Chaotic attractor reconstruction using small reservoirs -- the influence
  of topology
Lina Jaurigue
Forecasting timeseries based upon measured data is needed in a wide range of
applications and has been the subject of extensive research. A particularly
challenging task is the forecasting of timeseries generated by chaotic
dynamics. In recent years reservoir computing has been shown to be an effective
method of forecasting chaotic dynamics and reconstructing chaotic attractors
from data. In this work strides are made toward smaller and lower complexity
reservoirs with the goal of improved hardware implementability and more
reliable production of adequate surrogate models. We show that a reservoir of
uncoupled nodes more reliably produces long term timeseries predictions than
complex reservoir topologies. We then link the improved attractor
reconstruction of the uncoupled reservoir with smaller spectral radii of the
resulting surrogate systems. These results indicate that, the node degree plays
an important role in determining whether the desired dynamics will be stable in
the autonomous surrogate system which is attained via closed-loop operation of
the trained reservoir. In terms of hardware implementability, uncoupled nodes
would allow for greater freedom in the hardware architecture because no complex
coupling setups are needed and because, for uncoupled nodes, the system
response is equivalent for space and time multiplexing.