{"id":7068,"date":"2025-09-23T07:02:30","date_gmt":"2025-09-23T07:02:30","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/09\/23\/2509-16395\/"},"modified":"2025-09-23T07:02:30","modified_gmt":"2025-09-23T07:02:30","slug":"2509-16395","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/09\/23\/2509-16395\/","title":{"rendered":"Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs"},"content":{"rendered":"

Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs
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arXiv:2509.16395v1 Announce Type: new
\nAbstract: We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace, thereby reducing the effective dimensionality of training while preserving solution accuracy. The low-rank tangent subspace is defined layer-wise by the singular value decomposition (SVD) of the current network weights, and the resulting update is obtained by solving a well-posed, tractable linear system within this subspace. This design augments the underlying numerical solver with a parameter efficient EDNN component without requiring full fine-tuning of all network weights. We evaluate LR-EDNN on representative PDE problems and compare it against corresponding baselines. Across cases, LR-EDNN achieves comparable accuracy with substantially fewer trainable parameters and reduced computational cost. These results indicate that low-rank constraints on parameter velocities, rather than full-space updates, provide a practical path toward scalable, efficient, and reproducible scientific machine learning for PDEs.<\/div>\n

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\n Jiahao Zhang, Shiheng Zhang, Guang Lin
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Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs arXiv:2509.16395v1 Announce Type: new Abstract: We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace, thereby […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[3869,588,589],"class_list":["post-7068","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-ednn","tag-low","tag-rank"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7068"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=7068"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/7068\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=7068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=7068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=7068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}