Time: | June 18, 2025, 4:00 p.m. (CEST) |
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Meeting mode: | in presence |
Venue: | 47.02 Pfaffenwaldring 47 |
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Approximating functions that depend on parameters can be greatly improved by first analyzing the set of such functions as the parameters vary within a given domain. In the context of model reduction, this analysis relies on various notions of N-width, such as Kolmogorov or Gelfand N-widths, which involve linear or nonlinear encoders and decoders. In simpler cases, this relates to classical techniques like Singular Value Decomposition (SVD) or Proper Orthogonal Decomposition (POD), while more advanced approaches may make use of neural networks for learning efficient representations.
In this talk, I will introduce these methods with a focus on their application to the approximation of solutions to parameter-dependent partial differential equations (PDEs), leading to what we refer to as nonlinear reduced basis methods. I will then present practical numerical strategies for solving the resulting discrete systems, and share results on several challenging problems.
The results were obtained in collaboration with Hassan Ballout, Joshua Barnett, Albert Cohen, Charbel Farhat, Christophe Prud'homme and Agustin Somacal.