Development of learning methods for controlling highly non-linear calculations in structural mechanics

The safety of electrical installations is crucial both on a societal and industrial level, and EDF relies on numerical simulation and high-performance computing (HPC) for risk management and optimization of real systems. EDF's code_aster calculation code, focused on structural mechanics, uses the finite element method to solve various mechanical problems. However, simulations of certain scenarios involving costly nonlinear mechanisms sometimes require load management methods to ensure convergence, which demands high expertise. Continuation methods are used to track solutions and identify critical points, but their parameterization requires expertise. Concurrently, the increasing use of data science learning techniques offers opportunities, although these approaches are not always suitable for engineering simulation due to the need to strictly adhere to physics and the required data mass. This thesis is proposed to develop learning algorithms aimed at automating the control of nonlinear problems, with the objective of facilitating engineers' work by automatically selecting continuation methods and their parameters for specific industrial applications. The research work is organized around two main axes: continuation methods and learning methods. The goal is to create tools based on machine learning to support engineers in the field of nonlinear mechanics, especially for the choice of methods and parameters. The learning phases involve replicating classical strategies through supervised learning, then using a reinforcement learning method to go beyond the framework of the simple model. Finally, transfer learning is considered to reuse models for other nonlinear mechanics problems. Two applications are identified to test the developed algorithms: welding simulation for piping, involving viscoplastic behavior in thermomechanics, and simulation of frictional contact of vibration absorber blocks, requiring management of bifurcations and local time representations to improve convergence speed.

Doctoral Researcher: Elio Marquis

Scientific Advisors: Emmanuel Baranger, Pierre-Alain Guidault