A Multi-Fidelity Methodology for Reduced Order Models with
  High-Dimensional Inputs
Bilal Mufti Christian Perron Dimitri N. Mavris
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.