  A stochastic inverse heat transfer problem is formulated to infer the
transient heat flux, treated as an unknown Neumann boundary condition.
Therefore, an Ensemble-based Simultaneous Input and State Filtering as a Data
Assimilation technique is utilized for simultaneous temperature distribution
prediction and heat flux estimation. This approach is incorporated with Radial
Basis Functions not only to lessen the size of unknown inputs but also to
mitigate the computational burden of this technique. The procedure applies to
the specific case of a mold used in Continuous Casting machinery, and it is
based on the sequential availability of temperature provided by thermocouples
inside the mold. Our research represents a significant contribution to
achieving probabilistic boundary condition estimation in real-time handling
with noisy measurements and errors in the model. We additionally demonstrate
the procedure's dependence on some hyperparameters that are not documented in
the existing literature. Accurate real-time prediction of the heat flux is
imperative for the smooth operation of Continuous Casting machinery at the
boundary region where the Continuous Casting mold and the molten steel meet
which is not also physically measurable. Thus, this paves the way for efficient
real-time monitoring and control, which is critical for preventing caster
shutdowns.
