Abstract
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.
The objective of this talk is to establish a coherent comparative framework for robust nonlinear PROM construction across these two families: closure-based reduced representations and manifold-based reduced representations. The analysis addresses key practical questions, including the selection of closure variables, sensitivity to high-mode reconstruction errors, interaction with intrusive residual minimization, and compatibility with hyper-reduction. To this end, we investigate metric-aware basis and closure variants along with computationally scalable intrusive formulations using ECSW hyper-reduction [5].
Numerical investigations are performed on a parametric two-component Burgers benchmark under both in-sample and held-out-parameter evaluations. The comparison is organized around three performance axes—approximation accuracy, computational cost, and achieved speed-up—with the goal of extracting practical guidance on how each strategy can be strengthened and in which operational settings it is most appropriate.
Work with Yvon Maday.
References
[1] J. L. Barnett, C. Farhat, and Y. Maday, J. Comput. Phys., 492:112420, 2023.
[2] S. Ares de Parga, R. Tezaur, C. G. Hernández, and C. Farhat, Comput. Methods Appl. Mech. Eng., 2026.
[3] J. Aghili, H. Ballout, Y. Maday, and C. Prud’Homme, arxiv preprint, arxiv:2601.13712, 2026.
[4] S. Fresca and A. Manzoni, Comput. Methods Appl. Mech. Eng., 388:114181, 2022.
[5] S. Grimberg, C. Farhat, R. Tezaur, and C. Bou-Mosleh, Int. J. Numer. Meth. Eng., 122:1846–1874, 2021.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant No. 810367), project EMC2.
