Organization:
Funded by: | UT/EWI |
PhD: |  |
Supervisor: Daily supervisor: |   |
Collaboration: | - |
Description:
The main goal of this project is to understand the transferability and mesh independence of geometric learning approaches using graph neural networks. A crucial tool for this purpose is the use of discrete-to-continuum limits, which we plan to tackle in regimes of point clouds sampled from a probability distribution supported on an embedded manifold. Such a limit naturally gives rise to an instance of operator learning on manifolds.
This kind of framework further allows to treat various aspects of geometric and operator learning. One is the application to fast surrogate models of PDEs on manifolds defined on meshes representing physical geometries, such as models of biological fluid dynamics. Another aspect is theoretically quantifying the advantages arising from architectures that enforce invariance or equivariance with respect to certain symmetries, and when learning from data also satisfying such symmetries.