Abstract

While parameter estimation methods for complex engineering models are well-established, these tools often remain far out of the reach for many engineering problems due to the computationally expensive nature of the underlying models. The situation is typically far worse in settings where we also wish to estimate associated posterior distribution via Markov Chain Monte Carlo. In this work we present an approach which seeks to overcome this challenge by making judicious use of surrogate modelling and Bayesian experimental design. More specifically, we investigate Bayesian posterior inference in budget-limited settings where the likelihood can only be computed a fixed number of times. We reformulate posterior inference as a sequential Bayesian experimental design problem. The ‘unknown’ likelihood is characterised by a surrogate model, which is sequentially updated, along with with an ensemble of particles whose distribution will converge to the true posterior distribution. We show that this approach provides an effective approach to approximating the posterior distribution arising from computationally challenging Bayesian inverse problems, and which can easily be extended to dynamic posterior updating in data-streaming scenarios relevant to digital twinning. We demonstrate the efficacy of this method on different benchmarks and compare with state-of-the-art methodology.