De la physique dans les neurones : enrichir les modèles de données par la physique.

This thesis presents contributions towards addressing a major industrial challenge for industrial partner Safran: the rapid sizing of mechanical structures such as aircraft seats. The objective is to leverage previously-performed high-fidelity simulations to accelerate the analysis of new configurations while efficiently treating significant variability in the geometries, topologies, and behaviors of the structures considered. Although methods exist for reusing high-fidelity computations - such as Reduced Order Models (ROMs) - they remain limited to fixed or weakly-variable structures (often parameterized) and prove inadequate when information must be transferred across highly heterogeneous configurations, as encountered in Safran's use cases.In this context, artificial intelligence (AI) is a promising avenue in overcoming the limitations of traditional ROM approaches. While it offers attractive generalization capabilities, its deployment in industrial settings remains limited by a lack of guarantees in terms of mathematical precision, physical accuracy, reliability, and robustness. The methodology developed in this thesis introduces a hybrid AI-ROM framework that combines data-driven learning with physics-based modeling. It relies on the prediction of a reduced basis using a Graph Neural Network (GNN), trained on a limited number of high-fidelity simulations on unstructured meshes. The dynamic equations are then solved through projection onto this basis, in the spirit of classical ROM techniques. An adaptive enrichment phase dynamically completes the basis to ensure consistency with physical laws.Complementary developments based on neural networks are also proposed to accelerate well-established nonlinear solvers already deployed in industrial environments.The approach is validated on two original datasets, developed and released as part of this thesis. Inspired by real-world industrial cases from Safran, these datasets are characterized by high geometric and topological variability. Results demonstrate a reduction in computation time of up to 70% without significant loss of accuracy. This work thus introduces a promising strategy to efficiently handle non-parametrized geometries with ROMs, while preserving the physical validity of the solutions. It paves the way for a more practical integration of AI into industrial simulation pipelines.