Présentation
This international symposium concludes the annual chair by broadening the perspective developed throughout the lectures and seminars devoted to complexity reduction methods. The lectures provided a mathematical overview of reduced basis and related model reduction approaches, including their foundations, a priori and a posteriori error estimation, computational implementation, recent nonlinear extensions, and the increasing role of learning-based techniques.
The subsequent seminar series, given after each of the 8 lectures, gave the floor to industrial practitioners using these methods in demanding simulation environments. It highlighted both the achievements of complexity reduction in real applications and the remaining obstacles that must be overcome to meet current industrial needs, in particular in terms of reliability, certification, robustness, and compatibility with modern computing architectures and data-acquisition technologies.
The aim of this international symposium is now to bring together leading academic researchers in order to present the most recent advances in the field and to identify promising research directions. The talks will be delivered by experts from the academic community, with the intention of providing a state-of-the-art view of current mathematical, numerical, and computational developments. Special attention will be given to methods that combine efficiency with mathematically controlled accuracy, especially through reliable error estimation and certification. This issue is particularly important today, as many approaches inspired by artificial intelligence and machine learning produce impressive numerical results but still lack a complete numerical analysis framework, making it difficult to quantify errors or to design systematic strategies for improving accuracy.
Beyond the lectures themselves, the symposium is intended as a forum for discussion among academic researchers, industrial participants, and students in training. These exchanges should make it possible to challenge and refine the arguments put forward, to clarify the actual contributions of current methods, and to bring to light both the needs arising from applications and the limitations of existing approaches. By gathering specialists in approximation theory, numerical analysis, reduced-order modeling, scientific computing, machine learning, and industrial simulation, the symposium seeks to assess the present state of complexity reduction methods while opening perspectives on emerging methodologies and open problems, including digital twins, real-time optimization, uncertainty quantification, and the simulation of complex physical systems.
For this symposium the support of Collège de France, Inria, Sorbonne Université, Laboratoire Jacques-Louis Lions1 is greatly acknowledged.
1Part of the financial support has been provided by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant No. 810367), project EMC2.