Additional resources
NeuROM (Daby-Seesaram, Škardová, and Genet 2025b)
The reduced-order modelling code used to create surrogate models based on an hybridisation of standard reduced-order modelling methods such as the PGD and Deep learning methods is public and notebooks with tutorials are also available.
A few short courses relevant to model reduction are available on my github
- Course 1 Non-linear manifold learning: SVD and kernel PCA
- Course 2 Non-linear manifold learning: Autoencoders
- Course 3 NN-FEM, simplified implementation of NeuROM (Daby-Seesaram, Škardová, and Genet 2025b) in 1D to get started with solving PDEs in the HiDeNN framweork (Zhang et al. 2021)
PhD dissertation template
In collaboration with Flavien Loiseau, we made our Ph.D. thesis template openly available on Github.
Illustrations
Hybrid sparse neural network and Proper Generalised Decomposition (PGD)
The concept of the NN-PGD derived in (Daby-Seesaram, Škardová, and Genet 2025a) is illustrated in the following short clip.
References
Daby-Seesaram, Alexandre, Kateřina Škardová, and Martin Genet. 2025a. “Finite Element Neural Network Interpolation: Part II—Hybridisation with the Proper Generalised Decomposition for Non-Linear Surrogate Modelling.” Computational Mechanics, August. https://doi.org/10.1007/s00466-025-02676-4.
———. 2025b. “NeuROM.” Zenodo. https://doi.org/10.5281/zenodo.13772740.
Zhang, Lei, Lin Cheng, Hengyang Li, Jiaying Gao, Cheng Yu, Reno Domel, Yang Yang, Shaoqiang Tang, and Wing Kam Liu. 2021. “Hierarchical Deep-Learning Neural Networks: Finite Elements and Beyond.” Computational Mechanics 67 (1): 207–30. https://doi.org/10.1007/s00466-020-01928-9.