Inverse problems

Keywords: problèmes inverses, optimisation, bayésien, assimilation
Prerequisites: mathématiques de base (algèbre linéaire, analyse) – informatique (l’étudiant doit être « à l’aise » avec le langage informatique moderne de son choix)

Inverse problems are nowadays a fundamental aspect of the exploration of the physical properties of the Earth. The analysis of any data set and the quantification of a physical behavior requires the optimization or exploration of a set of parameters given measurement and prediction uncertainties. The modeling of physical systems requires the optimization of a set of forces, displacements, fluxes or chemical and electrical potentials through the resolution of sets of complex equations. Solid knowledge on inverse problems theory will allow students to dive deeply into too often eluded issues in Earth sciences. This class will explore concepts of data, models and uncertainties from a theoretical point of view and present methods including Bayesian techniques, optimization tools (gradient-based methods, simulated annealing…) and data assimilation (15h). A large part of the class will be dedicated to practicals based on real examples in seismology, climate science and space meteorology, during which students will implement and experience various inversion techniques.