Colloque - Sebastian Ares de Parga Regalado : Yvon Maday, chaire Informatique et sciences numériques

Yvon Maday Chaire Les chaires Collège de France Année 2025-2026 Colloque : Aspects mathématiques et appliqués des méthodes de réduction de complexité Yvon Maday, chaire Informatique et sciences numériques Colloque - Sebastian Ares de Parga Regalado : Yvon Maday, chaire Informatique et sciences numériques Sebastian Ares de Parga Regalado Résumé Recent 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.