{"id":9105,"date":"2025-12-15T07:02:30","date_gmt":"2025-12-15T07:02:30","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/12\/15\/2512-11090\/"},"modified":"2025-12-15T07:02:30","modified_gmt":"2025-12-15T07:02:30","slug":"2512-11090","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/12\/15\/2512-11090\/","title":{"rendered":"Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics"},"content":{"rendered":"

Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics
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arXiv:2512.11090v1 Announce Type: new
\nAbstract: Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build a low-dimensional surrogate model for complex evolution systems. Given time-dependent training data, we split the time domain into multiple overlapping windows, within which nonlinear dimension reduction is performed by auto-encoders to capture latent codes. Once a low-dimensional representation of the data is learned, a propagator network is trained to capture the evolution of the latent codes in each window, and a transcoder is trained to connect the latent codes between adjacent windows. The proposed windowed decomposition significantly simplifies propagator training by breaking long-horizon dynamics into multiple short, manageable segments, while the transcoders ensure consistency across windows. In addition to the algorithmic framework, we develop a mathematical theory establishing the representation power of WeldNet under the manifold hypothesis, justifying the success of nonlinear model reduction via deep autoencoder-based architectures. Our numerical experiments on various differential equations indicate that WeldNet can capture nonlinear latent structures and their underlying dynamics, outperforming both traditional projection-based approaches and recently developed nonlinear model reduction methods.<\/div>\n

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\n Biraj Dahal, Jiahui Cheng, Hao Liu, Rongjie Lai, Wenjing Liao
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Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics arXiv:2512.11090v1 Announce Type: new Abstract: Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,450,451,112],"tags":[84,103,657],"class_list":["post-9105","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-cs-na","category-math-na","category-stat-ml","tag-data","tag-model","tag-reduction"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9105"}],"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=9105"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9105\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}