Colloque - Sebastian Ares de Parga Regalado : Robust Nonlinear Projection-Based Reduced-Order Models: Comparative Assessment of Closure and Manifold Strategies

Yvon MadayChaire Informatique et sciences numériquesCollège de FranceAnnée 2025-2026Colloque : Aspects mathématiques et appliqués des méthodes de réduction de complexité - Sebastian Ares de Parga Regalado : Robust Nonlinear Projection-Based Reduced-Order Models: Comparative Assessment of Closure and Manifold StrategiesSebastian Ares de Parga RegaladoPostdoctoral researcher at the Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, SpainRésuméRecent advances in nonlinear model reduction indicate that overcoming linear Kolmogorov limitations requires principled combinations of projection-based approximation and data-driven modeling [3]. In intrusive PROM settings, PROM–ANN introduced latent-space closure reconstruction of truncated modal coordinates [1], while PROM–RBF and PROM–GPR generalized this mechanism through alternative regression operators for the same closure channel [2]. In parallel, projection-compatible nonlinear latent-manifold formulations based on POD-autoencoders (POD-AE), in the spirit of POD-DL-ROM [4], provide an additional pathway to nonlinear approximation while preserving Galerkin/LSPG online dynamics.