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

arXiv: https://arxiv.org/abs/2510.07904 · HTML: https://mlsanity.com/paper/2510.07904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 78 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [A Literature Survey of Benchmark Functions For Global Optimization Problems](https://mlsanity.com/paper/1308.4008/) (2013)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Polynomial-Chaos-based Kriging](https://mlsanity.com/paper/1502.03939/) (2015)
- [Bayesian Surrogate Analysis and Uncertainty Propagation](https://mlsanity.com/paper/2101.04038/) (2021)
- [Stochastic spectral embedding](https://mlsanity.com/paper/2004.04480/) (2020)
- [A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses](https://mlsanity.com/paper/1402.5830/) (2014)

## Abstract (arXiv)

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.