Structure-Preserving Approach for Reduced order models of Conservation Laws
SPARCL is a 4-year project, funded by the French National Research Agency (ANR) through the young researcher (JCJC) programme.
It will start in March 2025 and end in February 2029.
This project focuses on the development of structure-preserving reduced order models (ROMs) for conservation laws. Conservation laws are PDEs that model advection-dominated physical problems. The solution to these kinds of PDEs can exhibit discontinuities and therefore classical ROMs are likely to fail in this scenario.
The main goal is to advance ROMs for conservation laws by enhancing their accuracy and reliability, while retaining their computational efficiency. The first step, is to transfer structure-preserving properties from high-fidelity methods to ROMs. Then, we will explore new reduced basis construction techniques based on the choice of different norms and on sensitivity studies. Finally, we aim at providing confidence intervals for ROM predictions, improving in this way the reliability of the output.
People recruited will be part of the Laboratoire de Modélisation Mathématique et Numérique (M2N) in Paris.