An Integrated Uncertainty Quantification and Optimization for solving the 2025 NASA-DNV Challenge

This paper presents a methodological framework for tackling the NASA and DNV Challenge on Optimization Under Uncertainty. The challenge requires designing and calibrating an uncertainty model using limited empirical data and optimizing design variables under uncertainty. We propose an integrated approach based on Bayesian experimental design, emulators, efficient computational tools, and advanced calibration techniques. Parametric and non-parametric uncertainty models are compared, calibrated using strategies incorporating likelihood-free KNN and discrepancy-based filtering methods, imprecise probability and likelihood-based ABC inference using Transitional Markov chain Monte Carlo. Uncertainty-based optimization is also performed by different approaches, including grid search, genetic algorithms, and two-level stochastic optimization using Bayesian techniques supported by surrogate models. The framework refines the uncertainty model by systematically updating the distributions and selecting optimal experimental conditions to enhance learning efficiency. Our results highlight the efficacy of the approach in balancing performance, reliability, and risk-constrained objectives that are generally applicable in UQ-driven decision-making problems.

Keywords: Uncertainty quantification, Bayesian optimization, Approximate Bayesian computation, Surrogate modelling, Experimental design, Variational-auto-encoders, Robust risk-constrained optimization.