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

2025-10-09

AI Summary

High-dimensional engineering design optimization is challenged by the coupled effects of aleatory and epistemic uncertainties. Method: This paper proposes a multi-level surrogate modeling framework based on hierarchical orthogonal decomposition, adaptively constructing and updating multiple non-intrusive Kriging surrogates. It integrates uncertainty-sensitive data filtering, hierarchical sampling, and orthogonal projection to achieve efficient, high-fidelity mapping of large-scale design spaces. Contribution/Results: The method significantly enhances scalability and statistical robustness. On benchmark analytical test problems, it improves both computational efficiency and optimization accuracy by two to three orders of magnitude over state-of-the-art approaches, while incurring minimal computational resource overhead. It establishes a new paradigm for uncertainty-driven high-dimensional engineering optimization—balancing economic feasibility, predictive accuracy, and practical deployability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Optimizing large engineering designs under uncertainty constraints
• Developing scalable Kriging surrogates for high-dimensional problems
• Reducing computational resources while improving optimization accuracy

Innovation

• Multi-level approach optimizes high-dimensional problems efficiently
• Kriging-based surrogate maps design domain with fast scaling
• Hierarchical decomposition leverages uncertainty-informed data adaptively