  The aim of this work is to build a reduced-order model for parametrized
porous media equations. The main challenge of this type of problems is that the
Kolmogorov width of the solution manifold typically decays quite slowly and
thus makes usual linear model-order reduction methods inappropriate. In this
work, we investigate an adaptation of the methodology proposed in a previous
work, based on the use of Wasserstein barycenters, to the case of
non-conservative problems. Numerical examples in one-dimensional test cases
illustrate the advantages and limitations of this approach and suggest further
research directions that we intend to explore in the future.
