  The resolution of the Poisson equation is usually one of the most
computationally intensive steps for incompressible fluid solvers. Lately, Deep
Learning, and especially Convolutional Neural Networks (CNN), has been
introduced to solve this equation, leading to significant inference time
reduction at the cost of a lack of guarantee on the accuracy of the solution.
This drawback might lead to inaccuracies and potentially unstable simulations.
It also makes impossible a fair assessment of the CNN speedup, for instance,
when changing the network architecture, since evaluated at different error
levels. To circumvent this issue, a hybrid strategy is developed, which couples
a CNN with a traditional iterative solver to ensure a user-defined accuracy
level. The CNN hybrid method is tested on two flow cases, consisting of a
variable-density plume with and without obstacles, demostrating remarkable
generalization capabilities, ensuring both the accuracy and stability of the
simulations. The error distribution of the predictions using several network
architectures is further investigated. Results show that the threshold of the
hybrid strategy defined as the mean divergence of the velocity field is
ensuring a consistent physical behavior of the CNN-based hybrid computational
strategy. This strategy allows a systematic evaluation of the CNN performance
at the same accuracy level for various network architectures. In particular,
the importance of incorporating multiple scales in the network architecture is
demonstrated, since improving both the accuracy and the inference performance
compared with feedforward CNN architectures, as these networks can provide
solutions 1 10-25 faster than traditional iterative solvers.
