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The purpose of this work is to shed light on an algorithm designed to extract effective macroscopic models from detailed microscopic simulations. The particular algorithm we study is a recently developed transfer operator approach due to Schütte et al.  . The investigations involve the formulation, and subsequent numerical study, of a class of model problems. The model problems are ordinary differential equations constructed to have the property that, when projected onto a low-dimensionaldoi:10.1002/cpa.10057 fatcat:hfkkvktv4bhujpgmuieco7dj3q