In this talk, we will describe a class of algorithms for reconstructing unknown parameters in nonlinear PDEs. In the absence of observational errors, the convergence of these algorithms can be rigorously established under the assumption that sufficiently many scales of the solution are observed and that certain non-degeneracy conditions hold, which ensures identifiability of the parameters. This approach to parameter estimation is robust and can be applied not only to recover damping coefficients, but also external driving forces that are apriori only known up to its size in some norm. Moreover, it is applicable to a large class of nonlinear equations, including many of those that arise in hydrodynamics, such as the Navier-Stokes equations of incompressible flow, Rayleigh-Benard convection, the primitive equations of the ocean and atmosphere, or even dispersive-type models such as the 1D Korteweg-de Vries equation or 1D cubic nonlinear Schrödinger equation. We describe the derivation of these algorithms, address their convergence, and present related numerical results.