  In dynamical systems reconstruction (DSR) we seek to infer from time series
measurements a generative model of the underlying dynamical process. This is a
prime objective in any scientific discipline, where we are particularly
interested in parsimonious models with a low parameter load. A common strategy
here is parameter pruning, removing all parameters with small weights. However,
here we find this strategy does not work for DSR, where even low magnitude
parameters can contribute considerably to the system dynamics. On the other
hand, it is well known that many natural systems which generate complex
dynamics, like the brain or ecological networks, have a sparse topology with
comparatively few links. Inspired by this, we show that geometric pruning,
where in contrast to magnitude-based pruning weights with a low contribution to
an attractor's geometrical structure are removed, indeed manages to reduce
parameter load substantially without significantly hampering DSR quality. We
further find that the networks resulting from geometric pruning have a specific
type of topology, and that this topology, and not the magnitude of weights, is
what is most crucial to performance. We provide an algorithm that automatically
generates such topologies which can be used as priors for generative modeling
of dynamical systems by RNNs, and compare it to other well studied topologies
like small-world or scale-free networks.
