no code implementations • 1 Feb 2024 • Nicola Rares Franco, Simone Brugiapaglia
In recent years, deep learning has gained increasing popularity in the fields of Partial Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain practitioners with new powerful data-driven techniques such as Physics-Informed Neural Networks (PINNs), Neural Operators, Deep Operator Networks (DeepONets) and Deep-Learning based ROMs (DL-ROMs).
no code implementations • 18 Oct 2023 • Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino
Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail.
no code implementations • 3 Aug 2023 • Nicola Rares Franco, Stefania Fresca, Filippo Tombari, Andrea Manzoni
We also assess, from a numerical standpoint, the importance of using GNNs, rather than classical dense deep neural networks, for the proposed framework.