Uncertainty Quantification of Engineering Structures by Polynomial Chaos Expansion and Multivariate Active Learning

2026-06-17 · Source: stat.ML updates on arXiv.org · Field: Science & Research — Engineering & Applied Sciences, Mathematics & Computational Sciences, Artificial Intelligence & Machine Learning · Depth: Expert, extended

Summary

A novel adaptive sequential sampling strategy is proposed for constructing multi-output Polynomial Chaos Expansion (PCE) surrogate models, addressing the high computational cost of direct model evaluations in engineering applications. This method generalizes a single-output criterion by aggregating normalized variance contributions across multiple outputs, balancing variance-driven exploitation with distance-based exploration. Its performance is compared against non-sequential Latin Hypercube Sampling (LHS) using numerical examples, including a 2D mirror line singularity function, a reinforced concrete beam, and offshore wind turbine problems under wind and multiphysics coupling. Results consistently demonstrate that the proposed strategy improves surrogate accuracy, stability, and convergence behavior, particularly in controlling worst-case prediction errors and enhancing second-order statistics estimation, especially under limited sampling budgets.

Key takeaway

For Machine Learning Engineers or Research Scientists developing surrogate models for complex engineering simulations, you should consider implementing this multi-output adaptive sequential sampling strategy. It offers superior accuracy and robustness compared to static methods like LHS, especially when dealing with computationally expensive models producing multiple quantities of interest under limited sampling budgets. This approach will enable more efficient uncertainty quantification and reliable prediction of extreme events in your structural and mechanical analyses.

Key insights

Adaptive sequential sampling for multi-output PCE improves surrogate accuracy and stability by balancing variance exploitation and spatial exploration.

Principles

• Multi-output sampling benefits from aggregated variance information.
• Balancing exploitation (variance) and exploration (distance) is key.
• Adaptive sampling reduces variability across model runs.

Method

The method sequentially selects new samples from a candidate pool based on local contribution to output variance, balancing distance-based exploration and aggregated variance exploitation across all outputs.

In practice

• Apply to finite element models with multiple QoIs.
• Use for reliability analysis and limit-state evaluation.
• Improve UQ in complex engineering systems.

Topics

• Uncertainty Quantification
• Polynomial Chaos Expansion
• Adaptive Sequential Sampling
• Multi-output Surrogate Modeling
• Engineering Structures
• Finite Element Analysis

Code references

• NovakLBUT/MultTheta_engineering

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.