Computational challenges in forward and inverse large-scale wave propagation problems

Large-scale wave propagation problems arise naturally in applications such as aeroacoustics and seismic imaging. Their computational treatment raises two fundamental challenges: the efficient approximation of the forward model and the robust solution of the associated inverse problem. In the first part of this talk, I will discuss the design and analysis of domain truncation techniques that enable efficient simulations of wave propagation in unbounded domains. These methods rely on approximations of the Dirichlet-to-Neumann map, including perfectly matched layers (PML) and high-order absorbing boundary conditions (ABC). I will discuss their impact on the convergence of Schwarz domain decomposition and waveform relaxation methods, and highlight difficulties arising in spatially varying and anisotropic media. The second part turns to inverse problems and uncertainty quantification, motivated by seismic inversion. I will present a probabilistic framework that recasts Bayesian inference as a gradient flow in the space of probability measures. Within this framework, I will discuss how the choice of metric and preconditioning strategies influence the resulting discretization schemes for sampling the posterior distribution, as well as and their computational complexity, suggesting scalable and principled sampling strategies that would otherwise be computationally prohibitive.