Contexte et atouts du poste
The PostDoc will be hosted by the project team IDEFIX
Mission confiée
Our goal is to apply concepts from reduced-order models (ROMs) to solve inverse boundary value problems associated with frequency-domain wave equations.
The forward problem involves solving a linear partial differential equation (PDE) of the form A(μ, k)u = F, where F is a source, k is a wavenumber, and μ is the set of medium parameters.
Our goal is to estimate μ using recorded data.
In the one-dimensional inverse Schrödinger scattering case, we combined ideas from ROMs and data assimilation to reconstruct the scattering potential from scattering data.
These methods are computationally efficient compared to full waveform inversion (FWI), and they usually yield better reconstruction results than the classical Born approximation.
Furthermore, in the context of inverse boundary value problems for one-dimensional Helmholtz operators and two-dimensional Schrödinger operators, we have combined ROMs with FWI to obtain misfit functionals with improved convexity properties.
The postdoc's overall goal is to advance these methods to the Helmholtz equation in two dimensions and/or elasticity problems for subsurface imaging.
Principales activités
The mains tasks are:
Compétences
Technical skills and level required :
Languages :
Relational skills :
Other valued appreciated :
Avantages
Rémunération
Monthly gross salary : 2.788 euros/month