Projection-based multifidelity linear regression for data-scarce applications

TL;DR

This paper introduces two projection-based multifidelity linear regression methods that improve surrogate modeling accuracy in data-scarce, high-dimensional applications by combining low- and high-fidelity data through dimensionality reduction and data augmentation.

Contribution

The work develops novel multifidelity linear regression approaches using principal component basis vectors and explicit linear corrections, enhancing accuracy with limited high-fidelity data.

Findings

Achieved 3% - 12% improvement in median accuracy over single-fidelity methods.

Demonstrated effectiveness on hypersonic vehicle surface pressure prediction.

Methods are effective with as few as ten high-fidelity samples.

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.