# Multi-Fidelity Gradient-Based Optimization for High-Dimensional Aeroelastic Configurations
## 4 Discussion
Regeneration (rather than morphing) of the high-fidelity aerodynamic grids may also be a detriment due to discontinuous mesh topologies (thus causing noise in responses), although this effect would be present in the single-fidelity optimizations as well. Finally, the variation of VLM- and Euler-CFD-based aerodynamic loads and stresses with varying structural thicknesses may simply be poorly correlated because Euler takes shocks in the flow under consideration while VLM simply uses an empirical wave drag estimate. Potentially, only a subset of the objective and constraint functions may be poorly correlated (such as the stress constraint, which was not included in the shape-only cases). How well the responses are correlated may even vary spatially, for instance agreeing well for structural groups near the tip compared to inboard (with VLM likely agreeing better when shocks are weak or nonexistent). In addition, because the VLM does have a flat-plate-based viscous drag estimate (with kinematic viscosity being set very small for the present work) and RANS flow may have weaker shocks, VLM and RANS may potentially be better correlated in spite of RANS being higher-fidelity than Euler. A subsonic cruise condition may also see better correlation between VLM and Euler or RANS. In general, the handling of constraints is an area for improvement in gradient-based, multi-fidelity optimization. Handling constraints directly in SLSQP reduced the objective function more quickly and ultimately led to better satisfaction of the constraints compared to using a penalty function (again within SLSQP). The doubling of the objective function with penalty constraints also highlights the sensitivity of the process to weighting factors and the emphasis on constraint satisfaction versus objective improvement. The underlying BFGS method is inherently an unconstrained optimizer, and the extension of the multi-fidelity concepts to other approaches such as Sequential Quadratic Programming (SQP) is an area for future investigation. In addition to improving the smoothness and accuracy of aeroelastic gradients, the quality of the multi-fidelity correction is an area for further investigation and future improvement. The current two-point correction is sensitive to noisy responses at either point. While first-order consistency at the current design point is necessary to prove convergence, other approaches admitting additional data could improve the correction of the low-fidelity model and be more tolerant of numerical noise. Furthermore, data-driven approaches are desired for sizing the trust region and determining when to revert to single-fidelity optimization when convergence is slow. Alternatively, adjustment of the trust region heuristic and minimum trust region size may produce improved performance. Further expansion of the aerodynamic shape optimization may also help to demonstrate the scalability of the MF-BFGS approach. The design problem size can be expanded by increasing the airfoil degrees of freedom, as well as the number of airfoil sections. Optimization studies using Reynolds-averaged Navier-Stokes are also planned to explore performance with different fidelity combinations.