In recent years, multilayered hierarchical compositions of the well-known and widely used Gaussian process models called deep Gaussian processes are finding use in the approximation of black-box fu...

This paper demonstrates the development of purely data-driven, nonintrusive parametric reduced-order models for the emulation of high-dimensional field outputs using randomized linear algebra techn...

This work presents the development of a multi-fidelity, parametric and non-intrusive reduced-order modelling 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 responses with inconsistent representations, 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 latent space. Hence, simulations using incompatible grids or geometries can be combined into a single multi-fidelity reduced-order model 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 reduced-order model achieves comparable predictive accuracy at a lower computational cost. Furthermore, it is demonstrated that the proposed method can combine disparate fields without any adverse effect on predictive performance.

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.