Seminario de Probabilidad y Procesos Estocásticos

Resumen 

Rigid advection, where a spatial field shifts at constant velocity, provides a convenient baseline for spatio-temporal modeling, but its assumption of perfect correlation along the propagation path is unrealistic for most physical systems. This talk presents a unified perspective on transport modeling, addressing both simulation and estimation.

For simulation, we develop models that relax the rigid structure of simple advection by allowing richer velocity structures, from superpositions of different velocities to spatially varying velocity fields. These generalizations connect naturally to transport-diffusion dynamics and support nowcasting applications.

For estimation, we consider the problem of recovering latent velocity fields from evolving images. Using Gaussian processes with flow-based covariance structures, we produce smooth, spatially complete wind estimates from satellite imagery where standard algorithms struggle.