Kateřina Škardová, Alexandre Daby-Seesaram and I just published two companion papers in Computational Mechanics entitled “Finite Element Neural Network Interpolation: I - Interpretable and Adaptive Discretization for Solving PDEs” (DOI: https://doi.org/10.1007/s00466-025-02677-3; ArXiv DOI: https://doi.org/10.48550/arXiv.2412.05719) and “Finite Element Neural Network Interpolation: II - Hybridization with the Proper Generalized Decomposition for non-linear surrogate modelling” (DOI: https://doi.org/10.1007/s00466-025-02676-4; ArXiv DOI: https://doi.org/10.48550/arXiv.2412.05714).
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!