### A repulsion-based method for the definition and the enrichment of optimized space filling designs in constrained input spaces

#### Résumé

Due to increasing available computational resources and to a series of breakthroughs in the solving of nonlinear equations and in the modeling of complex mechanical systems, simulation nowadays becomes more and more predictive. Methods that could quantify the uncertainties associated with the results of the simulation are therefore needed to complete these predictions and widen the possibilities of simulation. One key step of these methods is the exploration of the whole space of the input variables, especially when the computational cost associated with one run of the simulation is high, and when there exists constraints on the inputs, such that the input space cannot be transformed into a hypercube through a bijection. In this context, the present work proposes an adaptive method to generate initial designs of experiments in any bounded convex input space, which are distributed as uniformly as possible on their definition space, while preserving good projection properties for each scalar input. Finally, it will be shown how this method can be used to add new elements to an initial design of experiments while preserving very interesting space

filling properties.

filling properties.