Multi-Fidelity Reduced-Order Modeling Applied to Fields with Inconsistent Representations

Abstract

Our ever-increasing capacity for high-performance computing has progressively elevated the role of physics-based simulations in the conceptual and preliminary phases of aircraft design. This virtualization of the early design process has allowed for additional design freedom and shorter development time while engineers continuously strive for cleaner and quieter aircraft. While modern high-fidelity simulations can provide results with great accuracy, their application is often hindered by their steep computational cost and the limited availability of computing resources. This is especially prohibitive for design problems requiring the analysis of many aircraft configurations and at several flight conditions. To overcome the overwhelming cost of high-fidelity simulations, these are often replaced in practice by cheaper surrogate models generated using a handful of previously obtained solutions. When applied to physics-based results, surrogate models are typically associated with the prediction of integrated quantities. Recently, a new form of surrogate modeling, referred to as Reduced-Order Modeling (ROM), was developed for the prediction of high-dimensional field quantities. In addition to providing physically richer results than conventional surrogate models, this form of approximation is especially relevant for multi-disciplinary applications where the physical quantities exchanged between the disciplines are typically fields.

As with most empirical models, the accuracy of a ROM is contingent on the amount of data used for their construction. While these models offer fast predictions, collecting a sufficiently large dataset to achieve the desired accuracy can be impractical when applied to high-fidelity simulations, especially when considering many design parameters. Hence, the main objective of this dissertation is to improve current ROM methods by requiring less high-fidelity data while maintaining adequate accuracy. Specifically, we consider a multi-fidelity approach that enhances a few high-fidelity solutions with results from an inexpensive low-fidelity simulation. While various multi-fidelity solutions exist for conventional surrogate models, few are available for reduced-order modeling. A major factor behind the scarcity of multi-fidelity ROMs is that simulations of different fidelity generally produce fields with disparate representations. As a result, this work focuses on this issue and investigate methods to allow the fusion of inconsistent fields.

This dissertation contributes to the field of reduced-order modeling by proposing a multi-fidelity method that employs manifold alignment to find a common low-dimensional representation of two datasets with heterogeneous fields. Once aligned, a single prediction model combines the multi-fidelity datasets with an approach inspired by existing fusion-based multi-fidelity techniques. Therefore, the developed method can combine fields from various models irrespective of their representations. The produced ROM then potentially has better performance than a single-fidelity model trained with the same computational budget. The viability of the proposed method is validated using two practical problems, i.e., the aerodynamic analysis of a transonic airfoil and a transonic wing. Multiple multi-fidelity scenarios are considered with different fidelity combinations, various model configurations, and inconsistent fields. In many cases, the developed method can effectively provide improved predictions compared to an equivalent single-fidelity approach despite fusing results with inconsistent representations. At worst, when the proposed method is applied to datasets with a large fidelity difference, the accuracy of the resulting ROM tends to that of a single-fidelity model. Also, the results show that the developed method behaves similarly to existing multi-fidelity ROM methods when joining high- and low-fidelity fields with a consistent representation.