A Multi-Fidelity Methodology for Reduced Order Models with High-Dimensional Inputs

• URL: http://arxiv.org/abs/2402.17061v1
• Date: Mon, 26 Feb 2024 22:47:03 GMT
• Title: A Multi-Fidelity Methodology for Reduced Order Models with High-Dimensional Inputs
• Authors: Bilal Mufti, Christian Perron and Dimitri N. Mavris (ASDL, Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia)
• Abstract summary: 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. Our approach is validated through two test cases: the 2D RAE2822 airfoil and the 3D NASA CRM wing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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.

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