IDEFIX

Our team is a joint research group beween Inria, EDF R&D and ENSTA.

Our research activity is dedicated to the design, analysis and implementation of efficient numerical methods for solving application-oriented inverse problems related to partial differential equations (PDEs).

Practical applications include non-destructive testing, X-ray, electromagnetic (radar) and ultrasound imaging, biomedical modeling and imaging, acoustics and sound modeling, spatial audio simulation, invisibility, and metamaterial design.

A generic problem would consist in determining the geometry (with unknown topology!) or physical properties of unknown targets from indirect measurements. In general, this type of problem is non-linear and severely ill-posed, thus requiring special attention from the point of view of regularization and non-trivial adaptations of classical optimization methods.

We are particularly interested in developing fast methods suitable for real-time applications or large-scale problems.

Our scientific research interests include:

• Theoretical understanding and analysis of forward and inverse mathematical models (PDE), including in particular the development of reduced models.
• Design and study of algorithms capable of handling non-linear problems, robust to noise or adapted to real-time imaging and audio.
• Development of new methods and advanced tools for HPC to solve large-scale forward and inverse problems.
• Development of prototype software for practical applications or general toolboxes, and consulting in industrial software development.