  It is well known that exact notions of model abstraction and reduction for
dynamical systems may not be robust enough in practice because they are highly
sensitive to the specific choice of parameters. In this paper we consider this
problem for nonlinear ordinary differential equations (ODEs) with polynomial
derivatives. We introduce approximate differential equivalence as a more
permissive variant of a recently developed exact counterpart, allowing ODE
variables to be related even when they are governed by nearby derivatives. We
develop algorithms to (i) compute the largest approximate differential
equivalence; (ii) construct an approximate quotient model from the original one
via an appropriate parameter perturbation; and (iii) provide a formal
certificate on the quality of the approximation as an error bound, computed as
an over-approximation of the reachable set of the perturbed model. Finally, we
apply approximate differential equivalences to study the effect of parametric
tolerances in models of symmetric electric circuits.
