{"ID":2883991,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.08517","arxiv_id":"2508.08517","title":"Projection-based multifidelity linear regression for data-scarce applications","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 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% - 12% improvement in median accuracy compared to single-fidelity methods with comparable computational cost.","short_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. Multifi...","url_abs":"https://arxiv.org/abs/2508.08517","url_pdf":"https://arxiv.org/pdf/2508.08517v1","authors":"[\"Vignesh Sella\",\"Julie Pham\",\"Karen Willcox\",\"Anirban Chaudhuri\"]","published":"2025-08-11T22:55:04Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.CE\",\"cs.LG\"]","methods":"[]","has_code":false}