  This contribution focuses on the development of Model Order Reduction (MOR)
for one-way coupled steady state linear thermomechanical problems in a finite
element setting. We apply Proper Orthogonal Decomposition (POD) for the
computation of reduced basis space. On the other hand, for the evaluation of
the modal coefficients, we use two different methodologies: the one based on
the Galerkin projection (G) and the other one based on Artificial Neural
Network (ANN). We aim at comparing POD-G and POD-ANN in terms of relevant
features including errors and computational efficiency. In this context, both
physical and geometrical parametrization are considered. We also carry out a
validation of the Full Order Model (FOM) based on customized benchmarks in
order to provide a complete computational pipeline. The framework proposed is
applied to a relevant industrial problem related to the investigation of
thermomechanical phenomena arising in blast furnace hearth walls.
  Keywords: Thermomechanical problems, Finite element method, Proper orthogonal
decomposition, Galerkin projection, Artificial neural network, Geometric and
physical parametrization, Blast furnace.
