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

Épisode de Informatique et sciences numériques (2025-2026) - Yvon Maday par Collège de France · 22 juin 2026 · 41 min

Yvon Maday

Chaire Informatique et sciences numériques

Collège de France

Année 2025-2026

Colloque : 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 Strategies

Sebastian Ares de Parga Regalado

Postdoctoral researcher at the Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain

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.

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