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Journal Articles
- 2024
[j5]Simone Brivio, Stefania Fresca, Nicola Rares Franco, Andrea Manzoni
:
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition. Adv. Comput. Math. 50(3): 33 (2024)- [j4]Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino:
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields. Adv. Comput. Math. 50(5): 96 (2024) - 2023
- [j3]Nicola Rares Franco, Andrea Manzoni, Paolo Zunino:
Mesh-Informed Neural Networks for Operator Learning in Finite Element Spaces. J. Sci. Comput. 97(2): 35 (2023) - [j2]Nicola Rares Franco, Stefania Fresca, Andrea Manzoni, Paolo Zunino:
Approximation bounds for convolutional neural networks in operator learning. Neural Networks 161: 129-141 (2023) - 2022
- [j1]Nicola R. Franco, Andrea Manzoni, Paolo Zunino:
A deep learning approach to Reduced Order Modelling of parameter dependent partial differential equations. Math. Comput. 92(340): 483-524 (2022)
Informal and Other Publications
- 2024
- [i14]Nicola Rares Franco, Simone Brugiapaglia:
A practical existence theorem for reduced order models based on convolutional autoencoders. CoRR abs/2402.00435 (2024) - [i13]Piermario Vitullo, Nicola Rares Franco, Paolo Zunino:
Deep learning enhanced cost-aware multi-fidelity uncertainty quantification of a computational model for radiotherapy. CoRR abs/2402.08494 (2024) - [i12]Nicola Rares Franco, Andrea Manzoni, Paolo Zunino, Jan S. Hesthaven:
Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction. CoRR abs/2404.18841 (2024) - [i11]Nicola Rares Franco:
Measurability and continuity of parametric low-rank approximation in Hilbert spaces: linear operators and random variables. CoRR abs/2409.09102 (2024) - [i10]Wietse M. Boon, Nicola R. Franco, Alessio Fumagalli:
Neural network solvers for parametrized elasticity problems that conserve linear and angular momentum. CoRR abs/2410.06975 (2024) - 2023
- [i9]Simone Brivio, Stefania Fresca, Nicola Rares Franco, Andrea Manzoni:
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition. CoRR abs/2305.04680 (2023) - [i8]Nicola Rares Franco, Stefania Fresca, Filippo Tombari, Andrea Manzoni:
Deep Learning-based surrogate models for parametrized PDEs: handling geometric variability through graph neural networks. CoRR abs/2308.01602 (2023) - [i7]Piermario Vitullo, Alessio Colombo, Nicola Rares Franco, Andrea Manzoni, Paolo Zunino:
Nonlinear model order reduction for problems with microstructure using mesh informed neural networks. CoRR abs/2309.07815 (2023) - [i6]Nicola Rares Franco, Daniel Fraulin, Andrea Manzoni, Paolo Zunino:
On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields. CoRR abs/2310.12095 (2023) - [i5]Wietse M. Boon, Nicola R. Franco, Alessio Fumagalli, Paolo Zunino:
Deep learning based reduced order modeling of Darcy flow systems with local mass conservation. CoRR abs/2311.14554 (2023) - 2022
- [i4]Nicola Rares Franco, Andrea Manzoni, Paolo Zunino:
Learning Operators with Mesh-Informed Neural Networks. CoRR abs/2203.11648 (2022) - [i3]Nicola Rares Franco, Stefania Fresca, Andrea Manzoni, Paolo Zunino:
Approximation bounds for convolutional neural networks in operator learning. CoRR abs/2207.01546 (2022) - 2021
- [i2]Michela Carlotta Massi, Nicola R. Franco, Francesca Ieva, Andrea Manzoni, Anna Maria Paganoni, Paolo Zunino:
Learning High-Order Interactions via Targeted Pattern Search. CoRR abs/2102.12974 (2021) - [i1]Nicola R. Franco, Andrea Manzoni, Paolo Zunino:
A Deep Learning approach to Reduced Order Modelling of Parameter Dependent Partial Differential Equations. CoRR abs/2103.06183 (2021)
Coauthor Index
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