Projection and Interpolation-based Reduced Order Modeling

Student: Gary Collins

Sponsor: Airbus

Despite advancement in computer power and numerical techniques, the scope and demands of computational problems have outpaced the ability to meet them in many engineering fields. This is especially true in the field of aerospace where many of the bleeding edge computational processes are bottlenecked by the turn-around time of generating solutions such as with multi-fidelity design optimization. However, reduced-ordered models (ROMs) provide a way of generating high-fidelity solutions at a significantly lowered computational cost and run-time. The ROMs of interest within aerospace engineering fall into two camps: projection-based models where the state and physical equations are solved in a reduced, projected space; and interpolation-based where black-box models (such as neural networks) are constructed to map the inputs and outputs of interest.

My research as a member of the A2SRL involves investigating ways of constructing and evaluating projection-based reduced order models and developing hybridized methods of projection and interpolation-based ROMs. Construction of projection-based ROMs focused on generating optimal projection bases for model reduction [1], and the evaluation of projection-based ROMs involved using adjoint-weighted residual error estimation to quantify the error of the ROM and as an adaptation mechanism [2]. Hybridization will shore up deficiencies in the intrusive nature of projection-based ROMs with interpolation-based techniques.

Figure 1: Error Estimation and Adaptation
Figure 2: Hybridized Model


[1] Collins, G., Fidkowski K., Carlos C., “Petrov-Galerkin Projection-Based Model Reduction with

an Optimized Test Space”, AIAA SciTech 2020, January 2020.

[2] Collins, G., Fidkowski K., Carlos C., “Output Error Estimation for Projection-Based Reduced

Models”, AIAA Aviation 2019, June 2019.