When: Nov 9th, 2022 – 11:00 – 11:30 AM
Where: Google meet link
Physics Informed Neural Networks for generation of structured grids on bounded domains
The generation of structured grids on bounded domains is a crucial point in the development of numerical models for solving differential problems. In particular, the representation of the given computational domain through a regular parameterization allows us to define a univalent mapping which can be computed as the solution of an elliptic problem, equipped with suitable Dirichlet boundary conditions.
In recent years, Physics Informed Neural Networks (PINNs) have been proved to be a powerful tool to compute the solution of PDEs replacing standard numerical models with deep neural networks : PINNs can be used for predicting the values on simulation grids of different resolutions without the need to be retrained.
In this work, we exploit the PINN model in order to solve the PDE associated to the differential problem of the parameterization on both convex and non-convex 2D and 3D domains, for which the describing PDE is known. The final continuous model is then provided by applying a Hermite type quasi-interpolation operator which can guarantee the desired smoothness of the sought parameterization. Finally, some numerical examples are presented.