New nonlinear model order reduction approaches for the acceleration of parametric CFD problems, relying on so-called registration methods, will be presented in this talk. Fluid dynamics problems are known to raise challenging issues when it comes to the construction of efficient reduced-order models to accelerate parametric studies. Indeed, the challenge stems from the fact that the so-called Kolmogorov width of the set of parametric solutions of interest usually decays very slowly for this type of problems, so that traditional reduced-order modeling techniques are often inefficient in these cases. Registration methods consist in finding appropriate nonlinear transformations of the solutions of the problem of interest so that the Kolmogorov width of the set of transformed solutions decays much faster. In this talk, we will present a new methodology to construct such appropriate transformations which give rise to very efficient reduced-order models, in particular for computational fluid dynamics problems. The potential computational gains of the approach will be illustrated in particular on the AirFrans dataset. Let us point out that Abbas Kabalan and Fabien Casenave (two co-authors of this work) won the first prize of the IRT System'X NEURIPS 2024 ML4CFD challenge with this methodology.
This is a joint work with Abbas Kabalan, Fabien Casenave, Felipe Bordeu and Alexandre Ern.