IEEE Systems, Man and Cybernetics Magazine - October 2021 - 21

dynamical systems for it to work on. More detailed models
may ask for more computing power, but we do have it now,
and, in turn, they greatly reduce the search space for
machine learning and allow it to focus its efforts.
Recent developments suggest that even the black box
approach in which the model has no knowledge of the actual
physicality of the process has a lot to offer for nonlinear
dynamic systems. The application of reservoir computing to
spatiotemporal chaotic systems allowed an expansion of the
prediction horizon-as we stated
earlier, the prediction of chaotic
behavior is hard, as two infinitesimally
close trajectories diverge
exponentially fast, and they separate
within the time period called the
Lyapunov time (compare with
Lyapunov exponents).
Pathak et al. [20] report the
extension of a reliable prediction
window from one Lyapunov time
interval to eight Lyapunov times
for a particular chaotic system
(Kuramoto-Sivashinsky equation).
This promising result, applicable
to wider classes of chaotic
systems, motivates our investigation
of its effects in wireless communications:
how do we convert information about the
future into gains in basic communication quality parameters,
such as sum rates and latency?
Improvement in these metrics has been a significant
driver of the technological progress, major argument for the
inclusion of the new approaches [massive multiple input,
multiple output [MIMO], and millimeter-wave] in new standards,
and defining aspect of the current wireless communications
generation, the 5G. In this analysis, we focus on the
sum rate increase, computational burden decrease, and
latency decrease [Figure 5(a)]. These results from simple
use case scenarios [Figure 5(b-d)] suggest a significant
direct benefit from the dynamical systems approach to system
state prediction and add quantitative incentives to our
initiative for dynamical systems research: even relatively
short prediction has a major effect on the observed variable,
justifying investing resources into it.
The scenarios are inspired by use cases on next-generation
networks. The colocated massive MIMO example [Figure
5(b)] explores the question of what benefit for sum rates
can we observe if we can predict changes in the channel state
information (CSI) between coherence intervals (periods
in which the CSI can be considered known and constant).
The distributed massive MIMO example [Figure 5(c)]
was used to compare the computational overhead for prediction
against the computation needed for the sensing,
processing, and recalculation of CSI updates. Finally, the
mobile multihop system example [Figure 5(d)] was set up
inspired by traffic scenarios (e.g., autonomous cars in
Network science
and the study of
complex networks are
additional promising
techniques for the
telecommunications
community's
emergent toolbox of
the future.
urban settings) to see how the predictability of motion
helps in minimizing the message delivery time. These
examples and their spatiotemporal variability link well
with the original work of Pathak et al. [20].
When we speak of models, their integration with machine
learning, and reservoir computing, it is interesting to note
that Pecora and Carroll [3], the same researchers who founded
the field of chaotic communications with their investigations
on the synchronization of circuits, have also recently
done major work on understanding
the effect choice of network connections
within the reservoir [21].
Depending on the dynamical system
the reservoir computer is trying to
predict the behavior of, the structure
of computer itself does in fact
matter: flipping some of the fixed
connections in the reservoir (the fullline
arrows in Figure 4) delivers different
prediction results for the
same inputs.
The design of structures, given
information about the application
domain, hence, becomes an important
segment of work and requires
understanding of complex networks.
Network science and the
study of complex networks are additional promising techniques
for the telecommunications community's emergent
toolbox of the future. The complexity is both a blessing
and a curse: unintended consequences may lead to massive
failures of complex networks of " smart agents " [22],
but carefully designed solutions have a lot of promise for
the future of technology facing a climate emergency and
the demise of current economic systems [23].
Conclusion
The time is now: the toolbox for dynamical systems has
been reinforced with machine learning techniques born
out of them, and the dynamics of wireless communications
offer much more to work with every day. This does
not mean that the work done in the past was not important;
we need to revisit it with the techniques and technology
we have today, and the results might have an
application that could not have been foreseen decades ago.
Again, to repeat the statement we began with, the question
is not whether we can treat everything in a wireless
network as a dynamical system but whether we can afford
to do so. The demand is high, as 6G and the generations of
wireless to follow will benefit from getting to know the
nature of the complex, dynamical world they are creating
and embedding into at the same time. It is hard to find a
use case of next-generation networks where we could not
see a nonlinear differential equation waiting to be modeled;
be it the " wetware " integration with the dynamics of
a human body, motion in a high-mobility scenario, myriad
October 2021 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 21

IEEE Systems, Man and Cybernetics Magazine - October 2021

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