  Despite significant effort in understanding complex systems (CS), we lack a
theory for modeling, inference, analysis and efficient control of time-varying
complex networks (TVCNs) in uncertain environments. From brain activity
dynamics to microbiome, and even chromatin interactions within the genome
architecture, many such TVCNs exhibits a pronounced spatio-temporal fractality.
Moreover, for many TVCNs only limited information (e.g., few variables) is
accessible for modeling, which hampers the capabilities of analytical tools to
uncover the true degrees of freedom and infer the CS model, the hidden states
and their parameters. Another fundamental limitation is that of understanding
and unveiling of unknown drivers of the dynamics that could sporadically excite
the network in ways that straightforward modeling does not work due to our
inability to model non-stationary processes. Towards addressing these
challenges, in this paper, we consider the problem of learning the fractional
dynamical complex networks under unknown unknowns (i.e., hidden drivers) and
partial observability (i.e., only partial data is available). More precisely,
we consider a generalized modeling approach of TVCNs consisting of
discrete-time fractional dynamical equations and propose an iterative framework
to determine the network parameterization and predict the state of the system.
We showcase the performance of the proposed framework in the context of task
classification using real electroencephalogram data.
