The paper considers the problem of estimating the unknown input of a nonlinear dynamical system, described by polynomial or rational differential equations, from a finite set of noisy output samples. Without additional information this problem is ill-posed since the unknown function may belong to an arbitrary infinite-dimensional space. We tackle this difficulty by designing a novel class of fast regularization algorithms that relies upon differential algebra techniques. Monte Carlo studies are used to demonstrate the effectiveness of the new approach. (c) 2006 Elsevier Ltd. All rights reserved.