Abstract: Fluid simulations are notoriously difficult to predict and control. As a result, authoring fluid flows often involves a tedious trial and error process. There is to date no convenient way of editing a fluid after it has been simulated. In particular, the Eulerian approach to fluid simulation is not suitable for flow editing since it does not provide a convenient spatio-temporal parameterization of the simulated flows. In this research, we develop a new technique to learn such parameterization. This technique is based on a new representation, the Advected Radial Basis Function. It is a time-varying kernel that models the local properties of the fluid. We describe this representation and demonstrate its use for interactive three-dimensional flow editing.