Abstract
We propose a spatiotemporally continuous framework of reservoir computing that has an inertial manifold. Using the theoretical results concerning the infinite-dimensional dynamical systems, we first propose a new model that guarantees the existence of a strong solution. Then, we prove that the proposed model actually has an inertial manifold, which is easier to deal with in practical situations. Furthermore, we also prove the following: given two input signals tending to different stationary states as time infinitely elapses, the corresponding stationary state of the reservoirs tend to different states.
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