Abstract: I will describe how one can construct a reduced order model from scattering data collected by an array of sensors. The construction is based on interpreting the wave propagation as a dynamical system that is to be learned from the data. The states of the dynamical system are the snapshots of the wave at discrete time intervals. We only know these at the locations of the sensors in the array. The reduced order model is a Galerkin approximation of the dynamical system that can be calculated from such knowledge. I will describe some properties of the reduced order modeland show how it can be used for solving inverse scattering problems.