Leibniz MMS Days 2024 - Abstract

Chen, Long

Data-driven aerodynamic shape design with distributionally robust optimization approaches

(joint work with Nico N. Gauger and Jan Rottmayer from RPTU Kaiserslautern-Landau)

We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. DRO aims to minimize the worst-case expected performance in a set of distributions that is informed by observed data with uncertainties. Building on the findings of the work [1], we study the connections between a class of DRO and robust design optimization, which is classically based on the mean-variance (standard deviation) optimization formulation pioneered by Taguchi. Our results provide a new perspective to the understanding and formulation of robust design optimization problems. It enables data-driven and statistically principled approaches to quantify the trade-offs between robustness and performance, in contrast to the classical robust design formulation that captures uncertainty only qualitatively. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

[1] Gotoh, Jun-ya, Michael Jong Kim, and Andrew EB Lim. "Robust empirical optimization is almost the same as mean-variance optimization." Operations research letters 46.4 (2018): 448-452.