In the context of uncertainty propagation in numerical simulations, substitute mathematical models, called metamodels or emulators are used to replace a physico-numerical model by a statistical (or machine) learning model. This metamodel is trained on a set of available simulations of the model and mainly relies on machine learning (ML) algorithms. Among the usual ML methods, Gaussian process (GP) metamodels have attracted much interest since they propose both a prediction and an uncertainty for the output, which is very appealing in a context of safety studies or risk assessments. However, these GP metamodels have limitations, especially in the case of very irregular models. The objective of the post-doctorate will be to study the applicability and potential of Bayesian-based deep learning approaches to overcome these limitations. The work will be focused on Bayesian neural networks and deep GP and will consist in studying their tractability on medium size samples, evaluate their benefit compared to shallow GP, and assess the reliability of the uncertainty associated with their predictions.