A Multi-Fidelity Methodology for Reduced Order Models with High-Dimensional Inputs
Bilal Mufti, Christian Perron, Dimitri N. Mavris
TL;DR
This work addresses the challenge of building accurate ROMs for high-dimensional input spaces in aerospace design by fusing output-space Procrustes manifold alignment with input-space multi-fidelity active subspace reduction and Hierarchical Kriging regression. The MF-PCAS framework non-intrusively couples POD-based latent representations with multi-fidelity surrogates to achieve favorable cost–accuracy trade-offs, demonstrated on 2D RAE 2822 and 3D NASA CRM wing problems. Key findings show MF-PCAS outperforms single-fidelity PCAS and reduces error by about 50% relative to MA-ROM in large-input scenarios, especially under budgets that combine high- and low-fidelity data. The approach offers practical impact for rapid, reliable aero-structural predictions across design spaces, with future work aimed at incorporating non-linear dimensionality reduction to better capture shocks and other nonlinear phenomena.
Abstract
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.