{"id":6049,"date":"2025-08-13T07:02:54","date_gmt":"2025-08-13T07:02:54","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/08\/13\/2508-08517\/"},"modified":"2025-08-13T07:02:54","modified_gmt":"2025-08-13T07:02:54","slug":"2508-08517","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/08\/13\/2508-08517\/","title":{"rendered":"Projection-based multifidelity linear regression for data-scarce applications"},"content":{"rendered":"<p>    Projection-based multifidelity linear regression for data-scarce applications<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2508.08517v1 Announce Type: new<br \/>\nAbstract: Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches that leverage principal component basis vectors for dimensionality reduction and combine multifidelity data through: (i) a direct data augmentation using low-fidelity data, and (ii) a data augmentation incorporating explicit linear corrections between low-fidelity and high-fidelity data. The data augmentation approaches combine high-fidelity and low-fidelity data into a unified training set and train the linear regression model through weighted least squares with fidelity-specific weights. Various weighting schemes and their impact on regression accuracy are explored. The proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight. In a low-data regime of no more than ten high-fidelity samples, multifidelity linear regression achieves approximately 3% &#8211; 12% improvement in median accuracy compared to single-fidelity methods with comparable computational cost.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Vignesh Sella, Julie Pham, Karen Willcox, Anirban Chaudhuri<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2508.08517\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Projection-based multifidelity linear regression for data-scarce applications arXiv:2508.08517v1 Announce Type: new Abstract: Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear regression targeting data-limited applications with high-dimensional outputs. Multifidelity methods integrate many inexpensive low-fidelity model evaluations [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,740,113,112],"tags":[84,2969,3505],"class_list":["post-6049","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-ce","category-cs-lg","category-stat-ml","tag-data","tag-fidelity","tag-multifidelity"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/6049"}],"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=6049"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/6049\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=6049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=6049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=6049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}