Latent Space-Based Bayesian Approach to the NASA and DNV Challenge 2025

This paper presents a latent space-based Bayesian methodology to tackle the NASA and DNV 2025 challenge on uncertainty quantification and design optimization. First, a Variational Autoencoder (VAE) is trained to investigate the distribution of the aleatory variables. From its latent-space representation, we conclude that a two-dimensional Gaussian distribution is suitable for modeling these uncertainties, thus enabling a data-driven calibration approach. Posterior estimates are obtained through a Bayesian updating procedure based on a multi-variational auto-encoder (MVAE), effectively aligning simulation outcomes with observed data. Subsequently, tight prediction intervals are computed by extensive Monte Carlo simulations, demonstrating coverage of the calibration results. For the design optimization problem, a Bayesian optimization framework is employed to solve three separate tasks. In the performance-based design, the control variables are optimized to maximize an expected performance measure under the calibrated uncertainty model. In the reliability-based design, the worst-case failure probability across epistemic parameter variations is minimized using an adaptive Gaussian process modeling strategy. Finally, an ϵ-constrained design is performed using dual-GP surrogates for the objective and constraint functions, thereby balancing performance enhancement and failure probability control.

Keywords: Bayesian calibration, Stochastic model updating, Aleatory uncertainty, Epistemic uncertainty, Bayesian optimization, Latent space.