A multi-objective optimization to characterize the diffusion of nanocavities in tungsten

We characterize the diffusion properties of nanocavities and their uncertainties by designing a multi-objective optimization approach. In this work, the nanocavity diffusion on the 0.3–4 nm size range is the input of a multi-scale simulation that is adjusted to reproduce experimental results of a systematic study of nanocavity growth with temperature up to 1773 K. Under irradiation, in the material microstructure, the damage evolution results from a complicated interplay of the defects and their clusters (formed from the vacancies and self-interstitials created) which diffuse, recombine and grow. The simulation of the whole experiment, based on an Object Kinetic Monte Carlo algorithm, can take several hours per condition which is a strong limitation for the optimization scheme. We describe the method that succeeds for our problem. Starting from a rough and random sampling of the space of parameters, we then consider that each simulation is one point of the hypersurface in the high dimensional space formed by the optimized parameters and objectives. We iteratively improve the characterization of this hypersurface where the objectives are optimum thanks to a systematic search of patterns formed by points on the coordinate planes. The non-dominated solutions, i.e. the equally good solutions, also named the Pareto front, are finally characterized. They draw two “valleys” in the subspace of parameters, delimiting the uncertainties on the searched diffusion properties, which cannot be reduced with the experimental data and the model in their current form.