PhD Position F/M Neural Linear Solvers and Preconditioners for General Sparse Matrices

Numerical simulation is a strategic tool crucial for research in several scientific fields, from Computational Fluid Dynamics (CFD) for aeronautics design to Darcy flow in porous media for CO₂ storage and geothermal energy. The performance of numerical simulators is a critical factor directly impacting both result quality and the ability to perform large-scale computations. Adapting industrial codes to fully harness the capabilities of modern supercomputers (including computational accelerators such as GPUs) is a major challenge.

In many numerical simulators, the resolution of ill-conditioned linear systems represents the most time-consuming step. The objective of this work is therefore to accelerate the convergence of preconditioned linear system resolution through Machine Learning. Two main approaches will be investigated especially for the coarse operator of two-level methods. 

In order to obtain convergence guarantees on the result, the candidate will also investigate hybrid algorithms where these trained models are directly plugged in classical iterative preconditioned linear system solvers such as PGMRES or PBiCGStab. The developed hybrid approaches will be assessed in terms of CPU/GPU cost and the number of matrix-vector products required to achieve convergence in representative test cases.

Master's degree or equivalent with a strong background either in Machine Learning, Mathematics or Computer Science.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities

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