Nonlinear Multi-Fidelity Reduced Order Modeling Method using Manifold Alignment

This study presents the development of a methodology for the construction of data-driven, parametric, multi-fidelity reduced order models to emulate aerodynamic flow fields with non- linear and discontinuous features. Realistic computational budgets often constrain the size of the high-fidelity dataset required to build a model with the desired predictive accuracy. In such cases, multi-fidelity models can be advantageous as they leverage an abundance of inexpensive low-fidelity data in conjunction with high-fidelity training data to improve the model’s predictive accuracy. This study formulates a multi-fidelity reduced order model that utilizes nonlinear dimension reduction and Procrustes manifold alignment to project and transform data from disparate sources such that they lie in a common latent space. An initial feasibility assessment of the method is performed for emulating the flow over a 2-D transonic airfoil and a high-speed blunt body. It is observed that, for problems with high input space and complex features, the predictive accuracy of the multi-fidelity nonlinear ROMs improves substantially over their linear counterparts. However, multi-fidelity linear models were superior to equivalent nonlinear models for smaller input space dimensions, which may provide a useful intuition for practitioners when constructing ROMs for their respective problems.