50 citations · 61 across the 12 of their papers we have counts for
13 papers
Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner
Nunzio Dimola, Nicola Rares Franco, Paolo Zunino
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenge…
Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction
Nicola Rares Franco, Andrea Manzoni, Paolo Zunino +1
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial diffe…
Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy
Piermario Vitullo, Nicola Rares Franco, Paolo Zunino
Forward uncertainty quantification (UQ) for partial differential equations is a many-query task that requires a significant number of model evaluations. The objective of this work…
A practical existence theorem for reduced order models based on convolutional autoencoders
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 practition…
Deep learning based reduced order modeling of Darcy flow systems with local mass conservation
Wietse M. Boon, Nicola R. Franco, Alessio Fumagalli +1
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which…
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields
Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni +1
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 tac…
Nonlinear model order reduction for problems with microstructure using mesh informed neural networks
Piermario Vitullo, Alessio Colombo, Nicola Rares Franco +2
Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solu…
Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks
Nicola Rares Franco, Stefania Fresca, Filippo Tombari +1
Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-de…
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition
Simone Brivio, Stefania Fresca, Nicola Rares Franco +1
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differentia…
Approximation bounds for convolutional neural networks in operator learning
Nicola Rares Franco, Stefania Fresca, Andrea Manzoni +1
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy…
Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces
Nicola Rares Franco, Andrea Manzoni, Paolo Zunino
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical op…
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations
Nicola R. Franco, Andrea Manzoni, Paolo Zunino
Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map.…
Learning High-Order Interactions via Targeted Pattern Search
Michela C. Massi, Nicola R. Franco, Francesca Ieva +3
Logistic Regression (LR) is a widely used statistical method in empirical binary classification studies. However, real-life scenarios oftentimes share complexities that prevent fro…