A reservoir computer is a sort of non-autonomous dynamical system that is driven by observations from an underlying source system. If we do not know the equations that govern the underlying source system, we can learn much about them by taking a trajectory of observations from the system and feeding them into a reservoir computer.

 

Driving the reservoir computer this way may induce an embedding from the source system onto the internal states of the reservoir. When an embedding is achieved, the reservoir dynamics replicate the source dynamics, even though the reservoir computer only had access to a single trajectory of (possibly low dimensional) observations.

 

In this talk, we explore the connections between reservoir computers and the celebrated Takens embedding Theorem. We can see the connection by observing that the delay embedding vector that is central to Takens' Theorem is a special case of a reservoir computer.