The partners of the Concace joint project, namely Airbus C R & T - Cerfacs and Inria,  have been studying and developing Krylov subspace solvers and associated software packages for the past few years for the parallel solution of large systems of linear equations. In this work, we will be interested in the solution of long sequences of symmetric non-Hermitian problems arising for instance from the solution of the Helmholtz equation in heterogeneous media in the context of a sensitivity or parametric study.
A key numerical component to ensure the robustness and the efficiency of these numerical methods is the so-called preconditioner, whose definition requires some a priori knowledge on the properties of the linear system or of the underlying problem. Classical approaches consist in exploiting this algebraic or analytic information. In this work, we intend to investigate how machine learning techniques could be used to improve a prescribed preconditioner or to fully learn one.

The objective of the postdoc is to contribute to the activities initiated in a preliminary study where a fixed-point iteration scheme was accelerated using unsupervised machine learning techniques.

The objectives of the proposed work are to:

• Adapt the learning process to account for the fact that the trained neural network will be used as a preconditioner in a subspace iteration method,
• Study the robustness with respect to the convergence rate and the attainable accuracy,
• Design an approach where the training phase is coupled with a regular solution of sequences of linear systems (active learning), possibly in a block solver framework.

• Subsidized meals
• Partial reimbursement of public transport costs
• Possibility of teleworking and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

2653€ / month (before taxs)