Development of a Multi-Fidelity Reduced-Order Model Based on Manifold Alignment

This work presents the development of a novel multi-fidelity, parametric, and non-intrusive Reduced Order Modeling (ROM) method to tackle the problem of achieving an acceptable predictive accuracy under a limited computational budget, i.e., with expensive simulations and sparse training data. Traditional multi-fidelity surrogate models that predict scalar quantities address this issue by leveraging auxiliary data generated by a computationally cheaper lower fidelity code. However, for the prediction of field quantities, simulations of different fidelities may produce high-dimensional responses with inconsistent dimensionality and topology, rendering the direct application of common multi-fidelity techniques challenging. The proposed approach uses manifold alignment to fuse inconsistent fields from high- and low-fidelity simulations by individually projecting their solution onto a common shared latent space. Hence, simulations using incompatible grids or geometries can be combined into a single multi-fidelity ROM without additional manipulation of the data. This method is applied to a variety of multi-fidelity scenarios using a transonic airfoil problem. In most cases, the new multi-fidelity ROM achieves comparable predictive accuracy at a substantially lower computational cost. Furthermore, it is demonstrated that the proposed method can readily combine disparate fields without any adverse effect on model performance.