A Multi-Fidelity Methodology for Reduced Order Models with High-Dimensional Inputs
<|reference_start|>A Multi-Fidelity Methodology for Reduced Order Models with High-Dimensional Inputs: In the early stages of aerospace design, reduced order models (ROMs) are crucial for minimizing computational costs associated with using physics-rich field information in many-query scenarios requiring multiple evaluations. The intricacy of aerospace design demands the use of high-dimensional design spaces to capture detailed features and design variability accurately. However, these spaces introduce significant challenges, including the curse of dimensionality, which stems from both high-dimensional inputs and outputs necessitating substantial training data and computational effort. To address these complexities, this study introduces a novel multi-fidelity, parametric, and non-intrusive ROM framework designed for high-dimensional contexts. It integrates machine learning techniques for manifold alignment and dimension reduction employing Proper Orthogonal Decomposition (POD) and Model-based Active Subspace with multi-fidelity regression for ROM construction. Our approach is validated through two test cases: the 2D RAE~2822 airfoil and the 3D NASA CRM wing, assessing combinations of various fidelity levels, training data ratios, and sample sizes. Compared to the single-fidelity PCAS method, our multi-fidelity solution offers improved cost-accuracy benefits and achieves better predictive accuracy with reduced computational demands. Moreover, our methodology outperforms the manifold-aligned ROM (MA-ROM) method by 50% in handling scenarios with large input dimensions, underscoring its efficacy in addressing the complex challenges of aerospace design.<|reference_end|>
@article{mufti2024a,
    title={A Multi-Fidelity Methodology for Reduced Order Models with
  High-Dimensional Inputs},
    author={Bilal Mufti, Christian Perron and Dimitri N. Mavris (ASDL, Daniel
  Guggenheim School of Aerospace Engineering, Georgia Institute of Technology,
  Atlanta, Georgia)},
    journal={arXiv preprint arXiv:2402.17061},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17061},
    primaryClass={cs.LG}
}