Hi @mathowl : Sorry for the confusion. Okay so coarse-grained simulations are indeed "dimensionally reduced" versions of original systems. Yes, a real lipid will access more configurations, but our 3 particle coarse-grained models will not have high frequency - low energy motions. Those motions are filtered out effectively. But still you can study many important phenomena. Also speed up certainly!
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But is it possible to reduce the dimension of the coarse-grained simulation using symmetries in the governing equations?
You asking about reducing the dimension of already dimensionally reduced coarse grained system? I think we will lose lot of information then. But I don't know if there will be any symmetry existing in the system. It might depend on specific systems I guess. Maybe we can discuss on it if I am understanding your query in a wrong way.
If there is a symmetry or some conserved quantity then you can reduce the system without losing any of the dynamics. I am not sure if that is the case for your set of equations. We can discuss it at a later time :o)