2025/10/09 by Ampellio, Enrico, Gjorgiev, Blazhe, Sansavini, Giovanni
#60G15 (Primary) 68T37 #90C26 (Secondary) #C.4 #FOS: Computer and information sciences #FOS: Electrical engineering #G.1.6 #G.3 #G.4 #I.2.3 #I.5.1 #J.2 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2510.07904
Engineering design involves demanding models encompassing many decision variables and uncontrollable parameters. In addition, unavoidable aleatoric and epistemic uncertainties can be very impactful and add further complexity. The state-of-the-art adopts two steps, uncertainty quantification and design optimization, to optimize systems under uncertainty by means of robust or stochastic metrics. However, conventional scenario-based, surrogate-assisted, and mathematical programming methods are not sufficiently scalable to be affordable and precise in large and complex cases. Here, a multi-level approach is proposed to accurately optimize resource-intensive, high-dimensional, and complex engineering problems under uncertainty with minimal resources. A non-intrusive, fast-scaling, Kriging-based surrogate is developed to map the combined design/parameter domain efficiently. Multiple surrogates are adaptively updated by hierarchical and orthogonal decomposition to leverage the fewer and most uncertainty-informed data. The proposed method is statistically compared to the state-of-the-art via an analytical testbed and is shown to be concurrently faster and more accurate by orders of magnitude.