Marcella Bonazzoli, Inria Saclay Centre at Institut Polytechnique de Paris (Palaiseau, France)

Title: One-shot and domain decomposition methods for inverse problems

Abstract:

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively, for instance by domain decomposition methods. In this framework, one-shot inversion methods iterate at the same time on the inverse problem unknown and on the forward and adjoint problem solutions. We are especially interested in the case where the inner iterations for the direct and adjoint problems are incomplete, that is, stopped before achieving a high accuracy on their solutions.
We analyze the convergence of one-shot methods for general linear inverse problems and fixed-point iterations for the associated forward/adjoint problems. In particular, we establish sufficient conditions on the descent step for convergence, which are explicit in the number of inner iterations. We provide numerical experiments, for linear and non linear inverse problems, to illustrate the convergence of these methods in comparison with the classical gradient descent method, where the forward and adjoint problems are solved exactly by a direct solver instead.
This is joint work with Tuan Anh Vu and Houssem Haddar.

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Referent: Dr. Marcella Bonazzoli, Inria Saclay Centre at Institut Polytechnique de Paris (Palaiseau, France)

Zeit: 11:45 Uhr

Ort: Hybrid (Room 32-349 and via Zoom)