Convergence acceleration of a nonlinear solver using statistical learning

Numerical simulation is widely used in industrial product design. However, its application in engineering often involves significant computational costs and expertise. This research project, carried out in collaboration with Michelin, ENS Paris-Saclay, and UTC, aims to investigate the contribution of learning-based methods (possibly physics-informed) to accelerate the convergence of a nonlinear solver. In particular, we focus on predicting the initialization of Newton-type solution algorithms by leveraging dimensionality reduction techniques and digital twin learning models. The effectiveness of these approaches is assessed on industrially relevant application cases related to tire modeling, where solving large-scale nonlinear systems remains a major computational challenge.