Polynomial chaos expansion for uncertainty propagation analysis in numerical homogenization of 2D/3D periodic composite microstructures

Multielement polynomial chaos Kriging-based metamodelling for Bayesian inference of non-smooth systems

“…Such models have gained significant popularity with manifold applications in diverse fields such as epidemiology [1,2], materials science [3,4], or reliability analysis [5], enabling researchers to make robust predictions to assist decision-making for complex systems. However, for both deterministic and stochastic computationally demanding simulators, formidable challenges arise when implemented in iterative procedures such as optimization [6], sensitivity analysis [7], parameter inference [8], or uncertainty propagation [9]. Despite the introduction of numerous surrogate models or meta-models in the literature over the past few years to replace intensive numerical models and alleviate the computational burden, their success mostly limits to deterministic simulators, while the consideration of stochasticity remains an open research topic.…”