aiqbench analysis
This research advances surrogate modeling by integrating low-fidelity simulations with scarce high-fidelity data to improve accuracy in complex engineering domains like hypersonics and aerospace braking systems. By leveraging projection-based dimensionality reduction and automated weighting schemes, the method achieves significant performance gains even when limited to twelve or fewer expensive samples. This approach offers a practical pathway for deploying machine learning models where traditional training datasets are prohibitively costly to generate.
Projection-based multifidelity linear regression for data-scarce applications
arXiv:2508.08517v2 Announce Type: replace-cross 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.
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.
Machine Learning (stat.ML); Computational Engineering, Finance, and Science (cs.CE); Machine Learning (cs.LG)
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
Mach. Learn. Comput. Sci. Eng. 1, 47 (2025)
https://doi.org/10.1007/s44379-025-00049-5 Focus to learn more DOI(s) linking to related resources
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