Waserstein model reduction approach for parametrized flow problems in porous media

TL;DR

This paper develops a Wasserstein barycenter-based reduced-order modeling approach for parametrized porous media flow problems, addressing challenges posed by slow solution manifold decay and non-conservative dynamics.

Contribution

It adapts Wasserstein barycenter methodology to non-conservative porous media problems, providing a novel reduction technique for complex flow simulations.

Findings

Numerical tests demonstrate the method's effectiveness in 1D cases.

The approach shows advantages over traditional linear methods.

Limitations and future research directions are identified.

Abstract

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.