Nicola R. Franco

According to our database, Nicola R. Franco authored at least 20 papers between 2021 and 2026.

Collaborative distances:

• Dijkstra number of five.
• Erdős number of four.

2026

Deep orthogonal decomposition: a continuously adaptive neural network approach to model order reduction of parametrized partial differential equations.

Nicola Rares Franco, Andrea Manzoni, Paolo Zunino, Jan S. Hesthaven

Adv. Comput. Math., June, 2026

A short tour of operator learning theory: Convergence rates, statistical limits, and open questions.

Simone Brugiapaglia, Nicola Rares Franco, Nicholas H. Nelsen

CoRR, March, 2026

Numerical solution of mixed-dimensional PDEs using a neural preconditioner.

Nunzio Dimola, Nicola Rares Franco, Paolo Zunino

Comput. Math. Appl., 2026

2025

Nonparametric estimation of conditional probability distributions using a generative approach based on conditional push-forward neural networks.

Nicola Rares Franco, Lorenzo Tedesco

CoRR, November, 2025

Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective.

Simone Brivio, Nicola Rares Franco

CoRR, June, 2025

2024

On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields.

Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino

Adv. Comput. Math., October, 2024

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, Andrea Manzoni

Adv. Comput. Math., June, 2024

Neural network solvers for parametrized elasticity problems that conserve linear and angular momentum.

Wietse M. Boon, Nicola R. Franco, Alessio Fumagalli

CoRR, 2024

Measurability and continuity of parametric low-rank approximation in Hilbert spaces: linear operators and random variables.

Nicola Rares Franco

CoRR, 2024

Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction.

Nicola Rares Franco, Andrea Manzoni, Paolo Zunino, Jan S. Hesthaven

CoRR, 2024

Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy.

Piermario Vitullo, Nicola Rares Franco, Paolo Zunino

CoRR, 2024

A practical existence theorem for reduced order models based on convolutional autoencoders.

Nicola Rares Franco, Simone Brugiapaglia

CoRR, 2024

2023

Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces.

Nicola Rares Franco, Andrea Manzoni, Paolo Zunino

J. Sci. Comput., November, 2023

Approximation bounds for convolutional neural networks in operator learning.

Nicola Rares Franco, Stefania Fresca, Andrea Manzoni, Paolo Zunino

Neural Networks, April, 2023

Deep learning based reduced order modeling of Darcy flow systems with local mass conservation.

Wietse M. Boon, Nicola R. Franco, Alessio Fumagalli, Paolo Zunino

CoRR, 2023

Nonlinear model order reduction for problems with microstructure using mesh informed neural networks.

Piermario Vitullo, Alessio Colombo, Nicola Rares Franco, Andrea Manzoni, Paolo Zunino

CoRR, 2023

Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks.

Nicola Rares Franco, Stefania Fresca, Filippo Tombari, Andrea Manzoni

CoRR, 2023

2022

A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations.

Nicola R. Franco, Andrea Manzoni, Paolo Zunino

Math. Comput., November, 2022

Learning Operators with Mesh-Informed Neural Networks.

Nicola Rares Franco, Andrea Manzoni, Paolo Zunino

CoRR, 2022

2021

Learning High-Order Interactions via Targeted Pattern Search.

Michela Carlotta Massi, Nicola R. Franco, Francesca Ieva, Andrea Manzoni, Anna Maria Paganoni, Paolo Zunino

CoRR, 2021