Speaker
Description
Agglomeration techniques for polytopal meshes play a key role in reducing the computational cost of large-scale simulations, especially when high-order methods or complex geometries are involved. We introduce a geometrical deep learning framework for automatic mesh agglomeration, in which a Graph Neural Network learns to partition the connectivity graph of three-dimensional meshes and to construct agglomerated elements that meet stringent quality criteria. The model exploits both geometrical and physical information of the underlying domain, achieving fast online inference and enabling fully automated preprocessing pipelines. Numerical experiments on heterogeneous media and on complex three-dimensional geometries reconstructed from medical images show that the proposed approach yields agglomerated meshes with improved quality metrics and reduced runtimes compared to classical heuristic strategies.
This perspective naturally connects to advanced discretizations for partial differential equations on polygonal and polyhedral meshes. An application area in which these methods are particularly useful is the mathematical modeling of neurodegeneration. On the one hand, data-driven agglomeration enables accurate yet computationally affordable representations of intricate and heterogeneous brain structures, such as cortical folds or ventricular cavities. On the other hand, robust PDE solvers on polytopal meshes provide an efficient tool to describe the spatiotemporal evolution of pathological agents in neurodegenerative processes, where transport, nonlinear interactions, and tissue heterogeneity play a central role.