Inverse scattering problems can be seen as an optimization problem in which a cost function has to be minimized. The cost function measures the discrepancy between a physical model written as a function of the sought parameters and the measured data. Due to the high computational cost of physical models, metamodels (also known as surrogate models) have gradually appeared as alternatives. Polynomial chaos (PC) expansions are a type of metamodel based on an explicit spectral decomposition of the physical model, allowing for an exact computation of the gradient of the metamodel. The gradient of the metamodel is then used to improve the performance of the global algorithm Particle Swarm Optimization (PSO).