Data-driven Model Updating Solution for the NASA and DNV Challenge 2025 on Optimisation under Uncertainty with Flow-based Neural Networks

Uncertainty quantification (UQ) remains critical in addressing complex engineering challenges, especially in safety-critical systems where scarce data and mixed uncertainties prevent robust decision making. This paper presents a data-driven model updating framework to address the NASA and DNV Challenge 2025 on Optimisation under Uncertainty using the invertible normalising flow-based neural networks, which emphasises high-dimensional systems with limited observational data and hybrid aleatory-epistemic uncertainties. Our methodology explicitly deals with the aleatory and epistemic uncertainties separately through a two-step model updating framework based on a preliminary sensitivity analysis. The aleatory variables are calibrated first globally and then the epistemic variables are calibrated locally. To process the time series response data, multihead transformer is adopted as the conditional network in the normalising flow-based model updating framework, which can summarise the complex data into fixed-length vector. The following design optimisation problems are tackled by the Particle Swarm Optimisation (PSO) with a Fully Connected Neural Networks (FCNNs)-based surrogate model. This work bridges machine learning with classical UQ methodologies, offering a practical pathway for safety-critical system design under aleatory-epistemic uncertainties.

Keywords: Uncertainty quantification, Model updating, Design optimisation, Normalising flow.