Created in partnership with Inria, the Computer Sciences and Digital Technologies Annual Chair reflects a shared determination to highlight the importance of this scientific discipline and the need to give it its rightful place.
Numerical simulation is now a ubiquitous tool in many scientific fields. First and foremost, it relies on mathematical models: abstractions of phenomena based on the identification of observable quantities and their interactions, described by equations linking these observable quantities, their variations and measurable parameters. Adapted to supercomputers, these models come to life, for example, by displaying images on screen or in virtual reality, like actors faithfully re-enacting a written scene.
The model is often too complex for a "paper and pencil" resolution, so we resort to computer implementations: each digital "actor" evolving in a computing center capable of performing up to 1021 operations per second. However, this computing power may be insufficient, especially when the aim is to offer increasingly precise three-dimensional (3D) images of the phenomenon - for example, of the quality of UHD 8K (2D) screens (using 7680 x 4320, i.e. over 33 million pixels), or even 4D including time.
To curb this explosion in calculations, complexity reduction methods have been introduced. These powerful methods, inspired by the theory of approximation and numerical analysis, involve intelligently selecting a small number of high-quality, previously simulated images (forming the reduced base) and combining them to generate new ones, at a cost that depends on the size of the base rather than the number of pixels that make it up.
Essential in industry, these methods not only enable us to better understand and predict phenomena without actually carrying them out in situ, but also to optimize or control processes in real time - the famous "digital twins". To guarantee their reliability, error estimates, a branch of numerical analysis, quantify the precision of the result and provide guidance for improving the model or enriching the reduced base.