Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty

• URL: http://arxiv.org/abs/2510.07904v1
• Date: Thu, 09 Oct 2025 07:59:16 GMT
• Title: Multi-level informed optimization via decomposed Kriging for large design problems under uncertainty
• Abstract summary: The state-of-the-art adopts two steps, uncertainty quantification and design optimization, to optimize systems under uncertainty.<n>Here, a multi-level approach is proposed to accurately optimize resource-intensive, high-dimensional, and complex engineering problems under uncertainty with minimal resources.<n>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.
• Score: 2.141079906482723
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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