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It is well known that exact notions of model abstraction and reduction fordynamical systems may not be robust enough in practice because they are highlysensitive to the specific choice of parameters. In this paper we consider thisproblem for nonlinear ordinary differential equations (ODEs) with polynomialderivatives. We introduce approximate differential equivalence as a morepermissive variant of a recently developed exact counterpart, allowing ODEvariables to be related even when they are governed by nearby derivatives. Wedevelop algorithms to (i) compute the largest approximate differentialequivalence; (ii) construct an approximate quotient model from the original onevia an appropriate parameter perturbation; and (iii) provide a formalcertificate on the quality of the approximation as an error bound, computed asan over-approximation of the reachable set of the perturbed model. Finally, weapply approximate differential equivalences to study the effect of parametrictolerances in models of symmetric electric circuits.

Guaranteed Error Bounds on Approximate Model Abstractions through Reachability Analysis