Together with Kateřina Škardová and Alexandre Daby-Seesaram we just submitted for publication two papers on “Finite Element Neural Network Interpolation”: Part I is on “Interpretable and Adaptive Discretization for Solving PDEs” and Part II on “Hybridisation with the Proper Generalised Decomposition for non-linear surrogate modelling”. Both preprints are on ArXiv: Part I and Part II.
We implemented our framework in a library called NeuROM, which is freely available, and as usual now we also publish jupyter notebooks to allow reproduction of the figures of the papers: Part I and Part II.
Definitely let us know if you are interested and want to collaborate on these topics!