Projection-based multifidelity linear regression for data-scarce applications

[2508.08517] Projection-based multifidelity linear regression for data-scarce applications Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2508.08517 (stat) [Submitted on 11 Aug 2025 ( v1 ), last revised 14 Aug 2026 (this version, v2)] Title: Projection-based multifidelity linear regression for data-scarce applications Authors: Vignesh Sella , Julie Pham , Karen Willcox , Anirban Chaudhuri View a PDF of the paper titled Projection-based multifidelity linear regression for data-scarce applications, by Vignesh Sella and 3 other authors View PDF HTML (experimental) 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 with limited, costly high-fidelity evaluations. We introduce two projection-based multifidelity linear regression approaches with linear and nonlinear features 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. We introduce a proximity-based weighting scheme with automatic weight selection strategy through cross-validation. The proposed multifidelity linear regression methods are demonstrated on approximating the surface pressure field of a hypersonic vehicle in flight and the temperature field on an aircraft disc braking system. In an ultra low-data regime of no more than twelve high-fidelity samples, multifidelity linear regression achieves approximately 2%-12% improvement in median accuracy and a higher $R^2$ score relative to single-fidelity methods at comparable computational cost. Comments: 36 pages, 16 figures, accepted in Machine Learning for Computational Science and Engineering special issue Accelerating Numerical Methods With Scientific Machine Learning Subjects: Machine Learning (stat.ML) ; Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG) Cite as: arXiv:2508.08517 [stat.ML] (or arXiv:2508.08517v2 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2508.08517 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Mach. Learn. Comput. Sci. Eng. 1, 47 (2025) Related DOI : https://doi.org/10.1007/s44379-025-00049-5 Focus to learn more DOI(s) linking to related resources Submission history From: Vignesh Sella [ view email ] [v1] Mon, 11 Aug 2025 22:55:04 UTC (1,946 KB) [v2] Fri, 14 Aug 2026 19:27:27 UTC (6,923 KB) Full-text links: Access Paper: View a PDF of the paper titled Projection-based multifidelity linear regression for data-scarce applications, by Vignesh Sella and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2025-08 Change to browse by: cs cs.CE cs.LG stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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