Vibroacoustics of complex media: Stochasticity, Non-linearity.

High accuracy numerical simulations are increasingly needed in various domains of science related to physics and engineering. They are crucial in, applications such as shape optimization based on the computation of Fréchet derivatives, Digital Twins allowing to monitor and predict the behavior of their physical counterparts in real time, or the design of periodic metamaterials that rely on a micro/meso-structure to deliver performance beyond that of their standard counterparts. However, the computational burden required to perform the associated simulations would be impractical if standard modeling techniques -e.g. the finite element method- were to be used. In order to tackle this issue, Model Order Reduction (MOR) methods and multiscale approaches have proved extremely useful as they enable considerable reduction of the computational cost with little to no impact on the accuracy of the simulations. While many MOR methods are available for linear problems, the literature is much sparser and scattered among many fields for nonlinear problems. By taking an interdisciplinary approach, this research proposal aims to address these unresolved challenges by the development of  efficient MOR schemes and multiscale approaches for nonlinear vibro-acoustic systems.