  Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several
industrial and geoscience flows and a well-studied system from a fundamental
fluid-mechanics viewpoint. However, controlling RBC, for example by modulating
the spatial distribution of the bottom-plate heating in the canonical RBC
configuration, remains a challenging topic for classical control-theory
methods. In the present work, we apply deep reinforcement learning (DRL) for
controlling RBC. We show that effective RBC control can be obtained by
leveraging invariant multi-agent reinforcement learning (MARL), which takes
advantage of the locality and translational invariance inherent to RBC flows
inside wide channels. The MARL framework applied to RBC allows for an increase
in the number of control segments without encountering the curse of
dimensionality that would result from a naive increase in the DRL action-size
dimension. This is made possible by the MARL ability for re-using the knowledge
generated in different parts of the RBC domain. We show in a case study that
MARL DRL is able to discover an advanced control strategy that destabilizes the
spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing
adjacent convection cells, and actively controls the resulting coalesced cell
to bring it to a new stable configuration. This modified flow configuration
results in reduced convective heat transfer, which is beneficial in several
industrial processes. Therefore, our work both shows the potential of MARL DRL
for controlling large RBC systems, as well as demonstrates the possibility for
DRL to discover strategies that move the RBC configuration between different
topological configurations, yielding desirable heat-transfer characteristics.
These results are useful for both gaining further understanding of the
intrinsic properties of RBC, as well as for developing industrial applications.
