  Fully-convolutional neural networks (FCN) were proven to be effective for
predicting the instantaneous state of a fully-developed turbulent flow at
different wall-normal locations using quantities measured at the wall. In
Guastoni et al. [J. Fluid Mech. 928, A27 (2021)], we focused on
wall-shear-stress distributions as input, which are difficult to measure in
experiments. In order to overcome this limitation, we introduce a model that
can take as input the heat-flux field at the wall from a passive scalar. Four
different Prandtl numbers $Pr = \nu/\alpha = (1,2,4,6)$ are considered (where
$\nu$ is the kinematic viscosity and $\alpha$ is the thermal diffusivity of the
scalar quantity). A turbulent boundary layer is simulated since accurate
heat-flux measurements can be performed in experimental settings, paving the
way for the implementation of a non-intrusive sensing approach for the flow in
practical applications. This is particularly important for closed-loop flow
control, which requires an accurate representation of the state of the flow to
compute the actuation.
