SimTech Colloquium: Nonlinear compressive reduced basis for the approximation of parameter dependant PDE's (Yvon Maday)

June 18, 2025, 4:00 p.m. (CEST)

Time: June 18, 2025, 4:00 p.m. (CEST)
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.

Yvon Maday is a Professor of Applied Mathematics at Sorbonne University and a member of the Jacques-Louis Lions Laboratory, which he led for several years. He divides his teaching and research activities between the university’s Paris and Roscoff campuses, where he has developed strong interdisciplinary collaborations. For over fifteen years, he has also served as a visiting professor at Brown University (USA). A specialist in numerical analysis, his research focuses on mathematical modeling, high-performance scientific computing, domain decomposition methods, and model reduction techniques. These methods are applied across a wide array of disciplines—including fluid mechanics, biology, and medicine—with a current emphasis on computational chemistry, where he serves as co-Principal Investigator of the ERC Synergy EMC2 project. Professor Maday holds both a PhD and a state doctorate from Université Pierre et Marie Curie (now Sorbonne University). He has held several scientific and administrative responsibilities, including Director of the Jacques-Louis Lions Laboratory, Head of the Mathematics Department at Sorbonne University, and President of the Société de Mathématiques Appliquées et Industrielles (SMAI). He also founded and directed the CEMRACS summer school and Institut Carnot SMILES, which promotes collaboration between academic research and industry. A Senior Honorary Member of the Institut Universitaire de France, he has received numerous distinctions, including the Grand Prix Jacques-Louis Lions from the French Academy of Sciences (2009) and the ICIAM Pioneer Prize (2019), recognizing his lifetime contributions to applied mathematics. He has just been appointed to the annual Chair in Computer Science and Digital Sciences at the Collège de France for the 2025–2026 academic year. Author of numerous publications, Professor Maday has mentored several generations of young researchers. Deeply committed to interdisciplinary innovation, he is also a co-founder of GIS Obépine, a national initiative for epidemiological monitoring through wastewater analysis.

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