Numerical simulation is now a ubiquitous tool used across many scientific fields. It is based primarily on mathematical models: abstractions of phenomena grounded in the identification of observable quantities and their interactions, described by equations linking these observable quantities, their variations, and measurable parameters. Adapted for supercomputers, these models come to life by generating, for example, images on a screen or in virtual reality, much like actors faithfully reenacting a written scene.
The model is often too complex for a “pen-and-paper” solution, so computer simulations are used: each digital “actor” operates within a data center capable of performing up to 1021 operations per second. However, this computing power may be insufficient, especially when the goal is to produce increasingly precise three-dimensional (3D) images of the phenomenon—for example, at the quality of 8K UHD (2D) screens (using 7,680 x 4,320 pixels, or more than 33 million pixels), or even in 4D by including time.
To curb this explosion in computational demands, complexity-reduction methods have been introduced. Powerful and inspired by approximation theory and numerical analysis, these methods involve intelligently selecting a small number of high-quality, pre-simulated images (forming the reduced basis) and combining them to generate new ones, with the computational cost depending on the size of this basis rather than the number of pixels they contain.
Essential to industry, these methods not only enable us to better understand and predict phenomena without conducting them in situ, but also to optimize or control processes in real time—the famous “digital twins.” To ensure their reliability, error estimation—a branch of numerical analysis—quantifies the accuracy of the results and guides efforts to improve the model or enrich the reduced basis.
Created in partnership with Inria, the Computer Sciences and Digital Technologies Annual Chair reflects a shared commitment to highlighting the importance of this scientific discipline and the need to give it its rightful place.
