Improving Neural Network Efficiency with Multi-fidelity and Dimensionality Reduction Techniques

Author

Vignesh Sella
Thomas O'leary-Roseberry
Xiaosong Du, Missouri University of Science and TechnologyFollow
Mengwu Guo
Joaquim R.R.A. Martins
Omar Ghattas
Karen Willcox
Anirban Chaudhuri

Abstract

Design problems in aerospace engineering often require numerous evaluations of expensive to-evaluate high-fidelity models, resulting in prohibitive computational costs. One way to address the computational cost is through building surrogates, such as deep neural networks (DNNs). However, DNNs may only be an effective surrogate when sufficient evaluations of the high-fidelity model are required such that the up-front training cost is amortized, or in situations that require real-time responses (such as interactive visualizations). Typically, the data requirements for adequately accurate training of DNNs are often impractical for engineering applications. To alleviate this issue, the proposed work utilizes output dimensionality reduction along with information from multiple models of varying fidelities and cost to develop accurate projection-enabled multi-fidelity neural networks (MF-NNs) with limited training samples. The dimensionality reduction leads to a more parsimonious network and the multi-fidelity aspect adds more training data from lower-cost, lower-fidelity models. Three approaches for MF-NNs that leverage proper orthogonal decomposition-based projections are introduced: (i) pre-training method, (ii) additive method, and (iii) multi-step method. The MF-NN is applied to approximate the optimal design of 2D aerodynamic airfoils given the performance and design requirements. The MF-NN leads to ∼ 27%computational cost reduction compared to single-fidelity neural networks at the same accuracy (90%), with the multi-step approach performing the best for this application.

Recommended Citation

V. Sella et al., "Improving Neural Network Efficiency with Multi-fidelity and Dimensionality Reduction Techniques," AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2025, American Institute of Aeronautics and Astronautics, Jan 2025.

The definitive version is available at https://doi.org/10.2514/6.2025-2807

Department(s)

Mechanical and Aerospace Engineering

Publication Status

Full Access

Comments

Advanced Research Projects Agency - Energy, Grant DE-AR0001208

International Standard Book Number (ISBN)

978-162410723-8

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2025 American Insstitute of Aeronautics and Astronautics, All rights reserved.

Publication Date

01 Jan 2025