Tackling the NASA and DNV 2025 UQ challenge : an Approximate Bayesian Computation Framework for Surrogate-Based Optimization Under Uncertainty

Performing an optimization task on a complex system can be challenging when input variables are not completely known and when there is inherent randomness in the system response. The first step is therefore to gather information to reduce these uncertainties. In this paper, we use a rejection algorithm based on approximate Bayesian computation to infer input distributions from a limited number of output observations. We define informative metrics to estimate the likelihood of each input variable using a computer model of the real system and variance-based sensitivity analysis. Further, we identify optimal control parameters accounting for both performance and probabilistic constraints. We utilize neural network surrogates to efficiently approximate key relationships, evaluate failure probability, and enable gradient-based optimization approaches.

Keywords: Stochastic model updating, Approximate Bayesian computation, Rejection sampling, Surrogate modelling, Uncertainty quantification.