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

arXiv: https://arxiv.org/abs/2402.17061 · HTML: https://mlsanity.com/paper/2402.17061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 74 references that are in the map.
- First posted on arXiv 26 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [Domain Separation Networks](https://mlsanity.com/paper/1608.06019/) (2016)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Derivative-Informed Projected Neural Networks for High-Dimensional Parametric Maps Governed by PDEs](https://mlsanity.com/paper/2011.15110/) (2020)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes](https://mlsanity.com/paper/2008.02386/) (2020)
- [A Fully Bayesian Gradient-Free Supervised Dimension Reduction Method using Gaussian Processes](https://mlsanity.com/paper/2008.03534/) (2020)
- [Manifold Alignment-Based Multi-Fidelity Reduced-Order Modeling Applied to Structural Analysis](https://mlsanity.com/paper/2206.06920/) (2022)

## Abstract (arXiv)

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.