Manifold Alignment-Based Nonintrusive and Nonlinear Multifidelity Reduced-Order Modeling

Abstract

This study presents the development of a methodology for the construction of data-driven, parametric, multifidelity reduced-order models to emulate aerodynamic flowfields with nonlinear and discontinuous features. Realistic computational budgets often constrain the size of the high-fidelity data set required to build a model with the desired predictive accuracy. In such cases, multifidelity 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 multifidelity reduced-order modeling method that uses 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 two-dimensional transonic airfoil and a high-speed blunt body. It is observed that, for problems with high input space dimension and complex features, the predictive accuracy of the multifidelity nonlinear reduced-order models improves substantially over their linear counterparts. However, multifidelity linear models were superior to equivalent nonlinear models for smaller input space dimensions, which may provide a useful intuition for practitioners when constructing reduced-order models for their respective problems.