In many scientific fields, there is an interest in understanding the way in which complex chemical networks evolve. The chemical networks which researchers focus upon, have become increasingly complex and this has motivated the development of automated methods for exploring chemical reactivity or conformational change in a black box manner, harnessing modern computing resources to automate mechanism discovery. In this work we present a new approach to automated mechanism generation implemented which couples molecular dynamics and statistical rate theory to automatically find kinetically important reactions and then solve the time evolution of the species in the evolving network. Key to this ChemDyME approach is the novel concept of kinetic convergence whereby the search for new reactions is constrained to those species which are kinetically favorable at the conditions of interest. We demonstrate the capability of the new approach for two systems, a well-studied combustion system, and a multiple oxygen addition system relevant to atmospheric aerosol formation.