/strong>\uff1a\u51b3\u5b9a\u8981\u5efa\u6a21\u7684\u5bf9\u8c61\u3002<\/li>\n\n\n\n<li><strong>\u6570\u636e\u6574\u7406<\/strong>\uff1a\u6536\u96c6\u5e76\u51c6\u5907\u8bad\u7ec3\u6570\u636e\u3002<\/li>\n\n\n\n<li><strong>\u67b6\u6784\u8bbe\u8ba1<\/strong>\uff1a\u9009\u62e9\u5408\u9002\u7684\u6a21\u578b\u67b6\u6784\u3002<\/li>\n\n\n\n<li><strong>\u635f\u5931\u51fd\u6570\u8bbe\u8ba1<\/strong>\uff1a\u5b9a\u4e49\u4e00\u4e2a\u8861\u91cf\u6a21\u578b\u6027\u80fd\u7684\u51fd\u6570\u3002<\/li>\n\n\n\n<li><strong>\u4f18\u5316<\/strong>\uff1a\u8c03\u6574\u6a21\u578b\u4ee5\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u56db\u3001<strong>\u7269\u7406\u5728\u6bcf\u4e2a\u9636\u6bb5\u7684\u878d\u5408<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6bcf\u4e2a\u9636\u6bb5\u5982\u4f55\u878d\u5165\u7269\u7406\u77e5\u8bc6\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5728<strong>\u95ee\u9898\u5b9a\u4e49<\/strong>\u9636\u6bb5\uff0c\u901a\u8fc7\u786e\u4fdd\u95ee\u9898\u5177\u6709\u7269\u7406\u610f\u4e49\u6765\u878d\u5165\u7269\u7406\u77e5\u8bc6\u3002<\/li>\n\n\n\n<li>\u5728<strong>\u6570\u636e\u6574\u7406<\/strong>\u9636\u6bb5\uff0c\u901a\u8fc7\u4f7f\u7528\u7269\u7406\u4e0d\u53d8\u6027\u6216\u5bf9\u79f0\u6027\u6765\u6269\u5145\u6570\u636e\u3002<\/li>\n\n\n\n<li>\u5728<strong>\u67b6\u6784\u8bbe\u8ba1<\/strong>\u9636\u6bb5\uff0c\u901a\u8fc7\u9009\u62e9\u672c\u8eab\u5c0a\u91cd\u7269\u7406\u5b9a\u5f8b\u7684\u6a21\u578b\u67b6\u6784\u3002<\/li>\n\n\n\n<li>\u5728<strong>\u635f\u5931\u51fd\u6570\u8bbe\u8ba1<\/strong>\u9636\u6bb5\uff0c\u901a\u8fc7\u52a0\u5165\u6267\u884c\u7269\u7406\u5b9a\u5f8b\u7684\u9879\u6765\u589e\u5f3a\u6a21\u578b\u3002<\/li>\n\n\n\n<li>\u5728<strong>\u4f18\u5316<\/strong>\u9636\u6bb5\uff0c\u901a\u8fc7\u4f7f\u7528\u4e25\u683c\u6267\u884c\u7269\u7406\u7ea6\u675f\u7684\u65b9\u6cd5\u6765\u589e\u5f3a\u6a21\u578b\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>\u4e94\u3001<strong>\u5b9e\u4f8b\u548c\u5e94\u7528<\/strong><\/p>\n\n\n\n<p>\u8bb2\u5ea7\u89c6\u9891\u5305\u62ec\u4e86\u5982\u6d41\u4f53\u52a8\u529b\u5b66\u5efa\u6a21\u3001\u65b0\u6750\u6599\u8bbe\u8ba1\uff0c\u4ee5\u53ca\u521b\u5efa\u7269\u7406\u7cfb\u7edf\u7684\u6570\u5b57\u5b6a\u751f\uff08\u865a\u62df\u6a21\u578b\uff09\u7b49\u5b9e\u4f8b\u3002\u8ba8\u8bba\u4e86\u7279\u5b9a\u67b6\u6784\uff0c\u5982<a href=\"https:\/\/nullthought.net\/?p=4287\" target=\"_blank\" rel=\"noreferrer noopener\">\u7269\u7406\u5f15\u5bfc\u795e\u7ecf\u7f51\u7edc\uff08PINNs\uff09<\/a>\uff0c\u4ee5\u53ca\u5b83\u4eec\u5982\u4f55\u7528\u4e8e\u89e3\u51b3\u5de5\u7a0b\u548c\u7269\u7406\u79d1\u5b66\u4e2d\u7684\u504f\u5fae\u5206\u65b9\u7a0b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fusing Physics and AI\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/yL0dOZZ1WKQ?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u534e\u76db\u987f\u5927\u5b66\u7684Steve Brunton\u6559\u6388\u5173\u4e8e\u201c\u7269\u7406\u5f15\u5bfc\u7684\u673a\u5668\u5b66\u4e60\u201d\uff08Physics-Informed Mac [&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":[39,63,71],"class_list":{"0":"post-4401","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"hentry","6":"category-tech","7":"category-36","8":"tag-ai","10":"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":"\u534e\u76db\u987f\u5927\u5b66\u7684Steve Brunton\u6559\u6388\u5173\u4e8e\u201c\u7269\u7406\u5f15\u5bfc\u7684\u673a\u5668\u5b66\u4e60\u201d\uff08Physics-Informed Mac&hellip;","_links":{"self":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/4401","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=4401"}],"version-history":[{"count":3,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/4401\/revisions"}],"predecessor-version":[{"id":6581,"href":"https:\/\/nullthought.net\/index.php?rest_route=\/wp\/v2\/posts\/4401\/revisions\/6581"}],"wp:attachment":[{"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4401"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4401"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nullthought.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4401"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}