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

TL;DR

This paper presents a novel multi-fidelity, non-intrusive reduced order modeling framework that effectively manages high-dimensional inputs in aerospace design, improving accuracy and reducing computational costs through machine learning and advanced dimension reduction techniques.

Contribution

It introduces a multi-fidelity, parametric ROM framework combining machine learning, manifold alignment, and dimension reduction for high-dimensional aerospace applications, outperforming existing methods.

Findings

Enhanced predictive accuracy over single-fidelity methods

Reduced computational costs compared to traditional ROMs

Outperformed manifold-aligned ROM by 50% in high-dimensional scenarios

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.