X-TMCMC: Adaptive kriging for Bayesian inverse modeling

The Bayesian inference of models associated with large-scale simulations is prohibitively expensive even for massively parallel architectures. We demonstrate that we can drastically reduce this cost by combining adaptive kriging with the population-based Transitional Markov Chain Monte Carlo (TMCMC) techniques. For uni-modal posterior probability distribution functions (PDF), the proposed hybrid method can reduce the computational cost by an order of magnitude with the same computational resources. For complex posterior PDF landscapes we show that it is necessary to further extend the TMCMC by Langevin adjusted proposals. The proposed hybrid method exhibits high parallel efficiency. We demonstrate the capabilities of our method on test bed problems and on high fidelity simulations in structural dynamics.