  We consider theoretically a network of directly coupled optical microcavities
to implement a space-multiplexed optical neural network in an integrated
nanophotonic circuit. Nonlinear photonic network integrations based on direct
coupling ensures a highly dense integration, reducing the chip footprint by
several orders of magnitude compared to other implementations. Different
nonlinear effects inherent to such microcavities are studied when used for
realizing an all-optical autonomous computing substrate, here based on the
reservoir computing concept. We provide an in-depth analysis of the impact of
basic microcavity parameters on computational metrics of the system, namely,
the dimensionality and the consistency. Importantly, we find that differences
between frequencies and bandwidths of supermodes formed by the direct coupling
is the determining factor of the reservoir's dimensionality and its
scalability. The network's dimensionality can be improved with
frequency-shifting nonlinear effects such as the Kerr effect, while two-photon
absorption has an opposite effect. Finally, we demonstrate in simulation that
the proposed reservoir is capable of solving the Mackey-Glass prediction and
the optical signal recovery tasks at GHz timescale.
